48
votes

### MO-Hard Questions

Here is a prime example of a MO-Hard question that doesn't appear on the unanswered list.
Polynomial bijection from $\mathbb Q\times\mathbb Q$ to $\mathbb Q$?
The title says it all. In fact, the ...

Community wiki

48
votes

### How can we attract more grad students?

I'll go against my best judgement and will reply to this with my own perception.
First of all, the best thing would be to ask graduate students directly. I don't know if there are any active efforts ...

- 647

36
votes

### Best of MathOverflow, or papers inspired by MathOverflow

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!...

Community wiki

32
votes

### MO-Hard Questions

This question is a very nice topological one, a cousin of Brouwer's fixed point theorem and related to several questions in the literature:
Suppose that $f$ and $g$ are two commuting continuous ...

Community wiki

29
votes

### What do you want to do in Rio?

If you have an excuse to mention MO in your abstract, please consider doing so. MO is mentioned in the paper I submitted for the proceedings and it will appear in one slide of my talk at the ICM.

- 29.9k

20
votes

### Best of MathOverflow, or papers inspired by MathOverflow

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 &...

Community wiki

20
votes

### MO-Hard Questions

I make no claim to the significance of any of these problems,
nor that they are even "hard"—some are too peripheral to attract interest.
With those caveats, here are a few of mine (in ...

Community wiki

20
votes

### How can I donate to MathOverflow — if I should?

Update: Donations are now possible, see this post: Donations to MathOverflow, Inc
[Apologies for the long delay in answering, I was on my honeymoon! I may update this quick answer after I get back to ...

- 42.5k

19
votes

### Best of MathOverflow, or papers inspired by MathOverflow

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. ...

Community wiki

16
votes

### Best of MathOverflow, or papers inspired by MathOverflow

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. ...

Community wiki

16
votes

### MO-Hard Questions

One I like very much is
Can we color $\mathbb Z^+$ with $n$ colors such that $a, 2a, \dots, na$ all have different colors for all $a$?
Among the failed proposed attempts, the ones that appeared ...

Community wiki

16
votes

### MO-Hard Questions

Simon Thomas asked in
Ultrafilters and automorphisms of the complex field
whether the existence of non-principal ultrafilters (over the natural numbers) suffices to imply the existence of a ...

Community wiki

16
votes

### MO-Hard Questions

I posted a question about a year ago on MO (and even further back on MSE) that remains elusive:
Randomly break a stick in five places.
Question: What is the probability that the resulting six pieces ...

Community wiki

16
votes

Accepted

### MO in the Notices of the AMS

The Opinion column "Mathematical Community" in the March 2011 issue, by John Swallow, asks, "Are mathematicians at the forefront of collaboration, with the advent of the Polymath Projects and Math ...

- 36.5k

15
votes

### Best of MathOverflow, or papers inspired by MathOverflow

As acknowledged in my note Explicit additive decomposition of norms on $\mathbb{R}^2$, it was sparked by answers by Noam D. Elkies and Suvrit Sra on MathOverflow Absolute value inequality for complex ...

Community wiki

15
votes

### Best of MathOverflow, or papers inspired by MathOverflow

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 ...

15
votes

### Mugs, Stickers And Shirts - Now With 100% More MathOverflow!

The swag is here!
The re-order shipment is now in stock and that information we've been holding for over a year now has been sent off to our warehouse so the orders can now be processed. Everything ...

- 101

15
votes

### How can we attract more grad students?

I don't believe MO can do anything to make most grad students comfortable posting here. It wouldn't be compatible with the culture of the site or how its users see it (and some of the comments on this ...

- 2,947

14
votes

### MO-Hard Questions

A question that fascinates me is the problem of characterizing the subsets $S$ of the unit circle $\mathbb T$ for which there is a power series with radius of convergence $1$ that, on $\mathbb T$, ...

Community wiki

13
votes

### Best of MathOverflow, or papers inspired by MathOverflow

A nice question by Michael Hardy, How many rearrangements must fail to alter the value of a sum before you conclude that none do?, led to a recent 6-author collaboration, 5 or 6 of whom are MO patrons ...

Community wiki

13
votes

Accepted

### Is there a way to measure the effectiveness of MO?

A lot of MathOverflow data is already available publicly.
An anonymized version of the entire Stack Exchange Network database is archived every few weeks and permanently on archive.org. It's easy to ...

- 42.5k

12
votes

### Best of MathOverflow, or papers inspired by MathOverflow

This MO question was the starting point for a joint work with Tao Mei where we study radial multipliers on the von Neumann algebras of hyperbolic groups. The paper is entitled Complete boundedness of ...

Community wiki

12
votes

### Best of MathOverflow, or papers inspired by MathOverflow

Keith Kearnes, together with co-authors Emil Kiss and Ágnes Szendrei, recently published a solution to Varieties where every algebra is free in this arxiv preprint. They prove a result under an even ...

Community wiki

12
votes

### It's been another year...MO exists since six years!

Happy birthday MO! While we're enjoying all this free cake, maybe we can take a moment to reflect on how (or even whether) MO has grown in the past year.
Out of curiosity, I put together some search ...

- 13.2k

12
votes

### Examples of mathematical exposition arising from MO answers

This paper resulted from a question on mathoverflow. This monograph on properties of 3-manifold groups has now appeared in print.

- 62.2k

11
votes

### Best of MathOverflow, or papers inspired by MathOverflow

Not sure if my recent paper "Equivalence: an attempt at a history of the idea" qualifies as one of the "best of Mathoverflow or papers inspired by Mathoverflow". But I am sure Mathoverflow was a force ...

Community wiki

11
votes

### Best of MathOverflow, or papers inspired by MathOverflow

The question, "How hard is reconstructing a permutation from its differences sequence?" posed by Mohammad Al-Turkistany,
was answered by
Marzio De Biasi,
who then wrote a paper, "...

Community wiki

11
votes

### Best of MathOverflow, or papers inspired by MathOverflow

Hannah Cairns's proof of Perron's theorem (discussed in this MathOverflow question) has been published in The American Mathematical Monthly as Perron’s Theorem in an Hour.

Community wiki

11
votes

### MathOverflow @ ICM2014 : We Want You!

Do we want more people? Yes, MO could certainly use many more people.
Of what kind? Exactly of the kind that come to the ICM: professional mathematicians of all ages, countries, and level, and ...

- 25k

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