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Should Radical integer be deleted?

A newly created article Radical integer has been listed for deletion. Should it be kept or deleted? Note that the article resolves a long-standing redlink in Algebraic integer listed on Wikipedia:Missing_science_topics/Maths8. Weigh in. Lambiam^Talk 17:50, 9 April 2006 (UTC)

I'm the one who listed it for deletion, because the given source (MathWorld) looked hinky and in a quick search I couldn't find the term clearly and independently attested. I'm not a number theorist, so if it's not something one of Eric Weisstein's buddies just made up one day, by all means say so. --Trovatore 17:59, 9 April 2006 (UTC)

Someone somewhere has got to have a short name for Algrebraic integer expressible by radicals, but this doesn't seem to be it. Septentrionalis 22:33, 10 April 2006 (UTC)

Radical extension, extension by radicals, or (most common, I think) pure extension is standard, and radical number I think I've seen. Radical integer is logical and has a MathWorld article to go with it, which speaks in its favor. It seems to me that all of this should be discussed somewhere in an article on solvable extensions, but I can't find any such article. Should I write one? I don't want people deleting it if I do. Gene Ward Smith 21:25, 13 May 2006 (UTC)

Let me summarize the history as I see it:

1. The article radical integer was sourced only to MathWorld and all the Google hits seemed to trace back there. So I nominated it for deletion as one of Eric Weisstein's neologisms (as you'll have gathered, I don't think the existence of a MathWorld article speaks particularly well in favor of it; it's not a strike against it per se, but certainly not enough support for an article by itself).
2. During the discussion it emerged that there was more than a not-so-interesting definition involved, but rather an actual putative theorem, which (if true) goes as follows: Consider all numbers that can be expressed by starting with the naturals and closing under addition, multiplication, subtraction, division, and extraction of natural-number roots. Intersect that class with the algebraic integers. Then any number in the intersection can be expressed by starting with the naturals and closing under the previous operations, without division.
3. That theorem, if it is one (which I think it probably is), is very interesting, and clearly justifies the creation of a term for an element of the class. Unfortunately at the current time the theorem cannot be sourced, except to MathWorld, which IMO is not reliable. Moreover I think it's a reasonable principle that sources for putative theorems ought to point the reader to an actual proof, and the MathWorld source does not do that. --Trovatore 17:26, 25 May 2006 (UTC)

It might be posible to get a better source, the theorem was discussed on the math-fun mailing list, which I presume is on the web somewhere. In an email to me Rich Schroeppel said he would try to dig up the archive when the tax season was over. If anyone is interested this would be great to follow through. --Salix alba (talk) 17:35, 25 May 2006 (UTC)

Oh, one more small point: What I said about "sourced only to MathWorld" is not strictly true; I'm including Weisstein's encyclopedia of math as part of MathWorld. With that addendum it's true. --Trovatore 17:35, 25 May 2006 (UTC)

• It seems to me if I understand the claim that Schroeppel's theorem is too trivial to use as a reason for an article. If μ is an algebraic integer, then it has a monic polynomial, and expressing it as a root expresses it without division. Expanding on that, the ring of integers in any number field has an integral basis; it can be written as c₁ μ₁ + ... + c_n μ_n, where the c's are ordinary integers and the μs are algebraic integers in the field, so in terms of this basis everything in the ring of integers is precisely everything which can be expressed without division.

• So, what exactly is the statement of this theorem? Gene Ward Smith 19:47, 25 May 2006 (UTC)

I think I've already stated it exactly; here's the example that came up as to why it's not trivial. The golden ratio is a root of x²−x−1=0, so it's an algebraic integer. It's also obtainable from the naturals by iterating the operations listed, including division, as

${\frac {1+{\sqrt {5}}}{2}}$

However it's not immediately obvious that you can get it from the naturals by iterating the operations not including division. But you can. It's

${\sqrt[{3}]{2+{\sqrt {5}}}}$

(Thanks to Lambiam for that representation.) Unless I've misunderstood it, the argument you give does not prove this. --Trovatore 19:55, 25 May 2006 (UTC)

Here's a sketch of an almost-proof. "Almost" because I'm left with a denominator of at most 2.

Let S be those numbers obtainable from the natural numbers by addition, subtraction, multiplication, division, positive integer roots. (I want to call this the maximal radical extension of Q, but I'm slightly concerned about roots of unity. Never mind.) Let R be the "radical integers", i.e those numbers obtainable from naturals by addition, subtraction, multiplication, and positive integer roots (but not allowing division). First I claim that any x in S is of the form y/d for some y in R and some integer d. This is done by induction on the structure of x. Clearly addition, subtraction, multiplication pose no problems. Integer roots also fine (i.e. $(y/d)^{1/n}=y^{1/n}d^{(n-1)/n}/d)$). Division is slightly more troublesome, you need some kind of "rationalising the denominator" trick.

So now suppose we have x = y/d as above, and suppose further that x is an algebraic integer; we want to prove that x is itself a radical integer. Let K = Q(y), and let O be the ring of integers of K, so x is in O. As Gene pointed out above, O has a finite Z-basis, and the basis elements are polynomials in y with coefficients in Q, so for a large enough integer m we find that mO consists entirely of radical integers. Split m into a product of powers of prime ideals in O, say $m=\prod _{P}P^{r_{P}}$. By looking at the rings $O/P^{r_{P}}$, we can find some large integer n such that xⁿ is congruent to either 0 or 1 modulo each $P^{r_{P}}$. Then $x^{2n}-x^{n}$ is in mO, so is a radical integer, say z. Then we have $x=\left({\frac {1\pm {\sqrt {z}}}{2}}\right)^{1/n}={\frac {2^{(n-1)/n}(1+{\sqrt {z}})^{1/n}}{2}}$, which is a radical integer possibly divided by 2.

Anyone buy that? Getting rid of that last 2 seems a little problematic. Dmharvey 00:26, 26 May 2006 (UTC)

Oh yeah, by the way you can apply that proof to the golden ratio case quite easily. We already have $x={\frac {1+{\sqrt {5}}}{2}}$ presented in the right form. Let O be the ring of integers of $\mathbf {Q} ({\sqrt {5}})$. Then the ideal (2) is inert in O because the polynomial $x^{2}-x-1$ is irreducible mod 2. So the quotient O/2 is GF(4), so cubes of anything nonzero are congruent to 1. So $x^{3}-1$ is in 2O, so is a radical integer. And indeed $\left({\frac {1+{\sqrt {5}}}{2}}\right)^{3}-1=(1+{\sqrt {5}})$ is twice an algebraic integer, so must be a radical integer, which is I suppose where Lambian's formula comes from :-) Dmharvey 00:33, 26 May 2006 (UTC)

OK, here's the rest of the proof to handle that annoying factor of 2. You need to treat the residue characteristic 2 a little carefully.

Again suppose x = y/d where x is an algebraic integer. Let $\theta =(1+{\sqrt {5}})/2$ be the golden ratio. Consider the extension $K=\mathbf {Q} (y,\theta )$, let O be its ring of integers. Again we can find some m so that mO consists entirely of radical integers. Consider all prime ideals P of O of residual characteristic 2, suppose their multiplicites in m are given by r_P. Take some high power of x, call it x₂, which is = 0 or 1 modulo each $P^{r_{P}}$. Then x₂ + θ is not in any $P$, because θ is not 0 or 1 modulo 2 (i.e. neither θ nor θ−1 is twice an algebraic integer). So some high power of x₂+θ, let's call it x₃, is congruent to 1 modulo every $P^{r_{P}}$. Then x₃−1 is = 0 modulo every $P^{r_{P}}$. Now consider all the other primes Q of various other residue characteristics, which have multiplicities $r_{Q}$ in m. Then some high power of x₃−1, let's call it x₄, is either 0 or 1 modulo each $Q^{r_{Q}}$, and is still 0 modulo every $P^{r_{P}}$. Now look at x₄+1; it's either 1 or 2 modulo each $Q^{r_{Q}}$, and it's 1 modulo each $P^{r_{P}}$. Since the residue characteristics of the Q are not 2, some high power of x₄+1, say x₅, is 1 modulo all of the $Q^{r_{Q}}$ and all of the $P^{r_{P}}$. So x₅−1 is in mO, and therefore a radical integer. If you unroll your way through x₅, x₄, x₃, x₂, back to x itself, you get that x is a radical integer. Whew! Dmharvey 02:48, 26 May 2006 (UTC)

Applause. Now get that published in the Journal of Number Theory and we can write an article about it :) --Lambiam^Talk 16:21, 26 May 2006 (UTC)

Update on the lists of missing math topics

The lists at Wikipedia:Missing science topics#Mathematics now contain entries from MathWorld, Springer Encyclopaedia of Mathematics, Charles Matthews' maths lists (thanks Charles!), St Andrew's, and PlanetMath. There are 15465 redlinks and 9700 bluelinks (in separate lists), which is a progress of 38.55% towards eliminating the redlinks. For many redlinks it is likely that the information exists on Wikipedia but under a different name, so creating redirects is a good way to advance that project forward. The harvest is great and the workmen are few[1] (since it's Easter today :) Oleg Alexandrov (talk) 22:21, 16 April 2006 (UTC)

And I finally got permission from Springer to use their lists in our project. Oleg Alexandrov (talk) 03:25, 25 April 2006 (UTC)

Really? That's very generous of them, I didn't think they would. I think mathworld wasn't willing. Neat! -lethe ^{talk +} 03:32, 25 April 2006 (UTC)

If Mathworld was not willing, how come the Wikipedia:Missing science topics was created to start with? Before I got there, all the math entries from there were copied from MathWorld, all the way to incomplete entries, like Archimedean Spiral Inv.... Oleg Alexandrov (talk) 03:37, 25 April 2006 (UTC)

I seem to recall a discussion here on the wikiproject talk page, where someone created a carbon copy of the mathworld index of topics, and someone emailed them, and they indicated that it was indeed a violation of their copyright. In fact, my recollection is that you were in this converation, though I could be mistaken. Anyway, I don't know where the content of Wikipedia:Missing science topics comes from, but unless I'm misremembering something, to have their index is a copyright violation. I guess I should see if I can find that old conversation. -lethe ^{talk +} 07:37, 1 May 2006 (UTC)

That's really good news. I'm not so surprised though, that Springer was willing but MathWorld not. There are people at Springer that are truly committed to what they're doing and I've seen Springer do things that strictly speaking, they did not need to do. --Chan-Ho (Talk) 07:27, 1 May 2006 (UTC)

listing variable names after formulas

I wonder what people think of these multiply-indented lists to define all the variables that appear in a formula. An example is found here. It is claimed that this format is somewhat standard here at wikipedia and is found in hundreds of articles, but I've never seen it, and furthermore don't really like it, I prefer instead a regularly indented paragraph of text. What are your opinions of this format? -lethe ^{talk +} 00:52, 22 April 2006 (UTC)

It takes too much space. -- 127.*.*.1 03:26, 22 April 2006 (UTC)

Yes, that is quite an unfortunate presentation style. A simple paragraph of explanation would be much better.  — merge 08:07, 22 April 2006 (UTC)

From a dyslexic point of view I have problems parsing large blocks of text and tend to find lists easier to read. I had a play about with a more compact format using tables. Compare

---

The Schrödinger equation is:	i		the imaginary unit,
	t		time,
$H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle \qquad$	${\partial \over \partial t}$		the partial derivative with respect to t,
	$\hbar$		reduced Planck's constant (Planck's constant divided by 2π),
	$\psi (t)$
	H(t)		the Hamiltonian - a self-adjoint operator acting on the state space.

---

The Schrödinger equation is:

$H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle \qquad$   

where i is the imaginary unit, t is time, ${\partial \over \partial t}$ is the partial derivative with respect to t, $\hbar$ is the reduced Planck's constant (Planck's constant divided by 2π), $\psi (t)$ is ...., H(t) is the Hamiltonian - a self-adjoint operator acting on the state space.

---

--Salix alba (talk) 09:27, 22 April 2006 (UTC)

If a list seems necessary, why not use a list?

The Schrödinger equation is:

$H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle \qquad$,

where:

• i is the imaginary unit
• t is time
• ${\partial \over \partial t}$ is the partial derivative with respect to t
• $\hbar$ is the reduced Planck's constant (Planck's constant divided by 2π)
• $\psi (t)$ is ....
• and H(t) is the Hamiltonian - a self-adjoint operator acting on the state space.

