Timeline for Why do Bernoulli numbers arise everywhere?
Current License: CC BY-SA 3.0
30 events
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| Aug 20, 2020 at 13:30 | answer | added | MathCrawler | timeline score: 1 | |
| Feb 13, 2020 at 20:49 | comment | added | Watson | Related: "Bernoulli numbers and the unity of mathematics" by B. Mazur. | |
| Apr 24, 2016 at 14:03 | history | edited | Amir Sagiv |
it is obviously a big-picture question. I think it has evolved to a big-list, and therefore will be more accesible with the tag
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| Aug 31, 2015 at 20:00 | comment | added | ACL | @gowers: As Douady says in his Algèbre et théorie galoisienne, beware of adverbs - « Nous ne supposons pas l'espace simplement connexe, nous le supposons simplement connexe. » | |
| Dec 12, 2014 at 6:25 | comment | added | Tom Copeland | Generalized Bernoulli polynomials defined by powers of the e.g.f. (used in Hizebruch's criterion for the Todd class) have a rich history in the q-calculus as noted in Thomas Ernst's writings. Doyon, Lepowsky, Milas show how the Bernoulli polynomials are related to vertex operator algebras. The Bernoullis are related to the Euler, Eulerian, zizgag, Gennochi, ordered Bell numbers, and polylogarithms. Since the e.g.f. is tied so closely to exp, they occur in expansions of trig and hyperbolic functions. Quantum groups, solitons, and solns.of the KdV equation, I've noted elsewhere. Now shoes, ... . | |
| Dec 10, 2014 at 20:07 | comment | added | Tom Copeland | Basically, where ever you see the derivative you could replace it with the Bernoulli polynomials and make some sense of it, but you are right, Ryan. I've never seen even one under my bed. Never seen an exponential there either. What was the OP thinking of?! | |
| Dec 10, 2014 at 11:58 | history | edited | user21574 | CC BY-SA 3.0 |
added 16 characters in body
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| Dec 10, 2014 at 4:37 | comment | added | Ryan Budney | I suppose I don't agree with the premise. Bernoulli numbers, it seems clear to me, do not appear everywhere. They're relatively rare objects that come up in fairly particular circumstances. If they appeared everywhere, I imagine I would be seeing them more often. | |
| Nov 27, 2014 at 2:37 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Nov 20, 2014 at 6:35 | answer | added | Zurab Silagadze | timeline score: 4 | |
| Nov 19, 2014 at 23:02 | answer | added | Lev Soukhanov | timeline score: 2 | |
| Nov 18, 2014 at 19:30 | answer | added | DavidLHarden | timeline score: 6 | |
| Nov 18, 2014 at 17:51 | answer | added | Tom Copeland | timeline score: 4 | |
| Jun 27, 2014 at 0:33 | comment | added | Tom Copeland | @Michael, I think P. Cartier discusses that and more in "Mathemagics." | |
| Jun 27, 2014 at 0:05 | comment | added | Michael Hardy | The also arise in the cumulants of the uniform distribution on the interval $[-1,1]$. If I recall correctly, the $n$th cumulant is $B_n/n$. ${}\qquad{}$ | |
| S Jun 26, 2014 at 20:25 | history | suggested | F. C. |
added the tag bernoulli numbers, obviously missing
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| Jun 26, 2014 at 20:15 | review | Suggested edits | |||
| S Jun 26, 2014 at 20:25 | |||||
| Oct 3, 2012 at 2:28 | comment | added | Tom Copeland | The Bernoulli numbers also occur in the solution of linear ODEs. See A. Iserles "Expansions that grow on trees." | |
| Apr 11, 2011 at 17:42 | history | edited | Charles Matthews | CC BY-SA 3.0 |
copy edit
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| Apr 11, 2011 at 12:54 | comment | added | Alex B. | @Tim You are right, I guess I didn't mean simply connected, but rather a complete graph or something like that. | |
| Apr 11, 2011 at 12:28 | answer | added | Neil Strickland | timeline score: 18 | |
| Apr 11, 2011 at 9:36 | answer | added | Stefan Waldmann | timeline score: 10 | |
| Apr 11, 2011 at 8:32 | comment | added | gowers | @Alex, I take it that by "simply connected" you mean "connected in a simple way". | |
| Apr 11, 2011 at 7:33 | answer | added | John Baez | timeline score: 46 | |
| Apr 11, 2011 at 4:42 | comment | added | Alex B. | Just a minor remark: the space of the areas you have mentioned might be simply connected. For example, the criteria for regular primes, the zeta values at even integers, and higher K-theory - these are all closely related areas. If you are willing to take on board everything we know and everything we conjecture to be true, then it follows that Bernoulli numbers appear in one of these if and only if they appear in all of them. Somewhat related is my answer here: mathoverflow.net/questions/45376/… | |
| Apr 11, 2011 at 4:19 | comment | added | 36min | That's a good point. So do you know how did he define it and what's his motivation? | |
| Apr 11, 2011 at 3:11 | answer | added | Henry Cohn | timeline score: 139 | |
| Apr 11, 2011 at 3:06 | answer | added | Scott Carter | timeline score: 14 | |
| Apr 11, 2011 at 2:56 | comment | added | yaoxiao | According to history of mathematics, at the beginning of Bernoulli's original idea, he did not begin defined as the Taylor coefficients of the function x/(e^x-1) at 0. | |
| Apr 11, 2011 at 2:41 | history | asked | 36min | CC BY-SA 3.0 |