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I am Boris Tsirelson, an experienced mathematician and less experienced wikipedian...

Articles I've written (started)[edit]

and also

Articles I've contributed to[edit]

On different wikis (if you like)[edit]

  • Entanglement (physics) [1] = [2]
  • Theory (mathematics) [3] = [4]
  • Plane (geometry) [5] = [6]
  • Probability space [7] = [8]
  • Proof assistant [9] = [10]
  • Measurable space [11]
  • Measure space [12]
  • Standard Borel space [13]
  • Measure algebra (measure theory) [14]

Quantum mechanics is not a physical theory[edit]

So, what is quantum mechanics? Even though it was discovered by physicists, it's not a physical theory in the same sense as electromagnetism or general relativity. In the usual "hierarchy of sciences" — with biology at the top, then chemistry, then physics, then math — quantum mechanics sits at a level between math and physics that I don't know a good name for.

— Scott Aaronson, "Quantum computing since Democritus", Cambridge 2013 (p. 110).

Notes for myself[edit]


Gravitational wave observation

User talk:Sheila Nirenberg

my sandbox + User:Tsirel/Frustrating discussions + Special:PrefixIndex/User:Tsirel/

Expert involvement 2011 survey

Special:OldReviewedPages + Who Writes Wikipedia?

Wikipedia:WikiProject Wikipedia reliability + User:History2007/Content protection

Lectures on Probability, Statistics and Econometrics

User:Mathbot/Changes to mathlists + List of probability topics + Lists of mathematics topics + List of integration and measure theory topics + List of geometry topics + Wikipedia:WikiProject Probability

Wikipedia:WikiProject Mathematics/missing mathematicians

Template:Disputeabout + Template:Citizendium + Gamma function#External links

Template:Onlinesource + Wikipedia:Wikipedia as an academic source + Wikipedia:Public domain image resources + Interface metaphor

User:CataBotTsirel + User talk:CataBotTsirel + Special:Contributions/CataBotTsirel + Catalog of articles in probability theory + Talk:Catalog of articles in probability theory + Wikipedia:Editnotice

User:Citation bot/use

Wikipedia:Manual of Style (mathematics) + Wikipedia:WikiProject Mathematics/Conventions + Template:Ref + Wikipedia:Citing sources + Cite.php (about "ref") + WP:Footnotes#Naming a ref tag so it can be used more than once + Wikipedia_talk:Footnotes#Mark-up would be better than encouraging people to remove reference information + Wikipedia:Line break handling + Wikipedia:How to edit a page + Help:Formula + Wikipedia:WikiProject Mathematics/Typography + User:KSmrq/Chars + Wikipedia:Footnotes + visits counter (thanks to User:Henrik) + encyclopaedia of math + Wikipedia:database download + Wikipedia:Pages needing attention/Mathematics + Wikipedia:Expert editors + Wikipedia:Expert retention + Wikipedia:Flagged revisions + Wikipedia:Template messages + Template:Main + Wikipedia:Text editor support + User:Cacycle/wikEd + User:Cacycle/wikEd help + Wikipedia:Tools/Editing tools + Template:TOClimit + Wikipedia talk:WikiProject Mathematics/Proofs + Wikipedia talk:WikiProject Mathematics/Proofs/Archive 1 + Wikipedia talk:WikiProject Mathematics/Proofs/Archive 2 + Wikipedia_talk:WikiProject_Mathematics/Archive_46#Proofs + Wikipedia_talk:WikiProject_Mathematics/Archive_46#Connected_space/Proofs + The pernicious influence of mathematics on science

Semimartingale + Itō_calculus + Kolmogorov extension theorem + Wasserstein metric + Transportation theory + Coupling (probability) + Product measure + Disintegration theorem + Regular conditional probability + There is no infinite-dimensional Lebesgue measure

Dvoretzky's theorem + Quotient of subspace theorem + Duality (mathematics)

Surreal number + Stone–von Neumann theorem + Heisenberg group + Infinite-dimensional holomorphy + Self-adjoint operator + Extensions of symmetric operators + Smooth infinitesimal analysis + Where Mathematics Comes From + Philosophy of mathematics + Mizar system + Frank Morgan (mathematician) + Entropy in thermodynamics and information theory + Entropy#Entropy and Information theory + Linear response function + Green–Kubo relations + Fluctuation theorem + Dispersion relation + Fluctuation dissipation theorem + Dynamical billiards + Schwarzschild coordinates + Quantum electrodynamics + Precision tests of QED + Kepler problem in general relativity

Alexander horned sphere + Antoine's necklace + Long line (topology) + Garden of Eden (cellular automaton) + Ham sandwich theorem + Knot group + Knot (mathematics) + Gordon-Luecke theorem + Boy's surface

