# Best of MathOverflow, or papers inspired by MathOverflow

This is a place to collect MathOverflow success stories!

Was some of your research inspired by something on MathOverflow? Do you know questions & answers that led to interesting research? MathOverflow citations? Open problems solved on MathOverflow? Then add your story in an answer! (One story per answer, please!)

If you want to help get this thread started, you can use this search to find MathOverflow citations on the arXiv or migrate some old stories from tea.mathoverflow.net.

• This question was suggested in this discussion. – François G. Dorais Aug 12 '13 at 15:07
• Is it really the case that the old success stories have to be migrated by hand? I'm surprised there's not a way to do this within the stack software or at least write a program to do it. – David White Aug 12 '13 at 18:22
• @David: Clarify what you're suggesting. What do you propose migrating this way? – François G. Dorais Aug 12 '13 at 18:27
• Hi. I felt that if we plan to have a single unified place for success stories (e.g. if someone wants to come and write an article about MO) then it doesn't make sense to have one place at tea for pre-migration and one here for post-migration. So the old success stories should be here, since it appears we can't add new ones to that old page. But it would take a long time to move them over one by one. I wish it could be done all at once. – David White Aug 12 '13 at 19:01
• @David: The thread at tea is mostly other stuff so it's best to do it manually. – François G. Dorais Aug 12 '13 at 19:10
• @DavidWhite tangentially, but one could add things in the old thread. – user9072 Aug 12 '13 at 21:15
• Many papers were inspired by questions raised on MO, but has any credit been given to those who raised the questions in the publications? I am just wondering. – qed Aug 24 '13 at 16:09
• @qed I know for a fact that in many instances, perhaps most, the MO question-asker is given credit and citations. Further, I know of several cases, and I expect that there are many more, in which the question-asker was invited to join as co-author. – Joel David Hamkins Dec 26 '16 at 15:02
• I wonder if the title should be changed from "Best of MathOverflow" to "Publications resulting from MathOverflow" (or maybe "inspired by"?). It has in fact developed into publication citing. – Joseph O'Rourke Apr 9 '17 at 1:57
• @JosephO'Rourke What you write is perhaps true. OTOH the ones which MO community considers the best are quite likely to rise to the top based on voting, so in this sense it might still be a fitting title. I'll point out that Todd Trimble recently commented on the title of this thread: Some people might feel uneasy citing their own work at a thread entitled "Best of MathOverflow", but perhaps that title should be interpreted broadly – Martin Sleziak Jan 21 '18 at 9:49

The MO question, "Shortest closed curve to inspect a sphere," was cited as the "initial stimulus" for the paper

He establishes a lowerbound of $6\sqrt{3}$ on the shortest inspection curve, more than $80$% of the conjectured $4 \pi$ lowerbound.

The answer to the question Length of Hirzebruch continued fractions was published as a short note On continued fractions of equal length .

The full answer to the question Decidability of diophantine equation in a theory by rainmaker in the case of Robinson’s arithmetic was written up in my paper Division by zero, in: Liber Amicorum Alberti: A Tribute to Albert Visser (J. van Eijck, R. Iemhoff, J. J. Joosten, eds.), Tributes vol. 30, College Publications, London, 2016.

This paper of mine (Arithmetic Restrictions on Geometric Monodromy) was inspired in large part by this question asked by Lisa S., though the original motivation is not so obvious in the final product.

The paper "Majority colourings of digraphs" by Paul Seymour, Stephan Kreutzer, Sang-il Oum, David R. Wood and myself has its origin in my question "Majority coloring for directed graphs".

• American spelling for MO, British for arXiv? – Gerry Myerson May 15 at 13:32

I asked a somewhat silly question, which silliness was pointed out by Tobias Fritz, which answer I cited just to be pedantic about a point in set theory in a paper I wrote recently.

Shengkui Ye, in the review in Math Reviews of Bela Bauer and Claire Levaillant, A new set of generators and a physical interpretation for the SU(3) finite subgroup D(9,1,1;2,1,1), Quantum Inf. Process. 12 (2013), no. 7, 2509–2521, MR3065503, cites the discussion at The finite subgroups of SU(n) as contradicting the claim by Bauer and Levaillant that "After 100 years of effort, the classification of all the finite subgroups of SU(3) is yet incomplete.''

The paper, "A quantitative obstruction to collapsing surfaces," by Mikahil G. Katz, arXiv abs, addresses the MO question, "Gromov-Hausdorff limits of 2-dimensional Riemannian surfaces" posed by sva (S. Alesker).

Abstract. We provide a quantitative obstruction to collapsing surfaces of genus at least $2$ under a lower curvature bound and an upper diameter bound.

The discussion initiated by my question Primes occurring as orders of elements of a finitely presented group led to the addition of Section 5 to:

Maurice Chiodo, On torsion in finitely presented groups, Groups Complexity Cryptology 6(1): 1-8 (2014). arXiv version.

Joachim König has answered my question Order of products of elements in symmetric groups in his paper A note on the product of two permutations of prescribed orders, to appear in European Journal of Combinatorics.

Leonardo Zapponi has answered my question Parametric solutions of Pell's equation in his paper Parametric solutions of Pell equations.

Ilya Bogdanov has answered my question Graphs with only disjoint perfect matchings on certain coloring in graphs, that emerged through research in quantum physics. This answer has inspired quite a bit of research:

Furthermore in Questions on the Structure of Perfect Matchings inspired by Quantum Physics, we generalize the question on inherited colorings to cover the full potential of quantum physics. One of my co-authors is Daniel Soltész, who I only met through MO. In this paper we cited Bogdanov's MO answere again (and called it "Bogdanov's Lemma").

The Q1 of the article is another MO question"Vertex coloring inherited from perfect matchings (motivated by quantum physics)", but i have little hope that I get so lucky again.

This is certainly, by far, my personal "Best of MO".

This MO question "Property $$\Gamma$$ in terms of correspondences" led us to answer two old open problems and to push further a third more recent result:

Jon Bannon, Amine Marrakchi, Narutaka Ozawa. Full factors and co-amenable inclusions, arxiv/1903.05395.

Thanks MO!!!

• push? publish?? – Gerry Myerson May 6 at 4:11
• I think it wouldn't hurt to edit in links to whatever you have written up (if your results are ready for publication). – Gerry Myerson May 6 at 6:57
• I see. Taka linked to the paper in the comment following his answer, which set this in motion. I'll link to the paper in the answer here... – Jon Bannon May 6 at 7:19

This preprint of Souvik Dey (on commutative ring theory) cites an MO post.