I would like to hear about other instances of the so-called 'increments' approach, first used by Roth to prove that a subset of $\mathbb{N}$ of positive upper density contained infinitely many arithmetic progressions of length 3. The original argument of Roth used a 'density increment' argument, ...
A week or so ago, I was saddened to read Jim Stasheff's post on the AlgTop mailing list, announcing the passing of Colin Day, after a long bout with cancer. I was thinking of reading Colin Day's PhD thesis in his memory, and trying to understand it (the title certainly sounds interesting); but I...
Martin Gardner kept voluminous correspondence with amateur and professional mathematicians worldwide throughout his career. His files are a treasure trove of information about all areas of recreational mathematics. Does anybody here know whether any portion of those files will be made available...
First of all, apologies for the really non-standard question/announcement. I know this is not what MO was intended for, but in this situation it is the easiest way to reach (perhaps) the right person. On my way back to London from some workshop in Ohio, I got stuck in NYC because of that infamou...
For $r > 0$, let $L(r) = \# \{ (x,y) \in \mathbb{Z}^2 \ | \ x^2 + y^2 \leq r^2\}$ be the number of lattice points lying on or inside the standard circle of radius $r$. It is easy to see that $L(r) \sim \pi r^2$ as $r \rightarrow \infty$. The Gauss circle problem is to give the best possible err...
Did Conway pay the wager for either of the proofs to the The Angel Problem? I'd check in on this every now and again when it was an unsolved problem and would like to know how the story ends. Anyone know more details?
« first day (386 days earlier) ← previous day next day → last day (3529 days later) »