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# p. 353. Proofs

• Timothy Gowers

### Abstract

‘Proofs’ is concerned with the concept of a proof, that is, an argument that puts a statement beyond all possible doubt. One of the most famous proofs in mathematics shows that the square root of two is irrational. It illustrates a technique known as reductio ad absurdum, or proof by contradiction. Further examples of mathematical induction and proofs are provided using the irrationality of the golden ratio, regions of a circle, Pythagoras' theorem, and the problem of tiling a square grid with the corners removed. Finally, three obvious-seeming statements that need proofs are outlined.

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