Distribution (mathematics) + Sensor + Generalized_function

Fundamental concepts of geometry + Primitive notion

Šahbazov + Miller + Stafford

User:Sullivan.t.j + User:Roboquant + User:R.e.b. + User:Gala.martin + User:GaborPete + User:Jmath666 + User:hirak 99 + User:Grubb257 + User:Michael Hardy + User:Trovatore + User:Thenub314 + User:Ptrf + User:3mta3 + User:Flavio Guitian + User:McKay + User:Jakob.scholbach + User:Plclark + User:Arthur Rubin + User:John Baez + User:Dradler + User:C_S + User:Hans Adler + User:JonAWellner + User:Linas + User:Pym1507 + User talk:DoronZeilberger + User_talk:Pwm86 + User:OdedSchramm

Wikipedia:Wikipedians with articles

Saint Petersburg Lyceum 239 + Wikipedia:The Core Contest + MediaWiki + Millennium Prize Problems + Bogdanov Affair


  • — <math> (\Omega,\mathcal{F},P) \,</math>, or (Ω, ℱ, ''P'')
  • — <math> \mathbb{R} \,</math> or
  • n = −1 — ''n'' = &minus;1
  • E ( P ( A | X ) ) = P ( A ).{{nowrap begin}}E ( P ( ''A'' | ''X'' ) ) = P ( ''A'' ).{{nowrap end}}
  • f ′ — f&nbsp;′
  • ∈ ∉ ⊆ ⊇ ∅ ± ∞ ℓ
  • {{disputeabout|'''inaccurate formulation'''|Not any basis is orthogonal|date=April 2009}}
  • {{Fact|reason=I know this is true, but where is it written?|date=April 2009}}

Table of mathematical symbols


∫ ∑ ∏ √ − ± ∞
≈ ∝ ≡ ≠ ≤ ≥
× · ÷ ∂ ′ ″
∇ ‰ ° ∴ ℵ ø
∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇
¬ ∧ ∨ ∃ ∀
⇒ ⇐ ⇓ ⇑ ⇔
→ ↓ ↑ ← ↔

&int; &sum; &prod; &radic; &minus; &plusmn; &infin;
&asymp; &prop; &equiv; &ne; &le; &ge;
&times; &middot; &divide; &part; &prime; &Prime;
&nabla; &permil; &deg; &there4; &alefsym; &oslash;
&isin; &notin; &cap; &cup; &sub; &sup; &sube; &supe;
&not; &and; &or; &exist; &forall; 
&rArr; &lArr; &dArr; &uArr; &hArr;
&rarr; &darr; &uarr; &larr; &harr;

Unicode character SCRIPT CAPITAL F (U+2131) can be typed as &#x2131; — ℱ

Category:Mathematical formatting templates

<s>cross out</s> cross out


== See also ==
* [[Wikipedia:How to edit a page]]
* [[Wikipedia:Manual of Style]]



==Further reading==

==External links==

References 1[edit]

  • <ref>{{citation|last1=Blyth|first1=Colin R.|last2=Pathak|first2=Pramod K. |year=1986|title=A note on easy proofs of Stirling's theorem|journal=American Mathematical Monthly|volume=93|issue=5|pages=376&ndash;379|url=}}.</ref> <ref>{{citation|last=Gordon|first=Louis|year=1994 |title=A stochastic approach to the gamma function |journal=American Mathematical Monthly |volume=101|issue=9|pages=858&ndash;865|url=}}.</ref>
  • <ref name="RY">{{citation|last1=Revuz|first1=Daniel|last2=Yor|first2=Marc|year=1994|title=Continuous martingales and Brownian motion|edition=2nd|publisher=Springer}} (see Exercise (2.17) in Section V.2, page 187).</ref>
  • <ref name="RY">{{citation|last1=Revuz|first1=Daniel|last2=Yor|first2=Marc|year=1994|title=Continuous martingales and Brownian motion|edition=2nd|publisher=Springer}} (see Exercise (2.17) in Section V.2, page 187).</ref>
  • <ref>{{citation|last=Durrett|first=Richard|author-link=Rick Durrett|year=1984|title=Brownian motion and martingales in analysis|place=California|publisher=Wadsworth|isbn=0-534-03065-3}}.</ref>
  • <ref>{{citation|last=Fulman|first=Jason|year=2001|title=A probabilistic proof of the Rogers–Ramanujan identities|journal=Bulletin of the London Mathematical Society|volume=33|issue=4|pages=397&ndash;407 |url=|doi=10.1017/S0024609301008207}}. Also [ arXiv:math.CO/0001078].</ref>
  • ==Notes==
  • <references />

References 2[edit]

