Talk:Mathematician

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Citations...[edit]

Maybe it's just me, but I expected an article about the "hardest" of the hard sciences to have a lot less subjective generalization than this one does (specifically, the "Motivations" section). For one thing, I doubt the section describes the motivations of every mathematician (if so, that definitely deserves a reference), so it would be nice to know where these described motivations are coming from, to get a sense of how well they can be expected to describe any given mathematician. For another thing, leaving aside the point about the section as a whole, there are multiple factual statements made in the section that should be cited, for example, "However, among academic mathematics, the majority of mathematical papers published in the United States are written by academics outside of mathematics departments." --Spameroo (talk) 02:20, 1 November 2013 (UTC)


"Sharpest minds"[edit]

This section seems pretty worthless. Just somebodies opinion on who the "sharpest" minds were in their own time. I will concede that some of it isn't very arguable... But wouldn't this kind of information belong more in article on the history of mathematics? I'm going to remove it for now. Perhaps a good justification for it can be presented here? --Jeremy (wouldn't sharpest minds be a good area for people with the most influence in the math world?)

Proofs by computer[edit]

I removed the phrase about proofs being verified by retards in the future because it's sensible. This might only apply to very specific areas in mathematics, if at all. Also I changed the phrase about the source of mathematical problems. Most of them come from within mathematics, only a small part comes from economics and the sciences, and those problems would be concerned applied mathematics. —Preceding unsigned comment added by Alterationx10 (talkcontribs) 02:53, 27 February 2008 (UTC)

Worthless Quotation from St. Augustine[edit]

If the article acknowledges that Augustine's famously hostile saying about mathematicians was in fact directed at astrologers, then why is the son of a bitch even in the mathematician article? Wouldn't it create less confusion to simply omit the quotation which has created some measure of confusion over the years?

Agreed, it is irrelevant to the article, especially without context. Woudl anyone object to its removal?--&m@ 21:00, 26 June 2006 (UTC)
Dump it I say!  :-) capitalist 03:17, 27 June 2006 (UTC)
Done.--Konstable 03:47, 27 June 2006 (UTC)

This article requires beans![edit]

I find the article rather confused: it does not know whether it is talking about mathematicians or mathematics. Some parts really should be moved or dropped. The Overview section is not about mathematicians! The Problems in mathematics section is not either. As it is now, the Differences section is only halfway about mathematicians.

We must set up a proper outline for what should be and what should not be in the article, and how it should be organized. PhS 08:14, 3 July 2006 (UTC)

More Interesting criticises of Mathematicians[edit]

As always, an interesting point would concern the racial and ethnic composition of mathematicians (I see below that the Jews have nice mathematical heritage). I think that a link to the Race and Intelligence article would be good here. People with low IQs tend not to make good mathematicians. Perhaps also some reference to common moral attributes of mathematicians (mathematics has been held in high esteem in one form or other by almost all historic civilisations - perhaps that statement is true by definition).

I see on wikipedia that most mathematicians in history have been held to be white - some comments on the nationality of these white mathematicians would be interesting. Perhaps it is also fair to comment upon how it is that racial and ethnic differences between mathematicians have often resulted in different 'types' and 'flavours' of mathematics - there would be some interesting issues concerning the foundations of mathematics here. How do mathematicians know whether or not what they are doing is actually *real* mathematics (the answer here is usually ZFC - though it has been a long time since I say the following comment in a journal : "And here we have computationally, apolitically and non-racially verified the authenticity and accuracy of our theorems via the use of a colour-blind ZFC diagnostic routine to make sure that it was not complete b******s....". Well, you get the point. I found the following website interesting (though it probably wasn't programmed in by a black guy : ) : http://metamath.org/ (the last comment was given when observing that all the countries associated with meta-math are white, but I'm not complaining, merely stating colour-blond fact. )

Nukemason2 21:47, 22 November 2006 (UTC)

Erdos/Renyi coffee[edit]

I always heard this quote was from P.Erdos. Wikiquote agrees here. Where does the information about the author being A.Renyi come from? --Kajetan Wandowicz 17:12, 14 December 2006 (UTC)

I asked about the origin of this quote on Talk:Paul Erdős some years ago. See the response there (though it doesn't say much). It's probably impossible to determine who really said it first. It's always more likely to be attributed to Erdős rather than Rényi, as he is the more famous of the two. --Zundark 17:49, 14 December 2006 (UTC)
In that case shouldn't that be clarified in the article? As we cannot determine who said that, there are three possibilities:
1. Sign the quote with Renyi's name.
2. Sign it with Erdos' name.
3. Say (in the article) that there exists a controversy.
Out of which, given that Wikiquote attributes it to Erdos, second option shlould be chosen. Considering what you just said, the third option is the best. Either way, the worst option is 1 - but this one is used. --Kajetan Wandowicz 20:06, 16 December 2006 (UTC)
No objections here from anyone, so changed. --Kajetan Wandowicz 11:17, 18 December 2006 (UTC)

