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user 6085
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 $\mathbb T$, con …
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 …
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 nont …
4
votes
Best of MathOverflow, or papers inspired by MathOverflow
A paper by T. Chartier, P.P. Pach and myself describing the status of "Can we color Z^+ with n colors such that a, 2a, …, na all have different colors for all a?" has just been published.
Coloring the …