---

 — merge 09:42, 22 April 2006 (UTC)

I wonder if those explanations of the symbols make this equation any more comprehensible to someone not familiar with the notation. If you don't know what the symbol is for partial differentiation then IMO it is very likely that you don't know what partial differentiation is and the same goes for the imaginary unit.--MarSch 09:55, 24 April 2006 (UTC)

I don't think it's necessary to explain certain things, such as the imaginary unit, time, or the partial derivative. Articles assume some basic knowledge, so we should rely on this (however, we should clearly attempt to make the number of assumptions as smallest as sensibly possible). Dysprosia 10:05, 24 April 2006 (UTC)

The Schrödinger equation is:

$H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle \qquad$

where H is the Hamiltonian, ψ is the state and t is time,

but even better is probably

A physical system with Hamiltonian H and initial state vector ψ₀ can be described at time t by the state vector ψ(t) which is a solution of the initial condition ψ(0) = ψ₀ and the differential equation called the Schrodinger equation

$H(t)\psi (t)=i\hbar {\partial \over \partial t}\psi (t)$

--MarSch 10:09, 24 April 2006 (UTC)

I'm in favor of lists for equations. The main reason is that I don't like to read the whole article - and lists of variables show a clear spot where I can find all the information I need. This is of course provided that its written properly. If the variables in the equation are fully clear, then theres no need. However, in the case of the schrodinger equation, almost none of the variables and symbols are familiar to most people. Also, most always, all variables do need description. Leaving out variables leaves the equation incomplete, and even a reader who assumes the right meaning might question himself, and end up having to double check the formula somewhere else. Stuff like simple operators probably don't need explaining, but I've found a good compromise in that respect to define the derivative of something rather than the dervative operator (for example: "dp/dt is the instantaneous rate of change of the momentum").

Another main consideration is consistancy. If equations are written in 5 or more different forms, users will have a harder time sorting through the formats to find what they need. Almost always, variables are written below the equation, and when they're not - I find it difficult to follow. The list format makes it easy to find the perhaps one or two variables you don't know, and refer back to it without losing your place.

We as editors should consider that wikipedia isn't only used by people wanting an in depth overview of a subject, but may also want a quick reference. Articles that distinguish different parts of the article (like equations, subject headers, examples vs generalities) are much easier to read and use. The faster a reader can find the information they are looking for is (in my opinion) far more important than making the page compact. Fresheneesz 07:25, 2 May 2006 (UTC)

AFD - How to get the prime factors of a number

I have nominated How to get the prime factors of a number for deletion. Comments welcome. -- Meni Rosenfeld (talk) 16:46, 26 April 2006 (UTC)

It seems like useful information, although it could be better written. Is this info in some other article? If not, maybe the article should stand. PAR 16:58, 26 April 2006 (UTC)

Please take comments on the merits to the AfD page. --Trovatore 17:04, 26 April 2006 (UTC)

Deleted. -lethe ^{talk +} 05:17, 1 May 2006 (UTC)

"Tone", pronoun use, etc. in math articles

The other day, I left a pretty extensive comment on Talk:Knot theory, in response to two editors who complained about the article's tone. One specific complaint was the use of pronouns and that the article sounded like a teachger giving a lesson. Now, I just noticed that Braid group has been tagged (by someone else) with a "tone" tag, and the talk page mentions for example, that the use of "we" is bad and that it sounds too much like a "math lesson instead of an encyclopedia".

My thought is that while some of the pronoun use could be favorably excised, I am definitely starting to get the feeling (especially after examining the articles in question) that these particular editors do not understand the conventions in mathematical writing, e.g. "We consider blah as doing blah..." is ok. They also may not understand that sometimes a procedural description should be given, e.g. "take such and such and do such and such...". See my long comment linked above. I would like to know what those who normally work on mathematics articles think about all this, so please drop by those pages and make some comments. --Chan-Ho (Talk) 03:58, 1 May 2006 (UTC)

We is pretty much mathematical jargon; one is better for the general reader. Charles Matthews 11:45, 1 May 2006 (UTC)

I believe the passive is the preferred thingy. "We consider..." becomes "... is considered". --MarSch 14:08, 1 May 2006 (UTC)

But then... "is considered", er, by whom? By a deity? (Igny 15:33, 1 May 2006 (UTC))

This reflects a certain diference about using We. In a statement like We can deform a knot in 4D it can easily be rewitten as a knot can be deformed in 4D and the prounoun can easily be dropped. However We consider... are subjective statments and in a paper the we is used to indicate the opinion of the authors. In wikipedia such subjective statements need appropriate qualification most mathematicians consider 4D knots to be very boring. --Salix alba (talk) 19:04, 1 May 2006 (UTC)

I've responded where requested; see for details. Passive is not preferred; just the opposite. Overuse of "one" also makes reading drag. Technical writing has a tradition of such conventions, not to its credit. --KSmrq^T 19:15, 1 May 2006 (UTC)

A MIT style guide says to use "we" in the active voice. I see now that I was mistaken in thinking it too personal, and yes, I did not understand mathematical writing conventions as pointed out by Chan. I will try to not be an ignoramus in the future. --Reader12 03:57, 2 May 2006 (UTC)

Well, you live and learn! I tried to carefully explain how the situation appeared to me without being patronizing or rude; I hope you weren't offended. At any rate, I think it's been a very fruitful discussion thus far with a variety of people voicing their thoughts and it's still ongoing! --Chan-Ho (Talk) 08:08, 2 May 2006 (UTC)

No, no offense taken. This has been very instructive to me. Thanks! --Reader12 21:40, 2 May 2006 (UTC)

I've just come across a great book on Algebraic topology by Allen Hatcher which can be downloaded [2]. To my mind he has a very good writing style, which avoids the problems of overly technical writing, whilst still being technically correct. I fell there is quite a bit which could be learnt by examining how he structures his writing. I think a lot of illustrations help, the sub project /Graphics has reciently been set up to try to improve the illustrations of the maths articles. --Salix alba (talk) 09:21, 2 May 2006 (UTC)

Naming: "fixed-point" vs "fixed point"

Several articles are named inconsistently. I prefer "fixed point". Any opinions? Post here or at Category talk: Fixed points. Staecker 21:18, 1 May 2006 (UTC)

It's my experience that "fixed point" is way more common in the literature, so we should stick with that.--Deville (Talk) 22:25, 1 May 2006 (UTC)

Not so fast; there's a grammatical distinction. As a noun phrase, we would write the "fixed point" of a recursive function, without the hyphen. But as an adjective, we often write "fixed-point" thingy, with the hyphen. In the case of theorem names, the former applies, as in "Brouwer fixed point theorem". And what about "Kleene fixpoint theorem"? It should redirect. --KSmrq^T 22:59, 1 May 2006 (UTC)

I don't mind making the distinction, but I don't think I understand as you've stated it. In "Brouwer FP Theorem," it sounds like an adjective phrase to me (modifying "theorem"). Is this an exception? When would the hyphen be appropriate? Something like "fixed-point set"? That sounds like an adjective phrase to me, but I never write it that way myself. Come to think of it, I don't ever use the dash regardless of context. (Except when I have to link to Lefschetz fixed-point theorem) Staecker 23:19, 1 May 2006 (UTC)

You want me to explain why punctuation conventions make sense?! I wish. I can say that I would never hyphenate in a situation like "Every rotation has a fixed point." The article on hyphen discusses some common rules. So why not "Brouwer fixed-point theorem"? I suppose because it's a ritual thing, with "theorem" doing the modifying. Or it's an example of the general guideline that hyphens are for clarity, and if we don't need them we don't use them. The still more general guideline is to tread carefully in this territory, and don't rush to accuse anyone of doing it wrong just because their choice is not yours. (But you knew that already, yes?) --KSmrq^T 02:47, 2 May 2006 (UTC)

My usage would be like KSmrq's. The underlying reason may be that a "fixed-point set" is a set which consists of fixed points (or is a fixed point, if you're doing category theory); but a "fixed point theorem" is a theorem about fixed points: a more distant relationship, analogous to the difference between mathematics and metamathematics. Septentrionalis 18:58, 5 May 2006 (UTC)

Are you sure there's an inconsistency? A fixed-point theorem (with a hyphen) asserts the existence of a fixed point (with no hyphen), and it is completely appropriate to use a hyphen in one case and not in the other, because of the difference in the way the phrase is being used. That is not an inconsistency. Michael Hardy 20:09, 5 May 2006 (UTC)

hyphens generally

By the traditional conventions concerning hyphens,

• A man-eating shark (with a hyphen) scares people away from beaches, whereas
• A man eating shark (with no hyphen) is a customer is a seafood restaurant.

The traditional usage is still followed by nearly all newspapers and magazines and in novels, and people are accustomed to seeing it. But many educated people, including many authors of scholarly papers and books no longer follow the traditional rule. I've tended to be conservative about it and I moved the Wikipedia article titled "light emitting diode" (with no hyphen) to light-emitting diode (with a hyphen) and have done the same with various other articles. I think in some cases, the hyphen is a magnificently efficient disambiguation device. Michael Hardy 20:14, 5 May 2006 (UTC)

Nice example, copied from hyphen:

semantic changes caused by the placement of hyphens:

• Disease causing poor nutrition, meaning a disease that causes poor nutrition, and
• Disease-causing poor nutrition, meaning poor nutrition that causes disease.

Michael Hardy 20:18, 5 May 2006 (UTC)

A fixed point theorem is a point theorem that was found to contain an error, which now has been repaired. Lambiam^Talk 21:13, 6 May 2006 (UTC)

Blahtex and wikimania

The poster deadline for wikimania is fast approaching. I think it would be really good if we could have some presence there as a step to getting meta:Blahtex integrated into the main encyclopedia sites. Neither User:Dmharvey or myself are able to attend, but posters can be submitted without having a physical presence. Questions: is anyone here planning to go to wikimania Aug 4-6, in Cambridge MA? Anyone happy to spend some time standing next to a Blahtex poster? For those who don't know Blahtex is a extension which converts LaTeX maths into the MathML XML markup which allows for improved rendering of mathematics in MediaWiki with moder browsers. --Salix alba (talk) 10:05, 2 May 2006 (UTC)

Bogus AfD of proof article

Loom91 has been goaded by Melchoir into nominating "Proof that 0.999... equals 1" for deletion, on the grounds that Wikipedia should not contain proofs like this. The archives of sci.math currently show well over a thousand postings related to this topic, which is therefore included in the sci.math FAQ; yet it appears that Wikipedia covers the topic far better. Those who are interested can register an opinion here. Caution: This topic (and perhaps this vote) attracts, um, non-standard thinkers, to put it delicately. (See the talk page archives for examples ad nauseam.) --KSmrq^T 10:31, 5 May 2006 (UTC)

Yeah, I feel bad about that; sorry, everyone! (In my defense, though, I did try to explain why the AfD would fail, after which I didn't think Loom91 would actually go through with it.) Well, at least it's attracting some fresh constructive attention, and it'll be useful to have on record. Melchoir 20:09, 5 May 2006 (UTC)

By the way, in case anyone hasn't seen it yet, the AfD closed with a keep. Melchoir 22:58, 5 May 2006 (UTC)

That's a understatement; it closed with a speedy keep, with overwhelming support and complaints about the nomination as violating WP:POINT. --KSmrq^T 22:31, 6 May 2006 (UTC)

Rewrite of Mode (statistics)

I rewrote the article Mode (statistics). Please review and correct errors, rewrite awkward sentences, simplify, embellish, supply sources, etc. It would further be nice to have some illustrations, both for a continuous density function and a histogram. Lambiam^Talk 20:40, 5 May 2006 (UTC)

AfD for List of Mathematical Formulas

Should this be kept, deleted, merged, or should there be a category of "mathematical formulas"? (I wonder what the morphisms would be.) Visit Wikipedia:Articles for deletion/List of Mathematical Formulas and contribute your two cents. Lambiam^Talk 21:04, 6 May 2006 (UTC)

As far as I can see, the chemists don't need Category:Formulas. We might not need it either, though. Charles Matthews 19:09, 7 May 2006 (UTC)

WAREL back?

See [3]. I don't read Japanese so I can't tell if the change is correct, but it's exactly the type of change we might expect from WAREL if he came back. --Trovatore 15:24, 10 May 2006 (UTC)

OK, I hate machine translation but it has its points. He changed the article to point to a nonexistent article on ja.wiki, called "Commutative field". It's WAREL alright; please block him with all deliberate speed. --Trovatore 15:41, 10 May 2006 (UTC)

KLIP (talk · contribs) blocked. -lethe ^{talk +} 17:20, 10 May 2006 (UTC)

James Stewart

Just created the page on Stewart, James Stewart (mathematician), your contributions would be most appreciated.--Jersey Devil 09:08, 11 May 2006 (UTC)  

TeX font size

There is a discussion at the Village pump that might interest a few people here. —Ruud 01:09, 12 May 2006 (UTC)

Koszul-Tate

Is there anybody here interested in tackling the Koszul-Tate derivation topic listed on the "wikipedia:Articles requested for more than two years"? Thank you. — RJH 15:45, 12 May 2006 (UTC)

WAREL

is back again at Field (mathematics). --Trovatore 02:39, 13 May 2006 (UTC)

JLISP (talk · contribs). -lethe ^{talk +}

Zeration

Can someone please review zeration? Thanks. Samw 03:28, 13 May 2006 (UTC)

I'd give it thumbs down, in regard the Δ numbers. That is just wrong, even if referenced in the paper. The rest is more-or-less accurate, although I believe it falis WP:N.

