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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.
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 …
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 …
- 12.4k
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 …
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 …