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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.

14 votes

Do mathematical objects disappear?

From A. A. Ivanov (The Monster Group and Majorana Involutions): [$\dots$] John Conway suggested calling the extensions of $^2E_6(2)$ the Baby Monster, the double extension the Middle Monster, and …
25 votes
Accepted

A conjecture in which both "if" and "only if" are near misses

False claim: A Hausdorff topological space is compact if and only if it is sequentially compact. It's believable if your intuition of Hausdorff spaces comes entirely from metric spaces (where the cla …
Adam P. Goucher's user avatar
16 votes

Extremely messy proofs

Hindman's theorem states that if we finitely colour the naturals, there exists an infinite set $S$ such that the sum of every finite non-empty subset of $S$ has the same colour. Hindman's original com …
7 votes

When were triples called monads for the first time?

P. T. Johnstone (who wrote several books on Topos Theory) gave a Category Theory lecture in which he said this was originally called 'the standard construction', then 'triples', and finally 'monads' - …
Adam P. Goucher's user avatar
4 votes
Accepted

What was the first elementary proof that $\pi(x)=o(x)$?

Leonhard Euler knew that the infinite product: $$ \prod_{p \textrm{ prime}} \left(1 - \frac{1}{p} \right)^{-1} = \sum_{n=1}^{\infty} \frac{1}{n} $$ is divergent (and used this to prove the infinitud …
Adam P. Goucher's user avatar
11 votes

What are examples of (collections of) papers which "close" a field?

Alfred Tarski essentially 'closed' the ancient field of Euclidean geometry. Specifically, he provided a simple first-order axiomatisation of Euclidean geometry (where a model is a set of points endowe …