  • <ref>{{harvnb|Pollard|2002|loc=Sect. 5.5, Example 17 on page 122}}</ref>
  • <ref>{{harvnb|Durrett|1996|loc=Sect. 4.1(a), Example 1.6 on page 224}}</ref>
  • <ref name="Pollard-5.5-122">{{harvnb|Pollard|2002|loc=Sect. 5.5, page 122}}</ref>
  • quoted in <ref name="Pollard-5.5-122">{{harvnb|Pollard|2002|loc=Sect. 5.5, page 122}}.</ref>
  • ==Notes==
  • <references />
  • ==References==
  • *{{citation|last=Durrett|first=Richard|author-link=Rick Durrett|title=Probability: theory and examples|edition=Second|year=1996}}
  • *{{citation|last=Pollard|first=David|title=A user's guide to measure theoretic probability|year=2002|publisher=Cambridge University Press}}

References 3[edit]

  • see {{harv|Durrett|1996|loc=Sect. 7.7(c), Theorem (7.8)}};
  • *{{citation|last=Durrett|first=Richard|author-link=Rick Durrett|title=Probability: theory and examples|edition=Second|year=1996}}
  • '''Theorem''' {{harv|Barany|Vu|2007|loc=Theorem 1.1}}.
  • *{{citation|last1=Barany|first1=Imre|last2=Vu|first2=Van|year=2007|title=Central limit theorems for Gaussian polytopes|journal=The Annals of Probability|publisher=Institute of Mathematical Statistics|volume=35|issue=4|pages=1593&ndash;1621|doi=10.1214/009117906000000791}}. Also [ arXiv].
  • as proven in [[#CITEREFArBaBaNa2004|Artstein, Ball, Barthe and Naor (2004)]].
  • * <cite id=CITEREFArBaBaNa2004> S. Artstein, K. Ball, F. Barthe and A. Naor (2004), [ "Solution of Shannon's Problem on the Monotonicity of Entropy"], ''Journal of the American Mathematical Society'' '''17''', 975&ndash;982. Also [ author's site].</cite>
  • '''Theorem''' ([[#CITEREFKlartag2007|Klartag 2007]], Theorem 1.2).
  • * <cite id=CITEREFKlartag2007>[[European_Mathematical_Society#2008 prizes|Klartag]], Bo'az (2007), [ "A central limit theorem for convex sets"], ''Inventiones Mathematicae'' '''168''', 91&ndash;131. Also [ arXiv].</cite>
  • <ref>[[European_Mathematical_Society#2008 prizes|Boaz Klartag]], " A central limit theorem for convex sets", Inventiones Mathematicae 168:1, 91&ndash;131. []</ref>

References 4[edit]


and have a label somewhere else ("equation (1)")

:<cite id="equation1" style="float:right;margin-right:2.5em">(1)</cite> <math>a = 0</math> and have a label somewhere else ("equation [[#equation1|(1)]]")

[derivation 1]

:<math>\frac{n(n + 1)}{2} + (n+1) = \frac{(n+1)((n+1) + 1)}{2}\,,</math><ref group="derivation"> Derivation of induction formula for summing consecutive positive integers: :<math> \begin{align} \frac{n(n + 1)}{2} + (n+1) & = (n+1)\left( \frac n 2 + 1 \right) \\ & = (n+1)\left( \frac n 2 + \frac 2 2 \right) \dots \end{align} </math></ref>

  1. ^ Derivation of induction formula for summing consecutive positive integers:

<references group="derivation" /> .


It's "a Euclidean" because it's pronounced "yoo-", not "oy-" like in German. Same reason for "a European" instead of "an European". But would still be "an Eulerian" though.

Usage of articles in math English[edit]

Should I write "if x and y are positive then a number z=x+y is positive" or rather, "if x and y are positive then the number z=x+y is positive"? On one hand, this z appears anew, it was not introduced before. On the other hand, given x and y, there exists only one z defined by that phrase. Boris Tsirelson (talk) 18:11, 12 October 2014 (UTC)