As for hyperexponentials, my first paper (in 1966) references an earlier paper by Donner and Tarski which discusses hyperexponentials on the ordinal numbers. I doubt the primacy of the 1987 paper. — Arthur Rubin | (talk) 04:29, 13 May 2006 (UTC)

Referencing something from 2004 makes it a bit young and possibly fails "established research". Dysprosia 08:44, 13 May 2006 (UTC)

Duly sent to AfD, see Wikipedia:Articles for deletion/Zeration. -- Jitse Niesen (talk) 08:47, 13 May 2006 (UTC)

Spanish category

I wrote the following on Category talk:Mathematics; copying here.

An anon recently changed the Spanish link to es:Categoría:Matemática from es:Categoría:Matemáticas, or perhaps the other way around. It seems that both categories exist and are populated. Would someone whose Spanish is better than mine like to go tell them? I don't know how they handle these things over there; I think things like {{cfm}} are set up language-by-language. --Trovatore 14:54, 13 May 2006 (UTC)

It looks like es:Categoría:Matemática was created just today, by one es:Usuario:Ingenioso Hidalgo, who then took it upon himself to go around recatting over a hundred articles, then apparently got tired. Unless this was discussed somewhere this doesn't strike me as good behavior; someone should let them know. I don't know if they have any equivalent to WikiProject Mathematics. --Trovatore 15:21, 13 May 2006 (UTC)

On second thought, I suppose someone will notice, as the recats will surely show up on some watchlists. --Trovatore 15:35, 13 May 2006 (UTC)

P-adic numbers

There is a discussion on decimal-style notation for p-adic numbers, and what would be appropriate to use, on the talk page Talk:P-adic number which we would like comments on. I added a section which uses a notation which is unusual but not unprecedented, in the section intended to convey the intuitive idea of a p-adic number. It seems to me the notation I used does that more successfully than any alternative for people used to decimal notation. Gene Ward Smith 21:14, 13 May 2006 (UTC)

Real number

User:Oleg Alexandrov seems to me to be engaging in abusive reverts on this page, to a previous verison which is arguably incorrect mathematically and which removes a lot of new material, material for which he has given no argument for removal. He also says, falsely, that my attempt to satisfy his previous criticims amounted to "writing a one-liner" which seems to prove he hasn't even seriously looked at the version he is reverting from. I think we need other people to weigh in at this point. I am very much opposed to simply allowing it to say the real numbers have a number line and calling that a definition. My proposal to say they have a number line, with no "room" to fit additional numbers in, is an attempt to make the one-line introduction correspond to an actual rigorous definition, which will not be the case if we allow Oleg's revert. Gene Ward Smith 22:32, 13 May 2006 (UTC)

Comments at talk:real number are encouraged. My version of things is that Gene is convinced enough that he is right that he is prefers repeatedly reverting to his version to discussing things on the talk page. Oleg Alexandrov (talk) 22:51, 13 May 2006 (UTC)

I think you need to take your own advice; your reckless reversion was done without any discussion. Gene Ward Smith 23:28, 13 May 2006 (UTC)

Regardless of who did what, there is a discussion running at the talk page now. Please engage yourselves there. -- 127.*.*.1 23:35, 13 May 2006 (UTC)

Islamic mathematics

User:CltFn has proposed to move Islamic mathematics to Middle-Eastern mathematics. Please comment at the talk page. —Ruud 02:36, 15 May 2006 (UTC)

A typesetting subtlety

See if you can spot the difference between this:

$a+b+c+d\,$

$+e+f+g+h\,$

and this:

$a+b+c+d\,$

${}+e+f+g+h\,$

without looking at the TeX code, and guess how and—perhaps more subtly—why the difference was achieved.

I think perhaps this should be borne in mind in editing math articles. Michael Hardy 02:37, 15 May 2006 (UTC)

This is presumably because TeX does not apply its operator spacing rules in the first case, while since you've forced an empty group in the second, it does. Preferrably if you're continuing a sum onto two lines, one would add a \quad of space in the second or add a text indent (via a ":"), instead of relying on empty groups. Dysprosia 03:02, 15 May 2006 (UTC)

Sadly, I spotted the difference instantly, and even knew exactly where to look. This has been with TeX for decades, and Knuth explicitly calls attention to it in The TeXbook (ISBN 0201134489, p. 196). You'd never guess he was the type to pay extraordinary attention to detail, now would you? ;-D

• "An extra ‘{}’ was typed on the second line here so that TeX would know that the ‘+’ is a binary operation."

The difference is a consequence of the operator handling rules. --KSmrq^T 04:27, 15 May 2006 (UTC)

Personally, I never noticed this until recently. I once asked Donald Knuth why he had issued an infallible pontifical decree about minute details of the design of the lower-case letter delta. He said it's because the design he prescribed was just obviously the right one. Anyway, in non-TeX mathematical notation, I've been something of a stickler about proper spacing with binary operations and binary relations, thinking all the while that there's no need to think about that in TeX, but in cases like this, there is. Michael Hardy 23:55, 15 May 2006 (UTC)

Dysprosia: How does a text indent via an initial colon achieve this result? It only adds space to the LEFT of "+". Michael Hardy 23:57, 15 May 2006 (UTC)

I wasn't exactly precise in what I was meaning above -- what I meant is that if one wants to continue a sum on two lines, one should add space to the left somehow, instead of keeping both lines of the sum aligned, for example

$a+b+c+d\,$

${}+e+f+g+h\,$

as opposed to

$a+b+c+d\,$

${}+e+f+g+h\,$

I probably should have added "and keeping the same indent" to the end of my comment. It's a shame that the TeX system in use here ignores initial spacing via quads and such. Dysprosia 08:46, 16 May 2006 (UTC)

Math error right on this page?

On this page there is a box telling us that hyperreal numbers, superreal numbers, and surreal numbers are "complex extensions"; in fact, they are all real closed fields. Gene Ward Smith 04:34, 15 May 2006 (UTC)

Zero-eigenvalue bifurcation

Could someone take a look at zero-eigenvalue bifurcation? It is proposed for deletion, but it do find some uses of this term on google scholar. —Ruud 00:17, 16 May 2006 (UTC)

The deletion, rather than redirection, seems summary and not necessary. Charles Matthews 11:03, 20 May 2006 (UTC)

I agreed with the deletion because I think that the term "zero-eigenvalue bifurcation" is hardly used by itself (in constract to more complicated phenomena like the "double zero-eigenvalue bifurcation", used as a synonym for "Bogdanov-Takens bifurcation"). But if you want to create a redirect, be my guest. -- Jitse Niesen (talk) 13:07, 20 May 2006 (UTC)

p-adic numbers notation

A debate is in progress at Talk:P-adic number about whether p-adic numbers should be written from right to left or from left to right. The article used to use the right-to-left notation, but was recently rewritten with the left-to-right notation. Contributions to the debate from a wider pool of wiki mathematicians would be helpful, to see if we can reach a concensus. Gandalf61 08:21, 16 May 2006 (UTC)

Okay, after some discussion on its talk page, I have now changed the p-adic number article to consistently use the right-to-left notation, but with a new section that mentions other alternative notations. Any comments on the partial re-write are welcome at Talk:P-adic number. Gandalf61 09:34, 26 May 2006 (UTC)

Moore closure

I propose to delete the bits about Moore closure in the article Kuratowski closure axioms; see Talk:Kuratowski closure axioms#Moore closure. --Lambiam^Talk 09:05, 16 May 2006 (UTC)

Fine topology (suggestion needed for better name)

I have created a new page on fine topology (as in classical potential theory), but as the title "fine topology" already seems to be taken by a page about general topology (i.e. 'finer topology' rather than "THE fine topology"), I have called my page "classical fine topology" - seems like there ought to be a better solution - any ideas? —The preceding unsigned comment was added by Madmath789 (talk • contribs) .

(Copied from my talk page, I don't have a good answer to this. Oleg Alexandrov (talk) 23:30, 16 May 2006 (UTC))

Call the page Fine topology (potential theory) and use a

{{dablink|[[Fine topology]] redirects here. For the use in potential theory, see [[Fine topology (potential theory)]]}}

at the top of Comparison of topologies? Kusma (討論) 23:43, 16 May 2006 (UTC)

Thanks for that suggestion - I have renamed the page. In a similar vein, I am tempted to write 2-3 articles on the subject of 'thin sets' and 'polar sets' (as used in potential theory, subharmonic functions etc.) and find that these terms also link to pages mainly about set theory. Would it be sensible to call my new pages 'thin sets (potential theory)' etc. What do more experienced wikipedians think? Madmath789 10:10, 17 May 2006 (UTC)

Nothing links to Fine topology, so it might be better to turn this into a disambiguation page rather than redirect to Comparison of topologies, thereby avoiding an awkward disambiguation phrase in Comparison of topologies. Nothing links to Thin set either. --Lambiam^Talk 11:07, 17 May 2006 (UTC)

Idea: when user clicks on an equation wikipedia explains it

Sorry if this is the wrong place / its already been suggested (I searched :-\), please direct me to the right place if here is incorrect (or tell me its not a worthwhile idea if you think so). This is a suggestion that when a equation is displayed (for example the one on this page) the user can click on the equation and is taken to a special page that explains the contents of the equation and what it means.

OK, let's try it:

$\int _{0}^{\infty }1\,dx.$

Weird! What I see is this:

UNIQ5f19c7bc44ccc704-math2f6e29f1133d184200000001

What I "should" see is this:

$\int _{0}^{\infty }1\,dx.$

When I click on it, it takes me to the right place.

Is this browser-dependent? Michael Hardy 01:50, 20 May 2006 (UTC)

You are seeing artifacts of one of the intermediate interpretation passes that mediawiki does during math markup. When all goes well (e.g. properly formed or properly messed up math syntax) you'll either see the math, or some nice error note. If something unexpected happens (e.g. math in links, math in image captions, etc) then mediawiki will mysteriously dump out that garbage. Basically, you're causing an error that isn't specifically handled by the markup engine, so it gets confused. It's totally browser-independent.

As for the suggestion, I think such a thing would overly burden the database and the authors. It sounds like you're suggesting that a new page be created to explain every equation. That's a lot of new pages to store, and a lot to write. That style of writing probably wouldn't be very popular, since most of us are used to explaining equations in neighboring text. Plus, it would be quite a large programming task to add that functionality into mediawiki. Staecker 02:07, 20 May 2006 (UTC)

Ahh no I meant something automatically generated. By definition a mathmatical equation is exact and parsable by a computer. It will be a bit of work by someone to make it function, but I thought I'd put it out there as an idea.

In the page I referenced above, the reason for the equation is explained, but at the level of someone who understands equations already, not to someone who has no idea what the $\sum$ means. I thought it would make wikipedia more accessible to non maths experts and require the time of one developer (and not the time of every maths editor).

See User:RickiRich\Math_Example for an example of what I think could be programatically created, and a description of How it could be created without too much fuss. After exams I'll have a go at this if no one else has.

--RickiRich 01:01, 22 May 2006 (UTC)

I don't think this is a good idea, I doubt it will get used by anybody if it gets implemented, and I doubt the developers will ever bother implementing that. You should at least get some support for this feature before you decide to do anything about it. But again, I don't think this wil lead anywhere. Oleg Alexandrov (talk) 04:07, 22 May 2006 (UTC)

What Oleg said. Dysprosia 06:31, 22 May 2006 (UTC)

I think it won't work. A significant obstacle is that mathematical symbols can have many different meanings, and a computer just ain't smart enough to distinguish which one you mean. For example, the + symbol could mean addition, or it could mean the span of two vector spaces, or the concatenation of two strings, etc. So much depends on context. (Also you probably wanted a forward slash in the title of that page, not a backslash. See Wikipedia:Subpage.) Dmharvey 21:43, 24 May 2006 (UTC)

Intriguing idea, but I don't think its right for wikipedia. There have been some development along similar ideas both MathML and OpenMath formats have had some aspect of representing the meaning of an equation rather that its purely visible representation. OpenMath in particular has seen a lot of work with people developing Content Directories which are domain specific collections of mathematical definitions. There has been numerous papers on the subject, but I don't think its gained much acceptance apart from as a means of converting from one computer algebra system to another. In the wikiworld meta:Semantic MediaWiki is a wikipedia extension which allows some form of semantic markup.

Why its not right for Wikipedia: basically the wiki concept follows KISS principle (Keep it simple stupid) and this sort of system gets rather complex. Hopefully all the relevant terms should be linked in the text anyway. --Salix alba (talk) 22:17, 24 May 2006 (UTC)

Massive edits foil comparison operation in article history

Sometimes an editor goes thru an article and changes many minor things at once. For example: spelling corrections; deleting unneccessary spaces; replacing & alpha ; with α; etc.. When this is done, the function which shows changes in the history often fails. It may begin matching an old paragraph to the wrong new paragraph and then it never gets back in synch (until one reaches a section header, if that was not changed). Of course, this makes it very difficult to check that the change was done appropriately.

