Why proofs?

June 4, 2011

« There is a traditional story about Newton: as a young student, he began the study of geometry, as was usual in his time, with the reading of the Elements of Euclid. He read the theorems, saw that they were true, and omitted the proofs. He wondered why anybody should take pains to prove things so evident. Many years later, however, he changed his opinion and praised Euclid. »

« We may say, with a little exaggeration, that humanity learned this idea [of proofs] from one man and one book: from Euclid and his Elements. In any case, the study of the elements of plane geometry yields still the best opportunity to acquire the idea of rigorous proof. »

« Geometry, as presented in Euclid’s Elements, is not a mere collection of facts, but a logical system. »

~ “How to solve it”, G. Polya.

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