Doctoral degree statistics in the US[edit]

Can I just remove this section? While mildly interestig from a trivial point of view, it's not particularly encyclopedic or relevant to the notion of mathematician.--Boffob 16:26, 16 March 2007 (UTC)

  • I originally added the statistics section to complement the demographic information in the section above it and also as an attempt to give a rounded picture as mathematicians as a whole. Admittedly it doesn't fit in too smoothly and could be rewritten, but I believe that most of the information is of sufficient value to keep in the article. Perhaps it could be merged with the demographics section. TooMuchMath 04:15, 5 April 2007 (UTC)

Demographics section reeks of POV[edit]

How about a demographics section that tells us what proportion of mathematicians are male vs. female, a breakdown by age, a breakdown by race/ethnicity (if we must...) and so forth? Why do I have to be told that some group or another is "underrepresented?" Can't I take the basic facts from the encyclopedia article and decide that for myself? Who determines the "proper" representation of each group anyway? I'm proposing that we either radically rewrite or eliminate this section entirely. Other comments? capitalist 03:00, 17 April 2007 (UTC)

Whoops, I had forgotten that I had this rant here. I see an IP came in and rewrote the section to eliminate the POV at least. It reads much better now!  :) capitalist 03:14, 11 July 2007 (UTC)
Under-represented comes from the social sciences and is typically taken to mean representation within the subgroup compared with the population as a whole. --lquilter 18:39, 5 November 2007 (UTC)

Age[edit]

It would be useful, I think, to address in the demographics section about the popular belief that mathematicians are most productive in their 20s and that by their 30s and certainly 40s their most "brilliant" years are over. Sources on this topic? --lquilter 18:39, 5 November 2007 (UTC)

Inaccurate distinction[edit]

The article states:

"Mathematics differs from natural sciences in that physical theories in the sciences are tested by experiments, while mathematical statements are supported by proofs which may be verified objectively by mathematicians."

While it is true that outside of mathematics, proofs are not applicable, it is a mistake to imply that experiments do not apply to mathematics. A very large number of areas of mathematics are subject to experiment. Not infrequently, experiment will reveal a pattern that can then be proved. In some finite cases, the experimental results will themselves constitute a proof. (There are even a respected journal, "Experimental Mathematics" (A.K. Peters), and several books discussing the role of experiment in mathematics.)Daqu (talk) 01:36, 31 May 2008 (UTC)