I think that it is probably impractical to correct this bug in the comparison. So I am suggesting that you-all try to avoid this situation in the first place. When you do such massive edits, please first do every other paragraph (to allow the software to get back in synch with an unalterred paragraph). Then do a separate edit to change the remaining paragraphs. Thank you. JRSpriggs 06:06, 20 May 2006 (UTC)

I think you'll need to provide a concrete example of this happening. Dysprosia 09:39, 20 May 2006 (UTC)

The most recent occassion on which this happened to me was in the 18 May 2006 edit of Constructible universe by UkPaolo, called clean up +spelling correction using AWB. See http://en.wikipedia.org/w/index.php?title=Constructible_universe&diff=53858793&oldid=53818751 and scroll down to the section named "L is absolute and minimal". JRSpriggs 09:05, 21 May 2006 (UTC)

For this example it would have helped if the diff algorithm ignored blank lines, that is, tried to match up the two versions after filtering out the blank lines (which should be re-inserted for the final presentation). I suppose there is a backlog of all kinds of wishes for the developers, and I don't know how important this really is, but it is relatively simple to implement. --Lambiam^Talk 18:48, 21 May 2006 (UTC)

I think that the problem is more difficult than Lambiam thinks it is. In the section to which I referred, the only blank line was the next to last paragraph. Yet the mismatching of paragraphs began at the first paragraph in the section. Apparently the diff-software cannot measure the similarity of the contents of two paragraphs until after it has decided irreversably that they are matching paragraphs. That matching of paragraphs appears to depend only on whether they are identical, followed by interpolation (guessing) between identical pairs of paragraphs. JRSpriggs 07:12, 22 May 2006 (UTC)

Blank lines were removed in the edit following each and every section title. This doesn't show up clearly in the diff, but start an edit on both versions and compare the contents of the edit boxes, and it will be obvious. If then the next paragraph is also modified, the diff algorithm can't line them up. The silly thing in this massive edit is that many of the changes have no substance and consist of replacing two spaces after a full stop by a single space. --Lambiam^Talk 10:06, 23 May 2006 (UTC)

You may want to mention this on Wikipedia:Village pump (technical) or check the bugZilla where there are currently 93 bugs related to the diff. In this case the edit summary gives some clue, the edits were done using the WP:AWB tool, they are mainly minor edits and it would be hard to break this up into smaller edits, by limitations of the software. --Salix alba (talk) 07:16, 23 May 2006 (UTC)

The problem is apparently caused by a feature of AWB, "Apply general fixes", which removes "excess white space" to which the diff algorithm is sensitive (Wikipedia:AutoWikiBrowser#"Set options"). --Lambiam^Talk 10:15, 23 May 2006 (UTC)

resolve a revert war at dual space

I find myself in a revert war at the article dual space. It's mostly about style; how much information is too much, whether material looks good or fits. this diff shows the difference between the two users preferred revisions. See also this old version for a much longer revision that I reverted. I am pessimistic with how talks on the talk page are going. We seem not to see eye-to-eye. I would like to get some more opinions. -lethe ^{talk +} 04:42, 23 May 2006 (UTC)

Compound Poisson process question

Probabilists out there, I wonder if you could answer a question posted at Talk:Compound Poisson process. Oleg Alexandrov (talk) 17:25, 24 May 2006 (UTC)

looks right to me. (and the changes i made were mostly cosmetic.) Lunch 19:10, 24 May 2006 (UTC)

I added a final line to the moment generating function calculation, which should clarify matters further. The variance result looks OK, by computing them in terms of the moment generating function. — Arthur Rubin | (talk) 20:27, 24 May 2006 (UTC)

Looks OK to me, too. Michael Hardy 21:17, 24 May 2006 (UTC)

... and generally, the nth cumulant of the compound Poisson distribution, following the notation now in the article, is λt times the n moment of the distribution of the random variable that the article (in its present form) calls D_i. This can be shown via the law of total cumulance. The cases n = 1 and n = 2 are just what now appears in the article. Michael Hardy 21:20, 24 May 2006 (UTC)

Widespread mathematical delusions

I'd like to hear some opinions about the new article Widespread mathematical delusions. At the moment, the article lists only one delusion, and I am not sure what the delusion actually is, but it has something to do with statistical independence. In fact, the article Widespread mathematical delusions criticizes the lead section of statistical independence. Can somebody make sense of the new article?

The user who created the article has also written some articles on eventology, a theory which I haven't heard about. The article on eventology lists ten references, all by the same author, including some papers in good Russian journals so we might want to keep the article even though it violates the Wikipedia:Vanity guidelines. -- Jitse Niesen (talk) 05:12, 25 May 2006 (UTC)

0.999... ≠ 1 must be pretty widespread. And misconceptions about infinity are pretty common. -lethe ^{talk +} 06:58, 25 May 2006 (UTC)

I can't make much sense out of this rant. The "intuitive" meaning offered in the article Statistical independence appears to me to be an informal way of saying P(B|A) = P(B). Using the standard definition of conditional probability, this means P(A ∩ B)/P(A) = P(B), or P(A ∩ B) = P(A) P(B), in other words: events A and B are independent. Where is the delusion? There is no shortage of delusions, including mathematical ones, and the field of statistics and probability theory is particularly rich, but this doesn't seem to be one of them. Its like having a diatribe against saying that 1 < 2 means that 1 is less than 2, while it means nothing except "1 < 2". To AfD? --Lambiam^Talk 11:16, 25 May 2006 (UTC)

I find it hard to understand exactly what this guy is ranting about, mainly because of the poor translation of his thoughts (presumably from Russian) into English. His maths seems to be correct, but only seems to show that conditional probability can be different in different situations. If this page is to be kept, it surely needs a different title? (and a lot of work on wording) I cannot believe that this really is a *widespread* delusion Madmath789 11:46, 25 May 2006 (UTC)

Whatever else it it is, it is surely OR. Paul August ☎ 11:51, 25 May 2006 (UTC)

The delusion consists in popular attempts to justify or to prove or to deduce the definition of independence of events: P(AB)=P(A)P(B) from other assumptions. Mathematical definitions do not demand proofs, especially in a preamble to encyclopaedic paper on probability theory. The criticism is directed only on style of a preamble. All other sections of paper “Statistical” are quite correct. Thanks for discussion. - Helgus 12:28, 25 May 2006 (UTC)

Helgus: I think you misunderstand what the lead section (what you are calling the "preamble") of Statistical independence, is saying. It is not trying to "prove the definition" rather it is simply trying to provide an intuitive understanding of the concept. In any case any criticism of that article belongs at talk:Statistical independence not in some other article. Paul August ☎ 15:52, 25 May 2006 (UTC)

Probably you are right. Especially it concerns the second section of paper. However the first section without doubts keeps within a well-known encyclopaedic category “Paradoxes in mathematics”. Russian mirror of this paper contains, for example, popular delusions which often meet at discussion on “Fermat's last theorem”, “Parallel lines in Lobachevsky's geometry”, “Events with zero probability”. Can be it is necessary to open a new category “Paradoxes in mathematics” into which this paper could enter? - Helgus 21:58, 25 May 2006 (UTC)

Yes AfD unless its moved to a different name and cleaned up to be less like Orignial Research, give it a bit of time though the page is less than a day old.

Also the eventology page is now proposed for deletion, although the other sub articles and the category are not. Either it should be all or none and I think AfD might be better than prod in this case. --Salix alba (talk) 12:58, 25 May 2006 (UTC)

If the page is to be kept, it should probably be renamed -- "delusions" is not quite neutral, perhaps "misconceptions" would be better. Dysprosia 13:03, 25 May 2006 (UTC)

The eventology pages look suspicious to me. The only reason I created Category:Eventology is too keep them all in one place. I agree that an AfD vote on all of them could be the things to do. Oleg Alexandrov (talk) 15:37, 25 May 2006 (UTC)

It really is OR and a rant. The title reads pretty bad as well, it probably should be deleted.--Jersey Devil 17:37, 25 May 2006 (UTC)

I've removed the prod tag from eventology, If we are to believe the references there, it isn't OR, although it may be non-notable. So I agree with Jitse's, I'm not sure we should delete this. Paul August ☎ 18:09, 25 May 2006 (UTC)

But User:Helgus is Oleg Vorob'ov, the author of 10 out of 11 of the references. Sounds like OR to me. Staecker 02:44, 26 May 2006 (UTC)

No, OR means writing about something which has not yet been published elsewhere. Paul August ☎ 02:48, 26 May 2006 (UTC)

You're right- sorry, I confused it with WP:AUTO. Not surefire grounds for deletion, but it gives me the willies. Staecker 02:57, 26 May 2006 (UTC)

Yes writing about your own work is problematic. And we should take special notice of such. Paul August ☎ 17:10, 26 May 2006 (UTC)

eventology, but not sub-pages now on AfD. --Salix alba (talk) 10:45, 28 May 2006 (UTC)

Lebesgue spine

Being a newcomer here, I would appreciate some brief advice: Lebesgue spine is listed somewhere as a missing link, but when I look at 'what links here', I only find things like Wikipedia:Missing science topics/Maths16. I could write a page about the Lebesgue spine, but would it be any use? Madmath789 20:35, 25 May 2006 (UTC)

Sure it would be useful. Paul August ☎ 02:45, 26 May 2006 (UTC)

Non-negative v. nonnegative

OED lists "non-negative" but Webster's lists "nonnegative". Is this a British/American usage split? I've looked through a few textbooks, but there doesn't seem to be any particular consistency (not all American books use "nonnegative" and not all European ones use "non-negative"). Any opinions? There seems to be a mix among Wikipedia articles (even within a single article) and titles. Thanks. Lunch 22:05, 25 May 2006 (UTC)

I use either when the mood strikes me. If there's no standard, what's the difference? Ryan Reich 22:39, 25 May 2006 (UTC)

I s'pose I was thinking consistency would make things easier to find, and any source I found was always self-consistent whereas the Wikipedia isn't. And now that I look through the textbooks sitting in front of me, four have "nonnegative" (five American authors) and only one has "non-negative" (two Frenchmen). Lunch 23:11, 25 May 2006 (UTC)

In my experience, in American papers and textbooks "nonnegative" is by far the most common. Older works may use "non-negative" to a greater frequency. --Chan-Ho (Talk) 01:52, 27 May 2006 (UTC)

Stone-Cech compactification name

Most of the references I've seen have a symbol over the "C", which I can't figure out exactly how to generate. (Also, there seems to be a convention that the "-" should be replaced by an n-dash "–".) — Arthur Rubin | (talk) 00:28, 26 May 2006 (UTC)

How about this: Čech? Dmharvey 02:51, 26 May 2006 (UTC)

When I open an edit window, below the Save page button is a box that says "Insert:", followed by numerous special characters. The character in question is one of them, and clicking on it causes it to be inserted into the edit box. JavaScript must enabled in the browser for this to work. --KSmrq^T 03:52, 26 May 2006 (UTC)

What a mess. We have Stone-Cech compactification and Stone-Čech compactification, and Čech points to neither, and probably we need Cech as a redirect as well. Dmharvey 02:56, 26 May 2006 (UTC)

Hm, apparently the redirect at Stone-Čech compactification is my fault; don't really remember doing it. Stone-Cech compactification should be moved to Stone-Čech compactification, but it won't let me move it because the redirect is to a different place. I'll tag the redir for speedy. --Trovatore 03:05, 26 May 2006 (UTC)

OK, fixed now. This time the endash thing came in handy. --Trovatore 03:12, 26 May 2006 (UTC)

How about Štone-Cech compactification? :-) -lethe ^{talk +} 04:01, 26 May 2006 (UTC)

Added. Hey, you never know. --Trovatore 22:34, 26 May 2006 (UTC)

Maths AfDs

A certain User:Mathguru has AfD'd Quasi-Hopf algebra and Quasi-bialgebra. I think it is notable, but as the author, I may be biased.Blnguyen | Have your say!!! 06:39, 26 May 2006 (UTC)

I'm a hair away from closing them both speedy keep. -lethe ^{talk +} 10:48, 26 May 2006 (UTC)

Too late now ... I closed them. -- Jitse Niesen (talk) 12:00, 26 May 2006 (UTC)

well, mathguru, Afd' the Australian Mathematics Competition as well.Blnguyen | Have your say!!! 08:00, 31 May 2006 (UTC)

Also closed as a speedy keep. -- Jitse Niesen (talk) 08:36, 31 May 2006 (UTC)

A query

Does anyone have a reference or proof for Kronecker's lemma? This has been bothering me, mainly in case absolute convergence of Σ x_n ought to be included. Charles Matthews 13:07, 26 May 2006 (UTC)

I think the statement is true as is stands, but I don't have a reference. Using summation by parts,

${\frac {1}{b_{n}}}\sum _{k=0}^{n}b_{k}x_{k}=S_{n}-{\frac {1}{b_{n}}}\sum _{k=0}^{n-1}(b_{k+1}-b_{k})S_{k},$

where $S_{k}$ are the partial sums of the x's. Pick any epsilon > 0, choose N so that $S_{k}$ is epsilon-close to s for k > N. Then the right hand side is

$S_{n}-{\frac {1}{b_{n}}}\sum _{k=0}^{N-1}(b_{k+1}-b_{k})S_{k}-{\frac {1}{b_{n}}}\sum _{k=N}^{n-1}(b_{k+1}-b_{k})S_{k}$

$=S_{n}-{\frac {1}{b_{n}}}\sum _{k=0}^{N-1}(b_{k+1}-b_{k})S_{k}-{\frac {1}{b_{n}}}\sum _{k=N}^{n-1}(b_{k+1}-b_{k})s-{\frac {1}{b_{n}}}\sum _{k=N}^{n-1}(b_{k+1}-b_{k})(S_{k}-s)$

$=S_{n}-{\frac {1}{b_{n}}}\sum _{k=0}^{N-1}(b_{k+1}-b_{k})S_{k}-{\frac {b_{n}-b_{N}}{b_{n}}}s-{\frac {1}{b_{n}}}\sum _{k=N}^{n-1}(b_{k+1}-b_{k})(S_{k}-s)$

Let n go to infinity. The first term goes to s, which cancels with the third term. The second term goes to zero. Since the b sequence is increasing, the last term is bounded by $\epsilon (b_{n}-b_{N})/b_{n}\leq \epsilon$. Dmharvey 13:41, 26 May 2006 (UTC)

Now transcribed to that controversial category Category:Article proofs. linas 01:43, 13 June 2006 (UTC)

Indiscriminate collection of information?

