56

Using MathOverflow should be an extension of the way you normally do mathematics, and the same rules you use to effectively solve problems can be used to make good MO questions. Just like solving problems, crafting good questions requires you to put in some effort!
Ask a focused question that has a specific goal
Be precise
Do your homework
Break it down
...

51

While the MathOverflow site is operated by Stack Exchange, Inc., the domain and the MathOverflow name are owned by the MathOverflow corporation. The MathOverflow corporation is completely independent from Stack Exchange and its mission is to ensure the continued operation of the site in a manner that meets the needs and expectations of the community.
On May ...

42

Mark Sapir solved an interesting open problem in group theory in this answer to a question of Narutaka OZAWA.

37

I'd propose the rule of active editing: if you value a stone soup question, then edit the question to make it better (clearer, broader, better thought out, more answerable) and ensure that it fits the answers. You might lose the original intent of the question, but that horse has already left the barn. By the time we reach the stone soup phase, there's ...

36

Our article D. Brumleve, J. D. Hamkins, and P. Schlicht, “The mate-in-n problem of infinite chess is decidable,” LNCS 7318(2012):78-88 was inspired directly by Richard Stanley's question Decidability of chess on an infinite board.
Abstract. Infinite chess is chess played on an infinite edgeless chessboard. The familiar chess pieces move about according to ...

33

A meta-answer: http://search.arxiv.org:8081/?query=mathoverflow&in= returns a list of 197 papers on the arXiv which mention MathOverflow.
Nearly all of these are actual citations, with a small number of papers about MathOverflow itself, and some number of papers which mention MathOverflow without giving full attribution according to the guidelines.
...

32

In April 2013 I discussed with Alan Sokal the following conjecture: if $P$ is a real polynomial with the property $|P(z)|<P(|z|)$ then some power of $P$ has positive coefficients.
We did not prove it at that time.
In August, Ofer Zeitouni asked on MO to describe all possible limits of the so-called empirical measures of polynomials with positive ...

31

You own all of your posts! You retain full copyrights and you can do anything you please with them.
However, by posting on MathOverflow, you release your content under the terms of the Creative Commons Attribution-ShareAlike 3.0 (CC BY-SA 3.0) license. This license allows MathOverflow, Stack Exchange and others to use your content under specific terms. This ...

27

This is an old and self-indulgent story; but it was such a charmingly unexpected bonus from my early use of MathOverflow, that I think it deserves to be recorded somewhere (my apologies for its length!):
tl;dr: As a serendipitous consequence of this MathOverflow question, the second answerer invited me to give my first-ever seminar talk as a grad student.
...

26

Ben Green's paper on (not) computing the Möbius function arose from this question on MathOverflow.
Abstract. Any function $F : \{1,\dots,N\} \rightarrow \{-1,1\}$ such that $F(x)$ can be computed from the binary digits of $x$ using a bounded depth circuit is orthogonal to the Möbius function $\mu$ in the sense that $\frac{1}{N} \sum_{x \leq N} \mu(x)F(x) = ...

26

History of MathOverflow
Milestones
September 28, 2009: MathOverflow goes online
October 10, 2009: MathOverflow is announced at the Secret Blogging Seminar
December 2009 Greg Kuperberg became the first user to reach 10k reputation
June 2010: featured in the AMS Notices.
October 2010: 10000 users
June 2012: 100000th post (including the deleted ones)
...

25

Tom Church, Melody Chan, and Joshua Grochow just posted their paper "Rotor-routing and spanning trees on planar graphs" to the arXiv here. It answers this MO question which was asked by Jordan Ellenberg.

25

The MO question
Norms of Commutators
is referenced in a paper by Ozawa, Schechtman and me that will appear in the PNAS. arXiv:1202.0986

23

Our article, C. D. A. Evans and J. D. Hamkins, Transfinite game values in infinite chess, where we investigate the range of transfinite game values arising in infinite chess, grew directly out of Johan Wästlund's question Checkmate in $\omega$ moves?.
In particular, we define the omega one of chess $\omega_1^{\frak{Ch}}$ to be the supremum of the ordinal ...

