ymb

what AMS is not doing, but probably should be

The American Mathematical Society (AMS) is the leading professional organization for mathematicians primarily based in research-focused institutions, particularly departments of mathematics with PhD programs. It is a large organization with approximately 30,000 members, including international members, retirees, and others. The AMS engages in many activities typical of professional organizations: it operates a publishing house, serves

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no worries yet

What happens if you feed ChatGPT some logical puzzles? I took one, from Smullyan’s textbook on basics of mathematical logics. It is easy to solve. Predictably, ChatGPT failed to do so, but in rather instructive ways. Here’s the puzzle: [On an island, the inhabitants are either knights, and always tell the truth, or knaves, and

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merge tree monoid

\(\def\Real{\mathbb{R}}\def\tree{\mathcal{T}}\) Consider a path metric space \(M\) and a continuous function \(f:M\to \Real\). For simplicity, all such pairs here will have sublevel sets of \(f\) compact (so that the function is bounded from below). Then one can form the so-called merge tree (see, e.g. here, for motivation, and some history), a new topological space (let’s

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