Don't pages like this, Derivative (examples), break with WP:NOT?--Jersey Devil 02:32, 27 May 2006 (UTC)

I have put it up for afd, your input would be appreciated.--Jersey Devil 02:36, 27 May 2006 (UTC)

Mathematics is Article Improvement Drive collaboration

Ladies and Gentlemen! Did you know that the article Mathematics is the current Article Improvement Drive collaboration? --Lambiam^Talk 22:40, 27 May 2006 (UTC)

Voted for it on the AID page. One user commented that it is in the top ten most viewed pages on Wikipedia and therefore must be a featured article.--Jersey Devil 23:01, 27 May 2006 (UTC)

Eventology AfD

The article Eventology (by the same author as Widespread mathematical delusions) has been nominated for deletion. --Lambiam^Talk 13:21, 28 May 2006 (UTC)

Delusions in probability theory and statistics on AfD

I've nominated the article Delusions in probability theory and statistics (earlier called Widespread mathematical delusions) for deletion. --Lambiam^Talk 22:31, 28 May 2006 (UTC)

Disambiguation of sinc function

There are two possible definitions of the sinc function, namely

$\operatorname {sinc} \,x={\frac {\sin x}{x}}\quad {\mbox{or}}\quad \operatorname {sinc} \,x={\frac {\sin \pi x}{\pi x}}.$

One possible way to handle this is to split the article sinc function in two, sinc function (normalized) and sinc function (unnormalized), similar to the usual disambiguation process. We are having a discussion on Talk:Sinc function (unnormalized) whether this is the proper way to go about it, and I'm solliciting others to join. -- Jitse Niesen (talk) 05:21, 31 May 2006 (UTC)

Possible confusion over 'subadditive'

There is an article Subadditive which discusses functions satisfying $f(x+y)\leq f(x)+f(y)$, and there is a link to this article from Sigma additivity in the category measure theory. There seems to be a different definition of 'subadditive' (and also 'countably subadditive') in use in measure theory:

$\mu (E\cup F)\leq \mu (E)+\mu (F)$

(used in developing the theory of 'outer measure'). My question is: do we need a separate page for subadditve set functions, or should we incorporate it into the existing subadditive page? (Or are subadditive set functions not notable and we do not need them?). I might be in a position to write something on the set function version of subadditive (if needed), but would appreciate some views about what might be done - and there are probably others better qualified to write such stuff anyway.Madmath789 11:27, 31 May 2006 (UTC)

I think you're right, subadditive (measure theory) deserves its own article. I don't know any measure theory, but I recall there being interesting theorems about set functions which are additive (on finite collections of sets) and countably subadditive. Dmharvey 11:37, 31 May 2006 (UTC)

Be bold! Write stuff, we move and fix later. Charles Matthews 11:46, 31 May 2006 (UTC)

Barry Simon article

The piece on Barry Simon is from a fan, it seems. Important guy for mathematical physics, and this should be better expressed and sourced, and have more technical stuff about the work. Charles Matthews 11:46, 31 May 2006 (UTC)

A good example of hagiography I guess. --CSTAR 18:54, 1 June 2006 (UTC)

E9 (Lie algebra)

My knowledge of Lie algebras is a single course, but this potentially confusing notation was never mentioned. Has anyone else heard of this? Septentrionalis 18:40, 1 June 2006 (UTC)

I have never heard of this notation. I note that my references list the notation as E₈⁽¹⁾. The subscript here is, as always, the rank. -lethe ^{talk +} 18:51, 1 June 2006 (UTC)

Please review

I have extensively revised and cleaned up Divisibility rule, so please take a look and help to improve it more. As I'm not fully experienced at all the editing tools, I'm sure the formatting and adherence to guidelines and standards could be improved.

I'd like to create a number of other pages related to mental math, so I'd like to get feedback on this one, the first I've heavily edited. (The current mental arithmetic has only the most basic, simple of techniques.

Walt 01:59, 2 June 2006 (UTC)

Category:Billion and cousins up for deletion

See Wikipedia:Categories_for_deletion#Category:Thousand. Oleg Alexandrov (talk) 18:57, 3 June 2006 (UTC)

Poincaré conjecture

Some Chinese news sources have picked up a story about a recent journal article by Cao and Zhu, experts on the Ricci flow, who have written what they (and the journal editors) claim is a "complete" proof of the geometrization conjecture, by giving more details of Perelman's work. Slashdot has also picked up on this. As a consequence, there has been several editors who have insisted on placing mention of Cao and Zhu's paper in the lead section. I have disagreed (see talk page discussion and also some of my edit summaries for extensive reasons). Please continue discussion there. I would also appreciate if people could pop in and check that things don't get out of control. Thanks. --Chan-Ho (Talk) 02:15, 6 June 2006 (UTC)

American Institute of Mathematics

The article on American Institute of Mathematics has been nominated for deletion by someone. R.e.b. 13:02, 6 June 2006 (UTC)

PlanetMath Exchange project milestone

The PlanetMath Exchange project has today reached a new milestone, with 40% of all PlanetMath articles reviewed.

For those of you who have not been following the project, I thought I would take this opportunity to report on the status of the project, and the progress which has been made to date. The purpose of the project is to review all PlanetMath (PM) articles (which are licensed under GFDL) and to incorporate any appropriate PM content not adequately covered on Wikipedia (WP).

There are over 4800 PM articles listed, of which over 1900 of which have been reviewed so far. Of the reviewed articles, 143 PM articles have been copied to WP, creating entirely new WP articles, and 121 have been merged into already existing WP articles. Additionally, a further 75 PM articles have been identified as needing to be copied, and 349 needing to be merged.

The project maintains 49 lists of PM articles grouped by topic (e.g. 11 Number theory, 26 Real functions, 54 General topology). The entire list of lists is compiled into a "Article lists" table, and statistics are maintained for each topic's list.

19 editors have identified themselves as participants, and 26 have reviewed at least one PM article (see Editor contributions).

Oleg Alexandrov, has provided several excellent tools to facilitate the project. He and Mathbot created the original 49 lists (first created in Feb 2005, and updated with new PM articles in March 2006). They also perform daily updates of statistics in the "Article lists", and "Editor contributions" tables. In addition, Oleg has created a convenient tool to assist in converting a PM article to wiki markup.

I heartily encourage everyone to join the fun.

Paul August ☎ 02:06, 8 June 2006 (UTC)

Direct logic up for deletion

See Wikipedia:Articles_for_deletion/Direct_logic -Dan 15:36, 8 June 2006 (UTC)

Another misguided nomination for deletion

Please vote at Wikipedia:Articles for deletion/American Institute of Mathematics. Michael Hardy 23:33, 9 June 2006 (UTC)

Yeah, R.e.b. told us already. -lethe ^{talk +} 00:48, 10 June 2006 (UTC)

I closed that AfD. -lethe ^{talk +} 00:54, 10 June 2006 (UTC)

Functional analyst needed

Hi, I left a question regarding the correct statement of the Ryll-Nardzewski fixed point theorem at Talk:Ryll-Nardzewski fixed point theorem. Cheers, AxelBoldt 04:10, 11 June 2006 (UTC)

As stated it's wrong. The semigroup is required to satisfy another property, that it be "distal". Also I don't think it can be used to prove existence of Haar measure on general locally compact groups, although I think for compact groups yes. I think this is in Rudin's functional analysis book for instance. Also see Frederic Greanleaf's little book (now horribly outdated) on "Amenable Groups".--CSTAR 12:41, 12 June 2006 (UTC)

Rewrite Poincaré_conjecture?

I invite interested parties to make comments at Talk:Poincaré_conjecture#Peer_review. --Chan-Ho (Talk) 12:48, 11 June 2006 (UTC)

Jaques Hadamard or Jacques Hadamard?

An anon recently redirected the wikilink in Chaos Theory from the first to the second. Is this legitimite? Are these the same person? — Arthur Rubin | (talk) 15:30, 11 June 2006 (UTC)

Yes, same person. Correct spelling is Jacques [4]. I have changed the Jaques page to a redirect and fixed the link in the single remaining article that used the wrong spelling. Gandalf61 15:53, 11 June 2006 (UTC)

Zipper theorem

I wanted to {{prod}} this article. But to be sure I thought I'd check. Is this article nonsense or not? I couldn't google the name, but that doesn't always mean anything. Garion96 ^(talk) 00:20, 12 June 2006 (UTC)

The theorem and its proof in the article are correct. The theorem was not known to me under this or any other name. --Lambiam^Talk 00:53, 12 June 2006 (UTC)

Thanks, so I won't {{prod}} it. Anyone here wants to clean that article up? Cause the way it looks now, it's not understandable for the non mathematician reader. Like me. :) Garion96 ^(talk) 12:04, 12 June 2006 (UTC)

Hmm, perhaps I should have looked at at the article again. It already is cleaned up. Thanks. Garion96 ^(talk) 12:05, 12 June 2006 (UTC)

I think it's a neologism. I think it should be deleted without some evidence of that name having widespread currency. Dmharvey 12:15, 12 June 2006 (UTC)

I've heard it referred to in that way ("zipper theorem"); dunno if that's enough evidence for you. I also can't think offhand of a place I've seen it in print, though. I could ask around. Lunch 18:53, 12 June 2006 (UTC)

I'm skeptical that the name is very common. I can't imagine the theorem would even have a name amongst mathematicians. So I think the term would only be used in certain kinds of introductory course work. Google gives no results (off Wikipedia), so nobody that has mentioned it, for example, in a course webpage. The only place I can think the term may exist is in some textbooks somewhere. Even in that eventuality, I don't know if it's worth having an article based on that amount of usage. I guess it does no harm, but I'm also hard-pressed to imagine a situation where we would want to link to it. --Chan-Ho (Talk) 19:18, 12 June 2006 (UTC)

Merge it into Limit of a sequence#Properties? —Blotwell 17:01, 13 June 2006 (UTC)

integrable systems

Over at Talk:Constant of motion, I've been reduced to babling and waving my hands to the effect that a "system of differential equations with constants of motion == integrable system == system with symmetries" and conversely, "non-integrable system == system with no constants of motion". However, it occurs to me that I know of no grand theorems making this claim. Are there any? Is this in fact a collection of small results in narrow fields that have accreted into a grand truth? Guidance? How can one make this clear at a college-math level? It doesn't help that the article integrable system is somewhat foreboding in its current form. linas 01:30, 13 June 2006 (UTC)

Maybe I'm being lame? Maybe its just the Frobenius theorem coupled to the idea that the submanifold has a natural symmetry, ergo by Noether's theorem has constants of motion? I've never had formal skoolin in this matter. linas 03:13, 13 June 2006 (UTC)

I think I'm grasping for Liouville's theorem (Hamiltonian). I swear this stuff goes in one ear and out the other. I'm babbling even now. linas 03:27, 13 June 2006 (UTC)

You make a good point about the current article being somewhat forbidding. I would go a step further. I don't think integrable system should redirect to integrability conditions. An integrable system usually (?) refers to a Hamiltonian system with a full set of Poisson-commuting flows. Naturally, integrability conditions do play a role, but there is more structure a priori in an integrable system. For the point about conserved quantities for an integrable system, since the Hamiltonian flows commute, there should be loads of conserved quantities. (As you ask, is there a general theorem here? Does Noether apply? etc). Hence a system without "enough" conserved quantities will be non-integrable. I'm not so sure about the converse. Silly rabbit 13:15, 13 June 2006 (UTC)