We also have an article Experimental mathematics, and more on the issue is said in the section Mathematics#Mathematics as a science. There is also Philosophy of mathematics#Empiricism. In my opinion, there is an essential difference though between the role of experimentation in formal sciences like mathematics and in the natural sciences. No amount of experimental "testing" will avail to establish the validity of, e.g., Goldbach's conjecture or the Riemann hypothesis. In mathematical experiments there is no null hypothesis, no tests of significance, because there is no chance factor and no experimental error. Every "experiment" done by computer is in a sense the production of a formally provable theorem, and not a test in the sense of the scientific method. "Exploration" captures the nature of the activity much better than "experimentation".  --Lambiam 17:06, 31 May 2008 (UTC)
I think I agree with almost everything you write, Lambiam, but none of it affects the truth of what I wrote. The word "exploration" perfectly captures the nature of the activity known as "exploration". But I was speaking about "experimentation", which is best captured by the word "experimentation".
There are differences in the nature of experimentation for any two sciences, but that does not invalidate the fact that experimentation is experimentation.Daqu (talk) —Preceding comment was added at 03:07, 2 June 2008 (UTC)
Can you give an example then of a mathematical statement, held by a mathematician of repute, that has been tested by experiment but is not supported by (mathematical) proof?  --Lambiam 17:04, 2 June 2008 (UTC)
I'm not sure what "held by" means here.Daqu (talk) 01:23, 3 June 2008 (UTC)
It means that the mathematician accepts the statement as being true, on an equal footing with (proved) theorems.  --Lambiam 12:07, 3 June 2008 (UTC)
Sorry, I don't see the relevance.Daqu (talk) 17:13, 3 June 2008 (UTC)
The relevance is as follows. The contested sentence in the article states: "Mathematics differs from natural sciences in that physical theories in the sciences are tested by experiments, while mathematical statements are supported by proofs which may be verified objectively by mathematicians." For this contrast to make sense, the physical theories referred to have to be theories that are embraced by physicists: they have been tested and withstood the tests (which typically at the same time falsified a rival theory). Likewise, the mathematical statements are not just any statements, but statements embraced by mathematicians: they have attained theoremhood. You say that this distinction is inaccurate (but concede that proofs are not applicable outside of mathematics). To invalidate the contested sentence, we then need examples where a mathematical statement is embraced by mathematicians, not by dint of theoremhood, but because it has withstood the tests.  --Lambiam 23:48, 3 June 2008 (UTC)
Probably the Riemann hypothesis is an example; but it depends on what you mean by "held by." Experiments have led most (or all?) mathematicians to believe it is true, but they don't "hold" it to be true, because they can't prove it. So they hold it to be an open question. Dicklyon (talk) 19:11, 3 June 2008 (UTC)
Another example is Goldbach's conjecture. The difference is indeed the status conferred on a statement that does not immediately succumb to experiment. Although the general theory of relativity is a theory, it is taught as part of the canon of physics, as being confirmed by stringent tests – although physicists realize that sooner or later it may fail a test and need to be replaced. Mathematical statements that appear to be true for a few cases that have been examined (few, because they are negligeable compared to the infinity of all cases), but whose truth is not supported by a deductive argument, never attain a similar status in mathematics. Errors in proofs aside, a theorem will not fail a test, so it is pointless to attempt to test a statement that you accept as a theorem.  --Lambiam 23:49, 3 June 2008 (UTC)
Sounds like a mathematician speaking! It's not at all pointless to test the validity of a proved theorem on a finite number of test cases. Just because you have accepted it as a theorem doesn't mean it's true! "Errors in proofs aside" is sort of like "no offense, but..." Dicklyon (talk) 00:02, 4 June 2008 (UTC)
Further, Sheepyouare, if you really want to discuss the philosophy of experiment, then it should be noted that no amount of experiment in the "experimental sciences" like physics, chemistry and biology can conclusively show any fact other than what happened in the experiment. (And even then, as you mention, just as with any experiment, there is the possibility of experimental error.)
I will say it one last time, and not again: Just because mathematics is subject to proof (and as you may know, not all propositions are subject to proof, as Gödel showed; the twin prime conjecture, for example, may be impossible to ever prove or disprove, regardless of whether it is true or false) does not mean that it is not subject to experiment as well. I do numerical experiments to test various mathematical propositions All The Time, and so do many other mathematicians. That's all I have to say on the matter.Daqu (talk) 05:54, 4 June 2008 (UTC)

In the word processor article, I changed "scientists" to "mathematicians and scientists". Does XKCD support this idea that mathematicians are not "merely" another kind of scientist? --68.0.124.33 (talk) 22:38, 10 December 2009 (UTC)

Rewrite[edit]

I believe this article needs /at least/ extensive work, and perhaps even a complete rewrite. Most of the sections on the article focus on mathematics, as opposed to mathematicians. This isn't necessarily a bad thing, because it's impossible to discuss one without overlapping into the other... I do have some more specific complaints:

1. The "Problems in Mathematics" section is mostly focussed on recent developments in mathematics. This isn't a bad thing, but the title is misleading and doesn't match the content.

2. I take it the "Motivation" section is intended to discuss the reasons why mathematicians are mathematicians, or at least what kinds of things mathematicians focus on. It seems like a poor place to talk about awards, as I don't really think major breakthroughs are performed just for a medal. Of course, even this perspective isn't NPOV... But even placing information there seems to imply that this is the case. It seems like the best solution would be to give the awards it's own section.

Regardless, the Motivation section seems like a good place to discuss Hardy (regarding the aesthetics of Mathematics), and Wigner (unreasonable effectiveness of mathematics). At the least, these seem like a good starting point as far as motivation is concerned. More recent material could include Lockhart's essay on mathematical pedagogy (a mathematician's lament).

3. I think the "Differences" section should be completely axed. Some of the content on conjectures and generalizations could be merged with the Motivation section. A discussion on the differences between mathematicians and scientists seems far more appropriate, but even the title of "differences" seems biased. I mean, why not call it similarities? Something like "Relationships between mathematicians and scientists" seems better, and more focussed.

4. The entire "Demographics" section is just talking about women in mathematics. This could be heavily expanded to include things like... What regions/countries have traditionally produced a lot of mathematicians? What regions/countries are producing a lot today? Has this changed a lot? Sexes? Races? etc etc...

