BookMathematics1945

The Psychology of Invention in the Mathematical Field

Jacques Hadamard

Hadamard surveyed working mathematicians on how they actually have ideas, and got answers closer to dreams and hunches than to logic. More anthropology than mathematics, and the better for it.

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EssayMathematics2002

A Mathematician's Lament

Paul Lockhart

Lockhart loves mathematics enough to be furious about how school murders it — drilling the notation of a thing while hiding the thing itself. The anger isn't a flaw in the argument; it's the evidence.

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PaperMathematics1994

On Proof and Progress in Mathematics

William P. Thurston

Thurston, a great geometer, describing how mathematics actually advances — through shared understanding, not just formal proof. Unusually generous about the kinds of knowing that resist being written down.

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EssayMathematics2017

Mathematics for Human Flourishing

Francis Su

Su's farewell address as president of the MAA, arguing that mathematics answers human longings — for beauty, for play, for justice. Warmer and more humane than the subject usually permits itself to be.

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EssayMathematics2000

The Two Cultures of Mathematics

W. T. Gowers

Gowers on the real divide between problem-solvers and theory-builders, written from inside by someone fluent in both. It's a quiet defense of the kind of mathematics that doesn't collect the prizes.

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BookMathematics1940

A Mathematician's Apology

G. H. Hardy

Hardy's defense of pure mathematics, written as his own powers were fading, candid about ambition, beauty, and growing old. It survives because it's so personal it nearly hurts to read.

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BookMathematics1954

Mathematics and Plausible Reasoning

George Pólya

Pólya on how mathematicians guess before they prove — the analogical, fumbling middle that finished theorems hide. A rare look at the thinking before the thinking gets cleaned up.

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