Thanks. What I've been reading gives the name completely integrable system to the case of a full set of commuting Poisson brackets. Your "not being sure about the converse" would imply that there are non-integrable systems with a "full set" of conserved quantities. That certainly sets my mind wandering in wild directions. linas 23:27, 16 June 2006 (UTC)

Nice start on integrable systems. It certainly has helped me organize some of my own wild wanderings. I'm clearly not an expert, but it seems to be tricky to give a good definition of an integrable system. (Ok, so first off, yes I meant what you call completely integrable: which is unarguably a better term ;) In particular, there are issues of local versus global integrability. What does global integrability mean anyway? Do the all the level submanifolds have to be closed? Do the constants have to be found explicitly, or can they just be given in some implicit sense? Can a locally completely integrable system have degenerate Poisson brackets on some small dimensional locus, and still have functionally independent integrals? (Here is the "lack of converse" possibility -- if it exists to begin with.) Silly rabbit 23:37, 17 June 2006 (UTC)

Thanks. I'd say a Lie group is the prototype for something that is "globally integrable". I don't know of any systems that are "provably integrable" (constants of motion implicitly given), but whose solution is unknown (no explicit form). I suspect one can find level manifolds that are not closed, certainly things like the horocycle flow ( aka Anosov flow on tangent space of SL(2,C)) has the flavour of being non-compact but this is an off-the-cuff remark. I believe that the whole area of sub-Riemannian geometry is permeated with integrable systems that have cuts and isolated singularities and the like. Next, chaotic systems have "regimes" of regular and chaotic motion that's interspersed; the KAM torus being the famous example, although the easy-to-understand variants are in difference equations. Then there's all this stuff about homoclinic orbitss, and stuff like Axiom A, which I dimly understand. Or things I dont:Smale's spectral decomposition theorem. I'm sort of learning this stuff as I go along.linas 04:57, 18 June 2006 (UTC)

Mathematicians for Wikipedia:Version 0.5 Nominations

On Wikipedia talk:WikiProject Mathematics/Wikipedia 1.0 there is a request for the most notable mathematicians whos biographies could be included in Wikipedia:Version 0.5 Nominations. Suggestions for celebratity mathematicians welcome. Possible also assesments of the quality of their article also welcome. --Salix alba (talk) 07:45, 15 June 2006 (UTC)

Thanks to great work by Lethe we now have a fairly comprehensive list of the the giants for mathematics on Mathematics/Wikipedia 1.0. A new template Template:maths rating has also been created together with a set of categories listing the quality and importance of mathematics articles. Mathbot will included these articles in Wikipedia:Version 1.0 Editorial Team/Mathematics articles by quality on a daily basis. Help is now needed in identifying the important maths articles and assigning then a grade (Feature Article/A/Good Article/B/Start/Stub), which can be done by including the template on the talk page. There are a few biographies which may be suitable for listing as good articles and several other on some key figures which are barely more than stubs and could do with expansion.

I'm also thinking that the list of mathematicians could make a good article in its own right, either as a section in Mathematicians or its own article, possible Influential mathematicians. --Salix alba (talk) 09:25, 16 June 2006 (UTC)

We already have list of mathematicians, but I guess you are thinking of a selective subset. I don't know if it is worth its own article. Oleg Alexandrov (talk) 15:37, 16 June 2006 (UTC)

Yes I was thinking of a more selective list, probably anotated as well, briefly describing their main acheivments. It could be an interesting way to tell the history of mathematics through the people involved and the new areas of study they started. This sort of presentation, is quite popular in science books aimed at the general reader and might appeal to certain wikipedia readers. --Salix alba (talk) 20:20, 16 June 2006 (UTC)

Well If you want a selective list one place to start would be Bell's Men of Mathematics. Paul August ☎ 20:55, 16 June 2006 (UTC)

Might I also suggest the obvious web site, MacTutor? --KSmrq^T 04:53, 17 June 2006 (UTC)

Probability/Measure theory glossary?

Does WP have a glossary that translates the language of probability theory to measure theory? I've got a complaint on my talk page that I'm trying to decipher; I don't understand Score (statistics) and Fisher information, although I suspect I would, if they were restated in terms of measure theory. The root of this interest is the rather astounding edit here, which is so remarkable, I abstract it here:

Fisher information is a powerful new method for deriving laws governing many aspects of nature and human society. B. Roy Frieden sets out in detail how Fisher information can ground a great deal of contemporary physical theory, including Newtonian mechanics, virial theorem, statistical mechanics, thermodynamics, Maxwell's equations, Lorentz transformation, general relativity, EPR experiment, Schrodinger equation, Klein-Gordon equation, Dirac equation, Rarita-Schwinger equation, and the fundamental physical constants. Frieden and coauthors have also used EPI to derive some established principles and new laws of biology, the biophysics of cancer growth, chemistry, and economics.

Surely, the ommission of M-theory and intelligent design is just an oversight? linas 00:38, 17 June 2006 (UTC)

See Talk:B._Roy_Frieden for a little bit of discussion and some links to external reviews of Frieden's work. He has some interesting ideas but, it seems, not quite the revolution he makes out for himself. The IP address of the edits is assigned to [http:/csc.canterbury.ac.nz Christchurch College of Education] in New Zealand. Maybe Frieden's been travelling? Lunch 03:49, 17 June 2006 (UTC)

user mathisreallycool

A new user mathisreallycool (talk · contribs) has made several edits which to my mind betray a fundamental lack of knowledge in certain mathematical topics. I have reverted several additions by this user, and I want to vet some other things by the user. For example, the article Konfisakhar space seems unobjectionable, it's referenced. However I've never heard of this idea, it's not in any of my texts, nor is it in my EDM2, and frankly, I find the idea of a fractal vector space hard to believe. Can someone (maybe with access to the book by Schaeffer) verify this concept? Otherwise, I shall want to AfD is. And maybe also this definition of semidirect products for monoids? -lethe ^{talk +} 07:14, 17 June 2006 (UTC)

A web search for Igor Konfisakhar suggests the work of a creative student, violating WP:NOR. The citation of the Schaeffer book is also not quite correct; the second edition (ISBN 978-0-387-98726-2) has two authors. I have no personal knowledge of the topic or the book, but I share your reservations.

PS: I've begun using 13-digit ISBNs, since the official transition is not far off. On online converter is available. --KSmrq^T 10:40, 17 June 2006 (UTC)

I've listed Konfisakhar space for deletion. "Professor Igor Konfisakhar" appears to be an undergrad, notable only for being a 3rd place winner in a Putnam prize contest, which is better 'n me but not good enough for this. linas 03:54, 18 June 2006 (UTC)

The reference work listed is searchable online at Amazon (see [5]). I find no reference to "fractal" or "Konfisakhar". Paul August ☎ 04:35, 18 June 2006 (UTC)

Problems at Propositional Calculus

(Copied from my talk page. Oleg Alexandrov (talk) 07:51, 17 June 2006 (UTC))

JA: Hi, could you help sort out the continuing tangles at Propositional calculus? First there was that improper name change last month, and I let it go because the user who did it seemed fairly competent and added some good stuff, but now the word "logic" seems to be inviting anonymous users to take the article out of the mathematical logic designation and add any sort of half-baked exposition that they can cook up. I don't know my way around the procedures well enough to keep dealing with sort of stuff. Much appreciated, Jon Awbrey 05:15, 17 June 2006 (UTC)

There had been some noise in the past about moving propositional calculus to propositional logic or classical propositional logic. The move to propositional logic was affected by Charles Stewart via WP:RM last month, then reverted by a history-destroying copy-paste by Jon Awbrey this week. I reverted the copy-paste (restoring the history), then reverted the proper move (preserving the history), so now we're back where we started. If the move is to happen, a case will have to be made again. -lethe ^{talk +} 07:59, 17 June 2006 (UTC)

Use "iff", not "if", in definitions!

Some editors appear to believe that there is a convention which requires the use of "if" in definitions rather than "iff" (short for "if and only if"). A definition is a proposition which equates a new term to a compound expression composed of old terms. So using "if" is wrong. One should use "iff" or an equivalent, such as: "if and only if", "is", "is the same as", "means", "is equivalent to", "when and only when", etc.. JRSpriggs 08:20, 17 June 2006 (UTC)

Though you are technically correct, I don't think it's such a problem to use just an "if" in a definition. It's tedious to always write "if and only if" (and the abbreviation is esoteric), and the full meaning can always be inferred. Of course to require "if" in definitions is certainly bad. -lethe ^{talk +} 08:29, 17 June 2006 (UTC)

I am complaining because thrice recently someone has changed "iff" to "if" in a definition. JRSpriggs 10:03, 17 June 2006 (UTC)

If I saw that happen, I would probably revert. -lethe ^{talk +} 10:25, 17 June 2006 (UTC)

Well, "if" is brief, commonly understood, and colloquial; "iff" is brief, not commonly understood, and precise. What to do? Personal, I dislike "iff", so I either write out "if and only if" or use a phrase like "exactly when". My feeling is that anyone who understands the meaning of "iff" and feels comfortable with it also has enough of that fabled "mathematical maturity" to not misinterpret a definition using "if". I am not aware of a WikiMath guideline, nor a Wikipedia guideline that speaks to this slightly delicate issue involving both accessibility and formal correctness.

A recurring challenge with a multinational pool of editors is melding one's own training and taste with that of others. I cringe whenever I see the word "ditto" in an article, as to me it screams of informality, not suitable for an encyclopedia. I'd love to see both "iff" and "ditto" banned, but I have no sense of how much agreement I would find for that view. --KSmrq^T 11:01, 17 June 2006 (UTC)

I would agree with abolishing "ditto" but not with abolishing "iff". Anyway, I agree with Ryan below. The precision afforded by the usage "iff" is useful for theorems, but not so much for definitions. -lethe ^{talk +} 11:18, 17 June 2006 (UTC)

This doesn't follow any mathematical practice I've ever seen, so why should we insist on it simply because it's technically right? We don't make policy here, just record it. Besides, to counter your argument, "iff" is logically absurd in this context since the term to be defined has no prior meaning; whether or not it applies is determined by the text of the definition. In other words, "only if" is vacuous if the term is unique, and if not, it is erroneous. Someone reading an "iff" definition for the first time will wonder if they've missed some other discussion of the term, and anyone else will be annoyed because it departs from the usual style. I agree with lethe, though: any change of one to the other should be reverted. This is a personal preference. Ryan Reich 10:57, 17 June 2006 (UTC)

We are certainly allowed to make policy here. What we don't do is invent subject matter for our articles. So we can't invent terminologies, but we can certainly decide on conventions for our terminologies. -lethe ^{talk +} 11:18, 17 June 2006 (UTC)

I'd argue more but apparently you agree with me. My objection to inventing policy in this sort of case is that the choices are not all equally acceptable; it's not like choosing an indentation style for C code, where many different styles all have their widespread adherents. I've simply never seen "iff" in a definition. Ryan Reich 11:30, 17 June 2006 (UTC)

I can't quote chapter and verse, but I remember seeing a mathematical style guide recommending "if" in definitions. Personally I prefer "when", to distinguish it from the notion of logical consequence (as in: You are in a dilemma when you don't know which way to turn), although some may decry the temporal connotation. --Lambiam^Talk 12:07, 17 June 2006 (UTC)

I much prefer "if", and that's what I observe as common mathematical practice. Dmharvey 12:57, 17 June 2006 (UTC)

I think "if" is somewhat unclear, but I have no problem with "only if", "if and only if", the equivalency arrow ($\Leftrightarrow$) and other such language. The term "iff" I object strongly to, at least in basic math articles, on the grounds that it is jargon that is unfamiliar to many basic students of mathematics who have not done proofs. But don't take my word for it - I've seen countless edits where amateurs have "corrected" iff to "if". Deco 13:53, 17 June 2006 (UTC)

Something unseemingly asymmetrical about accepting "only if" (⇐) and rejecting "if" (⇒). I must say I do not understand your position. -lethe ^{talk +} 14:04, 17 June 2006 (UTC)

The words "only if" do not imply "given the sufficient condition that", and it is a myth that "if and only if" is the conjunction of "if" and "only if". It is merely a way of clarifying "if" using the additional qualifier "only if" that only serves to strengthen that "no we don't mean this is just a necessary condition" but in fact an equivalency is intended. If I say "a number is prime only if it has exactly two factors", the intepretation is clear; it does not even suggest that there might be a prime which doesn't have two factors. Deco 17:23, 17 June 2006 (UTC)

Indeed, "only if" implies "given the necessary condition that", and "if" means "sufficient". And in mathematics, "if and only if" certainly is their conjunction, at least in a formal context, but since this is a formal phrase that is to be expected. Using it in an informal context evokes its formal meaning and is just confusing when you start to split hairs about what it really means, especially given that syntactically, it definitely looks like the conjunction of "if" and "only if". Stating "only if" in a definition is redundant, since the term is intended to be deciphered, not encoded: if I see a long string of conditions which happen to have a nice definition but I don't know it, I will not go looking for one until it's necessary; on the other hand, if I see an unfamiliar term I will go looking for its definition. Putting "only if" in the definition would just mean "whenever you see this term, you can be sure it means this phrase", which is exactly what the process of defining the term means anyway. Combined with the common-sense reason that people just don't talk like that, I say "only if" should stay out. Ryan Reich 18:03, 17 June 2006 (UTC)

I strongly support the use of "if" in definitions over either "iff" or "if and only if". By the way this has (of course) been discussed before. I will now provide for your reading pleasure this oldie but goldi, this blast from our past:

(Start of copied text from talk page archives)

Can I raise the question of whether we want iff in definitions? I don't. I think it's offputting to those not pure-mathematical 'native speakers'. And the idea that it's more rigorous is surely shallow.