Using the lost grammatical adage "when in doubt, rephrase", I'd use "if x and y are positive then z=x+y is positive". But it forced to pick from one of the two choices I vote for the second one. --RDBury (talk) 18:57, 12 October 2014 (UTC)
Thank you. Yes, I feel forced to choose, since really I write more complicated texts :-) such as "...then the/a function f defined by...satisfies..." (and instead of "function" it could be a longer noun group, like "separable reflexive Banach space" etc). Or do you think I can always rephrase? How? Really, I also feel more comfortable writing "the", but I got unsure, being confused by opposite opinions, like this: but when you introduce me someone, you say "a friend of mine" even though he is uniquely defined, if not by your words then by your gestures. Boris Tsirelson (talk) 19:54, 12 October 2014 (UTC)
It may sound strange, but I don't mind if slightly different styles (as long as they are "correct") are used in a longer text. It can help avoiding monotonic repetition, of which there is plenty anyway in mathematical texts. But in the present case, the second option gets my vote too. YohanN7 (talk) 20:49, 12 October 2014 (UTC)
Thank you. Having vote 2:0 (or even 3:0, counting myself) I get more sure. No, I do not find it strange... I also like some variations; but I face this case quite often. But wait, do you say that these "a" and "the" are both correct, or not? Boris Tsirelson (talk) 20:57, 12 October 2014 (UTC)
I'm not a native English speaker (I'm Swedish), but I'd say, as a guess, that both options are correct, but the first option seems unusual, it doesn't seem to fit. Perhaps it would fit in a bigger example with more ingredients. YohanN7 (talk) 21:07, 12 October 2014 (UTC)
It depends a bit on how you "read it out loud inside your head" when reading. An equation like z = x+y can "be pronounced differently" when given a context. YohanN7 (talk) 21:17, 12 October 2014 (UTC)
The Language Reference Desk may be a better place to post this question. As a native English speaker I am sure that it should be the and not a, because as you said there exists only one z defined by that phrase. --catslash (talk) 23:18, 12 October 2014 (UTC)
Thank you; if you are sure, also I am. Yes, I understand it is a language question; but sometimes math jargon differs from usual English. Boris Tsirelson (talk) 05:57, 13 October 2014 (UTC)


MathJax update, thanks to Nageh. Just to let you know, I have updated my mathJax user script to recent version 1.1 of MathJax. Notable change is the support for webfonts via CDN (i.e., no local font installation requirements). Details at the user script documentation page. Feedback welcome.

How to make SVG diagrams, thanks to Ryan Reich. This question sometimes comes up and it bears answering as often as possible, since a lot of people have never heard that we should be using SVG, and of those who have, few seem to have an easy way of actually accomplishing it. This is addressed at Help:Displaying a formula#Convert to SVG, but their proposed solution relies on a somewhat arcane and arbitrary invocation of two different utilities, followed by a roundabout filtration through two major software packages, which is necessitated by one of them (pstoedit) requiring a costly proprietary plugin to work properly. And the end result is still unusable if your diagram has diagonal lines. Here's the right way:

pdflatex file.tex
pdfcrop --clip file.pdf tmp.pdf
pdf2svg tmp.pdf file.svg
(rm tmp.pdf at the end)

Both pdfcrop and pdf2svg are small, free (if new and somewhat alpha) programs that work properly. I advocate pdflatex since with the alternative, you might be tempted to go the route of latex→dvips→pstopdf before vectorizing, and that runs into a problem with fonts that has to be corrected with one of the arcane invocations above. (There is a correct route, which is to replace that chain with dvipdfm, that I have never seen anyone suggest. Somehow, the existence of this useful one-step solution to getting PDFs from plain latex is always ignored.)

It has been road-tested on, most notably (for the complexity of its images) Triangulated category and found to work quite well.

I think for art like this it would be preferable to use .svg (a vector format) for the graphics instead of .jpg (a bitmap format), if possible. I use Adobe Illustrator for that but it's kind of expensive; the most popular free alternative seems to be Inkscape. —David Eppstein

"Editors making a challenge should have reason to believe the material is contentious, false, or otherwise inappropriate", according to Wikipedia:When to cite#Challenging another user's edits.

Per WP:POV fork, "The generally accepted policy is that all facts and major points of view on a certain subject should be treated in one article. As Wikipedia does not view article forking as an acceptable solution to disagreements between contributors, such forks may be merged, or nominated for deletion."


Mathematics (use of sources)

11.4) If editors disagree on how to express a problem and/or solution in mathematics, citations to reliable published sources that both are directly related to the topic of the article and directly support the material as presented must be supplied by the editor(s) who wishes to include the material. Novel derivations, applications or conclusions that cannot be supported by sources are likely to constitute original research within the definition used by the English Wikipedia.

From WPM talk:

I think that the OR rule together with the Copyright law make coverage of mathematics (or any other subject) impossible. You have to think (commit 'original research') to do mathematics. The only alternative is to blindly copy from 'reliable' sources which violates copyright. Of course, such copying and the verification that the source is indeed reliable also require thought (OR). So the rule against OR is an absurdity which should be repealed.
The reason we have a rule against OR is to try to avoid disputes about what is correct reasoning by appealing to an outside source. Notice that in mathematics, this is usually only necessary when one or more of the disputing parties is a crank or troll. However, refusing to allow an edit on grounds that it is OR is ultimately just an excuse for rejecting what we think is false without having to get the agreement of a crank or troll. JRSpriggs (talk) 03:05, 14 March 2011 (UTC)

This one is fairly complicated. I don't think it true that, outside of mathematics, OR and copyright makes coverage impossible. The problem is that an allowable rephrasing in most fields becomes OR in mathematics, as even a change in notation does not fall in the "routine arithmetic calculation" exemption in Principles 11.