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

29 votes
2 answers
2k views

Why did Dedekind claim that $\sqrt{2}\cdot\sqrt{3}=\sqrt{6}$ hadn't been proved before?

In a letter to Lipschitz (1876) Dedekind doubts that $\sqrt{2}\cdot\sqrt{3}=\sqrt{6}$ had been proved before: quoted from Leo Corry, Modern algebra, German original: Why did Dedekind doubt that $ …
43 votes
5 answers
9k views

Origins of names of algebraic structures

Consider the names of basic algebraic structures: 'group', 'ring', 'space', 'field', 'Körper', even the name 'structure' itself - all of them time-honoured terms, deeply rooted in our history and cul …
9 votes

Examples of results which were surprising but later shown to be natural.

In his Indiscrete Thoughts Gian-Carlo Rota writes: Every mathematical theorem is eventually proved trivial. The mathematician's ideal of truth is triviality, and the community of mathemati …
Hans-Peter Stricker's user avatar
10 votes

Thinking and Explaining

I'd like to take the occasion and sketch my view on reconstruction problems in graph theory: I see a graph as a set of subjects with a relation between (some of) them. Each node (= subject) has a limi …
Hans-Peter Stricker's user avatar