Charles Matthews 16:28, 21 Oct 2003 (UTC)

In the absence of an explicitly-stated convention, I think it's marginally more rigorous than "if". I have occasionally used "if" in a definition and meant "if but not only if", although not on Wikipedia as far as I remember. I'd suggest that if "iff" is undesirable, the best replacement for the non-specialist reader is "if (and only if)", since the rigorous alternative is to ensure that "if" is never used other than to mean "iff". Onebyone 16:49, 21 Oct 2003 (UTC)

I don't accept the 'rigour' argument, anyway. Using 'if' there is an implied 'one can assert' in front of mathematical propositions - which no one writes unless in a very careful formal treatment. Those who care about this can imagine it all anyway. Better, I think, just to use normal language: 'an X is a Y with property P'. I haven't checked whether the definitions of legal terms on Wikipedia make a point of this type of care. On the whole I think it's wasted: it's hard to imagine the user who needs it. Charles Matthews 17:58, 21 Oct 2003 (UTC)

Well, I agree that the pedantry is not worthwhile if it is off-putting for readers. On the other hand, I'll take no part in any kind of global edit to deliberately introduce ambiguity, even if that ambiguity can generally be resolved from context. You say "I think this care is wasted", but I suspect that for most mathematician authors it will require extra care to remember not to do this rather than extra care to do it!

"An X is a Y with property P" sounds good to me, especially in the standout definition at the top of the article. Nobody writes articles on topics other than maths saying "a person is a saint if and only if they have been canonised by the Church" or whatever. If there's a more formal section of maths in the article, I do think that "iff" and other jargon words should be used in that section exactly as the author would use them in any mathematical writing.

Onebyone 10:35, 22 Oct 2003 (UTC)

So, my understanding is that the Project isn't trying to prescribe, but is looking for some harmonisation. Charles Matthews 19:02, 22 Oct 2003 (UTC)

(End of copied text)

Paul August ☎ 18:38, 17 June 2006 (UTC)

Redirects in the list of mathematics articles

Currently we have 12102 articles in the list of mathematics articles. Out of them, 1070 are redirects (see the complete list). Redirects get created in several ways

1. Plugging in some redlink in the list (not anymore, as all redlinks are removed automatically)
2. Merging an article to a bigger article
3. Renaming an article.

In my view it is the third which makes for most redirects.

While redirects are very important, I see no good reason for why they should stay listed in the list of mathematics articles (I estimate that there are at least 2000 math redirects which are not there).

I wonder what people think of a big purge, removing all redirects from the list of mathematics articles. Of course, if at some point a redirect becomes back an article, my bot will add it back to the list. Thanks. Oleg Alexandrov (talk) 22:37, 17 June 2006 (UTC)

So if I create a redirect to a math article, but the redirect isn't already a redlink from the list, then it doesn't get added to the list? -lethe ^{talk +} 22:57, 17 June 2006 (UTC)

No. The bot adds to the list of mathematics articles via categories. So, if your redirect is made to be in a math category (which it won't, most of the time), the bot will add it to the list. Otherwise it won't. The primary purpose of list of mathematics articles is to list articles I think, not redirects, although a separate list of redirects to math articles may be found useful by some people. Oleg Alexandrov (talk) 23:55, 17 June 2006 (UTC)

Well whatever uses there may be for a list of math redirects, this list cannot serve, since it doesn't contain them all. Therefore, you have my full endorsement to remove them. There is simply no reason to have only some of the math redirects in a list, right? -lethe ^{talk +} 00:00, 18 June 2006 (UTC)

I'm not sure what purposes the list serves. Take Circular arc, which is currently a redirect to Arc (geometry), but the concepts are distinguishable and Circular arc might eventually grow into a separate article. In an index it would be reasonable to include it. If the purpose is to have a way to visit every maths article to check if its conforms to a new policy, then you'd prefer to skip it. (By the way, it currently is not categorized.) Perhaps math-categorized redirect pages could be listed, but rendered in italics, like with the All pages search. (<-This comment was by User:Lambiam who forgot to sign it. JRSpriggs 11:08, 18 June 2006 (UTC))

OK then, so if a redirect is important enough, it should be categorized, and then my bot will add it in. About making redirects italic, that is harder to do, as I would need to daily download a lot of articles to see which are redirects. Oleg Alexandrov (talk) 16:25, 18 June 2006 (UTC)

MathML / improved TeX support

Hi people. For those of you who have been watching developments concerning m:blahtex, MathML support on wikipedia, etc, I'm sure you've noticed nothing much has been happening for a while. Well, for the past few months, Jitse and I have been trying pretty damn hard to push buttons in the background to make things happen, but sadly the core developers simply haven't taken the bait. It seems to be a case of "yeah, it looks interesting, but we've got like 10,000 other things we're trying to do, and we just haven't got around to checking out the code yet...". It seems that wikipedia just doesn't have enough engineer-hours to give us the attention we need to get this going, and there's only so much pushing that Jitse and I can do without becoming annoying pains in the arse.

The status now is that I'm certainly not spending any more time on the code until I have some indication that there's a chance wikipedia is going to use it. And I've had enough of all the promotional "hey everyone isn't blahtex wonderful and y'all should be using it". It's tiring and not really my style. I enjoy writing code, not selling it.

So unless the people who hang out on this page somehow band together and make the developers realise that MathML is something that people want, the project is going to die a serene death. I took the initiative about a year ago, and wrote 13,000 lines of code to prove that it was possible. I'm happy to help out some more, and of course I look forward to the day when there is good mathml support in wikipedia. But someone else needs to take the initiative now, because I'm through.

Anyway, I think I'll go to bed now, make sure I'm bright and fresh to watch Australia defeat Brazil 6-0 tomorrow.

Good luck guys. Dmharvey 03:57, 18 June 2006 (UTC)

Perhaps a petition signed by the user community? Which is then passed up to Jimbo? This is an important chunk of code that is being laid at the feet of the sysadmins; surely its something that should be picked up. A few words of caution: (1) although the code may work well for you, sysadmins concerned with high-availability servers have a very very very different view of what it means "to run reliably". You might not have given them warm fuzzies on this issue. (2) The WP servers seem often overloaded, there may be unvoiced concerns about impacting performance. If you think these issues are under control, then a public appeal may be the right route to get attention. If they're wobbly, you might get blown out of the water. linas 04:18, 18 June 2006 (UTC)

I've explored the BlahtexWiki and I have to say, I'm quite impressed. I just have two main concerns for implementing MathML on Wikipedia, if those were fixed, I would gladly push the developers to implement it.

1. Browser compatability. Almost nothing works for me in IE 6.0
2. Fonts. It appears as if you need to download special fonts for MathML to display correctly. I'm not sure how many people would want to do that. Also, the radical symbols do not display correctly in Firefox for me.

I would be glad to push for the implementation of MathML in WP if we can somehow figure something out for those two problems. —Mets501 (talk) 04:26, 18 June 2006 (UTC)

There is no way around the issue of downloading fonts. As far as I can tell, Firefox often lacks some fonts by default. For IE I think one needs the MathPlayer extension.

It is no surprise the developers are weary at accepting a huge chunk of outside code, especially there is not really a huge demand for MathML from users. Any ideas of how to convince the developers to take this step would indeed be much appreciated. Oleg Alexandrov (talk) 05:14, 18 June 2006 (UTC)

Thank you, thank you, thank you for all of your work. Having written some mathematical typesetting code myself at one time, I have a feeling for what a challenge it is to do a good job. There are so many subtle issues of fonts and stretching and spacing and symantics and positioning and compatibility and on and on, that only someone who has been in the trenches can really appreciate the magnitude of this endeavor. It really takes a champion, like Roger Sidje on the Mozilla project or David Harvey on BlahTeX.

I believe I can speak to systems programmers with some credibility, and I would be happy to do so on behalf of BlahTeX. A noisy outcry from Wikipedia's technical writers might also prove influential. Beyond mathematicians, we have physicists, chemists, biologists, and engineers of all stripes, all of whom could benefit.

The latest word from the STIX Fonts Project is

"After reviewing the tasks required for completion of the project, September was established as a revised target for the beta test. The final production release will likely occur in December, but the TeX package may not be ready until January 2007."

Although the STIX project has not been exemplary in meeting its targets, it does appear that it is real, it is happening, and in a matter of months there will be little excuse to complain about a lack of fonts for MathML.

I cannot imagine that server load is a realistic concern. Currently MediaWiki converts <math> mkup to images, which requires parsing, pseudo-TeXing, image generation, and then serving the images. Unless BlahTeX is very poorly written indeed, it is unlikely to be more of a load. All BlahTeX has to do is transcribe TeX syntax to MathML syntax; and bloated as it is, MathML is still much smaller to serve than the equivalent image. Caching may be used currently to amortize the cost of image creation, but there is no good reason the same could not be done for BlahTeX. And, again, storing cached images requires more space than storing cached MathML.

That leaves the concern of bullet-proofing. For that, we have the empirical argument that the code has been tested against every single equation currently used at Wikipedia, of which there are hundreds of thousands. Yes, a few hundred do not translate; but that's a small matter of manual conversion because they depend on the bastardized TeX currently supported (texvc). In compensation, future editors will have use of a broader range of TeX features, something arrow-pushers will appreciate.

It occurs to me that if the developers are recalcitrant, perhaps Jimbo Wales might be persuaded. Pressure from the top could then be more effective than pressure from the bottom.

Thanks again for all the hard work so far. Given Wikipedia's culture of consensus, it seems only fair that others now help shoulder the burden. --KSmrq^T 10:33, 18 June 2006 (UTC)

But so what is the next step? Campaign to get it installed on test.wikipedia.org? What can we do to help? Send messages to mediawiki-l? I notice searching through the archives, that you have previously announced releases of blahtex to that mailing list, and they have never had any response. Have you ever had any dialogue with anyone from mediawiki development about this code? Whom do we talk to? -lethe ^{talk +} 10:43, 18 June 2006 (UTC)

---

At the risk of sounding too critical, how difficult would it be to make things work for the current "bastardized TeX"? The idea of breaking old revisions of articles without it being obvious why that is makes me kind of queasy ...

Is this a major issue? How do things fail after the change? Backwards compatibility is something that needs to be addressed, even if it cannot be guaranteed.

Not that I think this is a huge problem, if the scope is that small.

Otherwise, I'm with lethe. Whom do we talk to, and what's their favourite ice cream flavour (for bribes, you know)?

RandomP 11:00, 18 June 2006 (UTC)

We have a list of all the broken bastardized tex instances. There are a couple of hundred, which we've slowly been fixing, one at a time. We would obviously want to finish them off before we went live. -lethe ^{talk +} 11:21, 18 June 2006 (UTC)

---

I'd just like to qualify my remarks: it seems that even today, "history" won't get you anything like the old version of an article, at least when that article uses images from the commons.

I think it would be really cool if someone wrote, essentially, a simulated wayback machine for wikipedia, that went back to the wikicode, images, and math layout as they were when the revision was created. I thought that's what history was, but apparently, not so.

So that's not an issue either, and can we please have mathml now?

RandomP 14:09, 18 June 2006 (UTC)

Brief replies to above questions

• Linas's question about server overload. This is a complete non-issue for several reasons, some already mentioned by KSmrq. I haven't done any benchmarking for a while, but here's what I remember. Both blahtex and texvc spend almost all of their time (at least 90%) on PNG generation. Blahtex is somewhat faster at PNGs, maybe 2 or 3 times faster, since I switched to dvipng instead of using imagemagick+dvips. (And Brion Vibber has endorsed the use of dvipng in the past, ask Google for more information.) MediaWiki already has code for caching the images, so this time only gets spent during the first edit, not on subsequent page views or edits. Second, I haven't directly compared the parsing and mathml generation time of blahtex to the parsing time of texvc, but I do know that my desktop machine can generate mathml for the entire wikipedia corpus in about 30 minutes. There's 200,000+ equations in there, so it's not lightning speed, but you ain't gonna overload their servers. And MediaWiki also has code already for caching the mathml, so again that only happens on the first edit. Third, some tests Jitse and I ran a while back suggested that texvc's parsing is unbearably slow on long input data; blahtex on the other hand processes that kind of input really fast.
• Linas's point about reliability. Of course it's got bugs. All software has bugs, especially software that hasn't yet been exposed to the real world. Someone mentioned above that it's been tested against all the input in wikipedia and doesn't pretty darn well, which is a start, but of course that's not the point. The real question is whether it survives a determined adversary with source code access. Well, I don't know, I suppose most likely it's not secure. But all software has to start somewhere. I'm not asking to have the code installed tomorrow and force everyone to use it. Heck, at this stage I'm not even asking for the "minimal interesting configuration", which is that it's only available for registered users who select MathML in their preferences, and that we stick to texvc for all PNG output, and only allow mathml for the equations for which texvc can already generate graphics. All I'm asking for is that some core developer gives us more than ten seconds of their time to render an opinion. If they tell me the code is crap and I'm a chump, that's fine, I can live with that, at least it's an answer. If they tell me I need to rewrite it in COBOL, that's fine, it gives me something to do. If they tell me I need to write a comprehensive test suite, that's great, I can do that. But so far the longest reply I've had from people like Brion Vibber, Tim Starling, etc, is a one-line email from Brion:

It sounds great, but I've not had a chance to look at it yet...

