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Results tagged with ho.history-overview
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user 39521
History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
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 …
- 4,713
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 …
- 12.4k
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' - …
- 12.4k
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 …
- 12.4k
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 …
- 32.5k
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 …
- 12.4k