21

On January 30, 2014, Joel David Hamkins posted his 1000th answer on MathOverflow. Congratulations!

20

The paper A Counterexample to a Conjecture of Schwartz by Brandt, Chudnovsky, Kim, Liu, Norin, Scott, Seymour, and Thomassé answers this MO question of Felix Brandt. The question asks whether a weakened form of Schwartz’ Conjecture (a popular conjecture in Social Choice Theory) is true. The paper proves that even this weakened form of the conjecture is ...

19

This paper (details below) by Zhen Lin Low and Aaron Mazel-Gee cites not just MO but:
This collaboration would not have happened without the ‘Homotopy Theory’
chat room on MathOverflow.
arXiv.org > math > arXiv:1409.8192
From fractions to complete Segal spaces
Zhen Lin Low, Aaron Mazel-Gee
We show that the Rezk classification diagram of a relative ...

19

There are plenty of questions that it is uncontroversial that they need to be closed. However, let me propose
(Joel David Hamkins's proposed rule, with quid's addition) Give all
questions charitable readings, when doing so leads to interesting
mathematical ideas. Make sure, however, that all questions you answer
are somewhat in line with the ...

17

It's now at tea.mathoverflow.net!

17

Most of the time, the edits that I see on MO are respectfully and tactfully performed and small in scope, and gratefully received by the post's author as improvements. Occasionally though I see flare-ups over an edit, to the point where a post will be self-mutilated or self-deleted; (more rarely) there will be an edit war. I hope this answer can help to ...

15

This MO question was asked in December of 2011, in line with a reference request for a senior thesis on odd perfect numbers completed in 1978. Subsequently, the OP has tried numerous ways to get hold of the thesis's author.
On August 24, 2013 Jim (Condict) Grace (the thesis's author) popped in to MO to respond to the original question.

14

I am frequently asked whether exponentials are "linearly independent". That is if we have
a sequence of distinct complex numbers $\lambda_j$, whether
$$\sum_{j} a_j\exp(\lambda_j z)\equiv 0$$
implies that all $a_j=0$. If the linear dependence above holds in all complex plane, this
question was answered by A. F. Leontjev. All his books exist only in Russian, ...

14

The question whether there is a non surjective bounded linear operator on $\ell_\infty$ that has dense range was answered in this paper by Amir Bahman Nasseri, Gideon Schechtman, Tomasz Tkocz, and me. An interesting aspect of the proof is that it uses a theorem proved by computer scientists to get a counterexample. So, in some sense, this question about ...

14

Where's the rule that says I have to wear pants?
MathOverflow doesn't have formal rules about every possible thing that could come up. Roughly, you should think of this site as a large seminar. Be nice. Treat others with the same respect you'd want them to treat you. We're all here to learn together. Be honest. If you see misinformation, vote it down. ...

14

My joint article with Justin Palumbo, The rigid relation principle, a new weak choice principle (Mathematical Logic Quarterly 58(6):394-398, 2012) grew out of our answers to my question, Does every set admit a rigid binary relation? (and how is this related to the Axiom of Choice?), which grew out of Mike Shulman's question, A rigid type of structure that ...

14

My MO question Conjugation of group extensions was answered by Ycor. As a result, we wrote a joint note
Conjugate complex homogeneous spaces with non-isomorphic fundamental groups published in C. R. Acad. Sci. Paris, Ser. I, 353 (2015) 1001–1005.

13

The analog of the famous law of iterated logarithm for maximum eigenvalue of a random Gaussian matrix was asked here. Zeitouni's MO-answer was expanded (after significant effort) to a full answer for the limsup (including constants) and a partial answer for the liminf by Elliot Paquette and Ofer Zeitouni arxiv.org/abs/1505.05627 !

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