He also replied on the mailing list once, here's what he said:

Neat!

I understand 100% where he's coming from, but it's still incredibly frustrating.

• Mets501's question about fonts. As KSmrq points out, the STIX fonts project is going to get there eventually, not tomorrow or the next day, but eventually. I believe it will solve all the font problems, because e.g. Firefox will just be able to bundle the fonts in the default installation and it will all Just Work. So for now, no good answer, but eventually, yes.
• Mets501's question about browser compatibility. Short answer: it sucks. Firefox/Mozilla is the best out there in my opinion, and it's not quite good enough yet. (I've heard about your problem with broken radical signs; I believe it's a recent regression.) I think the reason browsers haven't quite made it yet is because there just isn't the content out there yet. Well, we can change that, because if wikipedia switched on mathml support, it would overnight become the largest repository of mathml on the web. (I don't have stats for that, it's just a guess.) And here's something else: when I first mentioned to the firefox people, like roger sidje, that wikipedia was planning mathml support, suddenly a whole raft of mathml-related bugs in firefox got fixed, bugs that had been lying around unattended for 2-3 years. These open-source guys love wikipedia. If we deliver, they will follow. On the other hand, I don't have any illusions about MSIE.
• RandomP's question about backward compatibility. It's a minor problem in my opinion. See http://blahtex.org/errors.html for a complete list, as of March. Maybe that list looks long, but remember it's across 13 languages, and represents about 0.1% of the total. We could fix them all in a few days. And anyway, Jitse's glue software falls back on texvc if blahtex fails, so it's easy to make the problem vanish entirely.
• Everyone's question about who to talk to. I don't know. I've run out of ideas and energy. That's why I'm turning the initiative over to all of you. If enough of you make enough noise, and if the powers that be are hearing voices other than that of the guy who wrote the program, maybe something will happen. Dmharvey 12:28, 18 June 2006 (UTC)

Caching: As KSmrq suggests, the MathML is cached and hence it needs to be generated only once.

Backward compatibility: To expand on what David says, the code as currently written uses texvc to generate HTML and PNG and blahtex for generating MathML. If texvc fails, then blahtex will also generate PNG. Therefore, the few formulae that are not understood by blahtex (for instance because they use invalid latex syntax) will still be rendered as PNG, but there won't be any MathML. In other words, just like the present situation. -- Jitse Niesen (talk) 13:02, 18 June 2006 (UTC)

my email

I sent this email to mediawiki-l just now:

---

From: lethe at charter dot net
Subject: Blahtex: what's the next step
Date: June 18, 2006 8:08:37 AM CDT
To: mediawiki-l@Wikimedia.org

David Harvey and others has been working hard on Blahtex, the next generation in MediaWiki math rendering technology. Visit http://www.blahtex.org/ for more information and http://wiki.blahtex.org/go/Main_Page for a running demo hosted by Jitse Niesen.

Harvey suggests that blahtex will afford a significant performance advantage, but the main impetus is the ability to render MathML. Support for MathML is not widespread at the moment, so the need for Blahtex is not urgent, but it is the future, and we have reason to believe that Wikipedia's adoption could goad browser developers to speed their efforts (the answer to the old chicken and egg of who comes first, browser support or use by web pages could be: Wikipedia comes first).

It has to happen someday, and today is as good a day as any. Harvey says the software is ready for the next step, and wants to move forward, but doesn't know whom to talk to in order to make this happen. I'm writing you to voice my full support for Harvey's and Niesen's efforts, to find out what needs to be done to take the next step towards rolling this software out, and to ask if there is anything I can do to help the developers to get this software ready for deployment.

Thanks
lethe

Discussion continued

I'm not a developer, nor am I Jimbo, but putting myself in their shoes I'd be much more worried about the font issue than about accepting an apparently well-tested huge chunk of outside code. In fact, not being in their shoes this worries me. Many people access Wikipedia from computers they have no control over, and are in no position to download and install fonts for, even if willing to do so. Others may try to and fail. Most wouldn't even try, and miss out on all Wikipedia has to offer that involves formulas. I think it is important to keep blahtex alive, but aim at introduction after the availability of the required fonts has become common. --Lambiam^Talk 13:53, 18 June 2006 (UTC)

Thus MathML won't be enabled by default. Only people who know what it is, have capable computers, and want to see it, will see MathML. When the day comes that every windows, mac, and linux computer has by default MathML able browsers and plenty of fonts, then we can have MathML by default. But for today, let's have Blahtex which is smarter in all ways. This is a non-issue. -lethe ^{talk +} 14:22, 18 June 2006 (UTC)

Yes, I agree. I will help push for this to be implemented as much as I can. I do think, however, that the default should not be MathML (yet). Users who sign up for an account should be able to select MathML from the preferences page, but the option should link to a page called Wikipedia:MathML, which would say what MathML is, which browsers support it, and which fonts/whatever is needed for MathML to work. I would definitely not give up on this project and I hope that it will be implemented soon (I love experimenting on the BlahTeX wiki!) —Mets501 (talk) 16:54, 18 June 2006 (UTC)

We've really got to stomp out some myths. The most important fact is that BlahTeX only adds capability to MediaWiki, it does not force removal or breakage of anything that already works. A complete set of mathematics fonts will be available Real Soon Now to everyone on every platform with every browser. Don't have the necessary fonts on the computer you happen to be using? Not a problem; stick with the old-fashioned images and HTML hacks. Browser not set up to support MathML? Not a problem; don't ask for MathML. In other words, adoption of MathML is strictly voluntary.

So why BlahTeX? Because it offers so much more than texvc, which is old and seriously deficient. BlahTeX handles a broader range of TeX input, including things that are currently a real pain to work around. Even when it generates PNG output, not MathML, BlahTeX is superior to texvc.

And why MathML? Because it is the future of mathematics on the web, for reasons such as the following.

• A text-to-speech processor can read MathML aloud for vision-impaired users, or for ordinary folks who merely want to know how a formula is spoken.
• All the fonts and layout of a MathML display can be scaled up or down, just like the rest of the text on a web page, to either zoom in on a detail or zoom out for an overview.
• MathML can include arbitrary Unicode characters, something texvc is unlikely ever to do.
• A MathML formula is smaller and faster to serve than a PNG.
• MathML can allow internal line breaks, while images cannot.
• Programs like Mathematica allow cutting and pasting MathML formulae, so an equation can be transfered easily for evaluation or graphing.
• MathML has already found favor on technical blogs, like The String Coffee Table.
• Because MathML is built on XML, it can be processed with XSLT and used across diverse media. In particular, MathML will be much more compatible with print than any fixed-resolution PNG rendering.
• One of my favorite benefits is that the contents of a MathML formula are available to search in my browser, whereas a PNG is an opaque monolith.

Note that the MathML 2.0 Recommendation from W3C was released on 2001 February 21, and the 1.0 version dates back to 1998 April 7. That's an eternity ago in web time!

But to reiterate: BlahTeX offers considerable benefits even for those who do not choose to view MathML. It can't hurt. It can only help. Please support its rapid adoption by MediaWiki, in whatever way suits you best. --KSmrq^T 19:22, 18 June 2006 (UTC)

I think you should put that in an email to the mailing list. Perhaps wait until mine shows up and make it a reply so it's all in one thread though. We want to generate some noise so that it seems like there is a whole rabble of us clamoring for this. And of course we have to quelch the false assumptions that people will make to justify not using the software. -lethe ^{talk +} 19:29, 18 June 2006 (UTC)

Request for book recommendations

Maybe this is not the place for this (I am aware that this is not un all-purpose forum), but here it goes. I intend to order some math books from Amazon, but I'm not sure what to get. As it seems to me that there are some very good mathematicians here, I think you could help me a lot with some recommendations. Now for some background, to understand what I specifically need: I'm an undergraduate math student (though also an economics graduate and working economist) and I pursue math mostly for my own curiosity and because I truly enjoy it (more than economics :D). I need something mainly appropriate for self-learning, so I'm targeting good classic texts on major fields or other good books. I prefer books that don't shy away from advanced/abstract concepts, but preferably give motivation for concepts and some intuitive explanaition/interpretation. Also, I learn the most from books which include examples worked-out in detail and/or solved relevant problems. Also, note that unfortunately cost is an issue, so don't recommend too many books that are only somewhat helpfull (though by all means recommend books that you consider good, even if they are not very popular). Hope that you will have some advice for me... AdamSmithee 20:48, 18 June 2006 (UTC)

A great place to ask this question, which is indisputably appropriate (unlike here, which is apparently disputably so :)) is the sci.math newsgroup. You can get there through Google groups if you don't already know. This page is really just for discussing the Wikipedia mathematics project. Ryan Reich 20:57, 18 June 2006 (UTC)

I am sure that we could give a great deal of advice (though some of us will contradict each other!), but we do need a bit more info about your mathematical interests and level: which branches of maths are you most interested in? what sort of level are you at in that level? Perhaps it might be best if you could tell us some maths books that you believe you have mastered, and we could suggest some books that would make a "good next step"? Madmath789 21:02, 18 June 2006 (UTC)

Myself, I'm a graduate student and I like algebraic geometry and sometimes number theory. Or did you mean him? :) Ryan Reich 21:42, 18 June 2006 (UTC)

LOL! I did mean 'him', but our edits crossed, and I got the indentation wrong :-) (but if you want some suggested reading on algebraic geometry, I can probably oblige :-) ) Madmath789 21:46, 18 June 2006 (UTC)

The most affordable route is used books, especially if you live in or near a decent university or college. Some of the much older books are easier to learn from, because not so long ago mathematics texts had a bad habit of being horribly written for learning, though packed full of detail for reference. More recently there may have been a corrective swing, so that one can benefit from both a modern viewpoint and decent pedagogy. But in a field like algebraic geometry, the really old stuff has lots of geometry while the modern stuff has almost none. Depending on your tastes, one may appeal more than the other. Another fact about older books is that often recent books try not to duplicate the work of the early masters, so if you want to get the original insights from the folks who had them you have to step back in time. It reminds me of something that was said about the programming language ALGOL, that it was an improvement on many of its predecessors, and also on many of its successors. Lastly, it is vital to choose books at the right level at the right time, lest an otherwise great book become a doorstop. --KSmrq^T 22:39, 18 June 2006 (UTC)

Well, first of all tx for replying! As I said, I know this is not the place (and I'll probably try sci.math, which I didn't know about), but I tried it because I came to trust many of you guys. As for my background and interests: I'm an undergraduate student in math at this time. So far, my exposure was almost entirely to Romanian textbooks, which are very tightly written and unfortunately are generally very good for reference but not for learning (this is somewhat of a characteristic of Romanian academic books). On the other hand, I've read quite a few American graduate level textbooks in economics and I noticed that, generally, they are much better for learning (also, reading some freely available online math books lead me to believe this is also true for math). To give an example, at this time I'm struggling with linear connections and covariant derivative, but my (Romanian) books insist to much on tightely written modern coordinate-free stuff, giving virtually no motivation and no explanation, and I'm having trouble understanding why the stuff is defined that way, what does it mean and what is it good for.

At this moment my interests are rather wide and I just want to get a reasonable background in the main fields. However, I do have a sweet spot for abstract algebra, and I'm interested in probability and statistics (including links to measure theory, numeric analysis etc.) for the aplications to economics. But I'm also very interested in stuff like differential geometry for instance. As an example of one book that I have heard about, and I might get, I know about Jacobson's 'Basic Algebra' (though I don't know how that is), but I have no idea what else is there.

Regarding level, it is hard to say what undergraduate in Romania means compared to other education systems, but it is possibly more advanced than American undergraduate level (?maybe?). AdamSmithee 23:25, 18 June 2006 (UTC)

Hi, I suggest browsing Dover Publications online catalogue (use Google to find, I am lazy :P). They republish a lot of classical and important texts. By rule of thumb, eastern Europe is more advanced in beggining of undergraduate studies. -- 127.*.*.1 01:14, 19 June 2006 (UTC)