Mathematics · History & Philosophy of Mathematics
Proof & Certainty
A topic within History & Philosophy of Mathematics, itself one of 9 topics in that field and part of Mathematics.
Reading for History & Philosophy of Mathematics
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No prior grounding assumed.
- BookA Mathematician's ApologyG. H. Hardy, 1940
A working mathematician's defence of pure mathematics as an art form judged by beauty rather than utility.
- BookHow to Solve ItGeorge Pólya, 1945
A general heuristic for attacking any problem: understand it, plan, execute, then look back at what the solution taught you.
Then
Assumes you know the vocabulary.
- EssayThe Unreasonable Effectiveness of Mathematics in the Natural SciencesEugene Wigner, 1960· 14 pages
Asks why mathematics invented for its own sake keeps turning out to describe physical reality, and offers no comfortable answer.