5. Doctoral degree statistics in the US should at the least be merged with the Demographics section... But if we include this, why not also include the doctoral statistics for other countries? This might be too much.

6. ...Do we really need all those quotes? How do these kinds of tidbits give anybody an idea of what mathematicians do? This seems like the kind of material that people include because they just love the quotes. I mean, I love the quotes too! But they make the article seem unprofessional. —Preceding unsigned comment added by Sticktwig (talkcontribs) 22:16, 14 January 2009 (UTC)

The issues listed here are all worthy of consideration (see also sections "Article Is In Sorry Shape", and "Pruning content more about mathematics than mathematicians" below. Paul August 18:28, 16 November 2009 (UTC)

I agree, the section on "Differences with Scientists" is a bit vague. Physicists prove their theories mathemtically, not experimentally. — Preceding unsigned comment added by 220.255.2.160 (talk) 03:30, 2 November 2011 (UTC)

Mathematcs vs Science[edit]

leodams was Mathematics differs from natural sciences in that physical theories in the sciences are tested by experiments, while mathematical statements are supported by proofs which may be verified objectively by mathematicians. —Preceding unsigned comment added by 71.192.210.54 (talk) 00:14, 30 January 2009 (UTC)

What you just described is a difference between mathematics and natural sciences, and has already been addressed in the article on mathematics... —Preceding unsigned comment added by 192.149.109.70 (talk) 19:01, 15 February 2009 (UTC)

More info wanted[edit]

This article could do a better job of describing a job as a mathematician. What is their average pay? for example. --DocDeel516 discuss 00:25, 31 January 2009 (UTC)

Misleading Statement[edit]

"Two channel DNA microarrays are used when one wants to compare data from one sample, against some other sample (which will often be a reference sample)". This implies that this is only used with two channel DNA microarrays, when the method is also used with oligonucleotide arrays (in which case the two channels are on separate arrays). —Preceding unsigned comment added by Zoolium (talkcontribs) 10:40, 15 January 2010 (UTC)

the definition of mathematician[edit]

whoever wrote this self contradictory definition, will you please present the source of this definition, or elsewise, stop reverberating my editing!!!!!!!!!!!!!!!!!!!! —Preceding unsigned comment added by Aarsalankhalid (talkcontribs) 22:55, 1 March 2009 (UTC)

Yeah, whoever keeps putting the mathematician as "somebody who celebrates the beauty of mathematics" needs to stop. That is not a mathematician. There are many people who appreciate the beauty of mathematics, but are not mathematicians.

Another example could be: I appreciate music, but I am not a musician. See? —Preceding unsigned comment added by Sticktwig (talkcontribs) 18:49, 2 March 2009 (UTC)

it says: A mathematician is a person whose primary area of study and/or research is the field of mathematics... so you could say that an engineer who taught math and only live lecturing them is one of the mathematicians? I think that some level of abstractness is needed... How much? Let's argue...--kmath (talk) 22:57, 8 May 2009 (UTC)

It is an issue - there is also the issue that some major mathematicians would not have considered it their 'primary' area of research too - though the terminology was different then (natural philosophy etc.) Newton would probably not have considered himself PRIMARILY interested in mathematics... he was nuts about biblical numerology, had major legal and political involvement later in life, and by today's standards might be known just slightly for being a physicist (as opposed to a mathematician, though it may have been seen differently then). To ensure that the definition covers everyone it should, regardless of the standards of their time, and not too many - like the engineering-inclined maths teacher, perhaps the article could define a mathematician as

'An individual who has contributed results widely recognised as relevant to the progress of mathematics in itself'

though preferably much better-worded than that. Of course formal qualifications can't be included in the definition, and not everyone will be happy with it - perhaps the only honest approach is to start off with exactly that - a statement that what defines a mathematician is widely disagreed upon - and then follow up with more than one reasonable definition.

Article Is In Sorry Shape[edit]

There is too much about mathematics and too little about mathematicians here. I suggest we look at the Scientist article for ideas of how to improve this one, since it appears to be a better made article on an analogous subject. The "Problems" section should go and the "Differences" section should be reworded to be about mathematicians vs scientists instead of the current mathematics vs science (and get a slightly more descriptive title). Does anybody else agree? Jaimeastorga2000 (talk) 19:38, 20 June 2009 (UTC)

Yes see new section immediately below. Paul August 18:18, 16 November 2009 (UTC)

Pruning content more about mathematics than mathematicians[edit]

I cut the following form the article since it is more about mathematics than mathematicians, perhaps some of it could be merged into mathematics:

The publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals. In particular, mathematics is not a closed system, in that there is no shortage of open problems; in fact, at any given time, there are infinitely many potential open problems which mathematicians have not stumbled upon. The diversity of mathematics also allows for problems, which, in certain contexts, may not be solved or are undecidable in particular theories!
Recently, an important problem in the field of number theory was resolved by the mathematician Andrew Wiles; this is known as Fermat's Last Theorem. The problem remained open for approximately 350 years making it one of the oldest problems in the history of mathematics.
Another recently resolved important problem, in the field of differential topology, is the Poincaré conjecture. Like Fermat's Last Theorem, this conjecture withstood 100 years of attempts at its solution, but was eventually resolved by Russian mathematician Grigori Perelman in 2003. A peer review was completed in 2006, and the proof was accepted as valid.[1]
The Poincaré conjecture belonged to a larger class of open problems (prior to its proof) known as the Millennium Prize Problems. These problems concern such diverse fields of mathematics such as algebraic geometry, algebraic number theory, differential geometry, theoretical computer science and so forth. For any one of these problems, there is a US$1,000,000 award for its solution. However, many mathematicians consider the prestige to be of a greater value than the actual sum of money.

There is a a lot more like it that needs removing in my view. Paul August 19:39, 15 November 2009 (UTC)

I think I wrote that content at some point. My point of view is that "mathematics" and "mathematician" are connected, and thus one cannot mention one without mentioning the other (as an analogy, consider "axiomatic set theory" and "set-theoretic topology" :)). For instance, should the article cover some famous mathematicians in the past, or should the article also consider what mathematicians, in general, do? I feel that both ideas should be a fundamental part of the article, but the former is certainly the most important. However, when I added the content under the current "motivation section", I kept in mind the section title, and as such described "mathematics" in relation to "mathematician". Do you think that some of this content should be merged into mathematics instead? If so, feel free to do that. With regards to the above content, I actually mentioned "mathematician" in the last three paragraphs, although not to a significant extent. As such, I do not think (correct me otherwise) that there is mention of either Andrew Wiles or Grigori Perelman (who are famous mathematicians). Could you please expand slightly on your point? Cheers, --PST 03:54, 16 November 2009 (UTC)

Hi PST. Yes obviously "mathematics" and "mathematicians" are interrelated. And yes, the article should (and does to some extent) "cover some famous mathematicians" and "consider what mathematicians, in general, do". Perhaps some of the content above about Wiles and Perelman, as "famous" present day mathematicians could be reworded to be more from a "mathematician" slant than a "mathematics" one, and so retained in the article. This might help dispel the naive notion that all of mathematics is already known. Let me give that a try.

By the way reading some of the discussions above I see that a few other editors have expressed similar concerns to mine. For example immediately above in the section "Article Is In Sorry Shape", Jaimeastorga2000 says: "There is too much about mathematics and too little about mathematicians here" and suggests that we should look at Scientist for ideas on improving the article. That seems like a good idea to me. Also in the section "Rewrite" an editor complains that "most of the sections on the article focus on mathematics, as opposed to mathematicians" and lists a series of specific issues to be addressed. All of which seem worthy of consideration. I might also try to give some attention to these.

Regards, Paul August 18:11, 16 November 2009 (UTC)

"Applied Mathematician"[edit]

Does anyone else have a problem with the definition of applied mathematician given in the intro:

     Conversely, some mathematicians may provide insights into other fields of research—these people are known as applied      
     mathematicians.

Ignoring the fact that it is not a mathematic use of the word conversely, I would say that many mathematicians who are not applied mathematicians have provided insight into other fields of research, many of them posthumously. Isn't an applied mathematician someone who does applied mathematics. —Preceding unsigned comment added by 159.91.213.146 (talk) 20:41, 1 March 2011 (UTC)

There are a number of problems with the introduction. This foolish article lacks any discussion of applied mathematics and applied mathematicians. Until that mistake is fixed, there should be no discussion of applied mathematics in the lede.
It is bizarre that this article has a whole section on category theory and foundations and nothing on applications.  Kiefer.Wolfowitz 16:21, 27 February 2012 (UTC)

Most mathematicians are applied mathematicians[edit]

I referred to a 1990s study of research mathematics in the USA, which found that the majority of academic authors of MR-reviewed papers were in departments outside of mathematics. This study was referenced by the outside review of USA mathematics around 2000, by a panel that included Lennart Carleson, which I assume is known to full professors and other sufficiently wizened.  Kiefer.Wolfowitz 16:30, 27 February 2012 (UTC)

  1. ^ Elusive Proof, Elusive Prover: A New Mathematical Mystery