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### Other applications of the 'increment' approach

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 ...

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### How to find Colin Day's PhD Thesis

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 ...

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### What is happening to Martin Gardner's files?

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 ...

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### Anything going on for a mathematician stuck at New York?

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.
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### What is the status of the Gauss Circle Problem?

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) ...

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### The Angel Problem - was the bet paid?

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 ...