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" "It so happens that one of the greatest mathematical discoveries of all times was guided by physical intuition.
George Pólya (December 13, 1887 – September 7, 1985) was a Hungarian mathematician and professor of mathematics at ETH Zürich and at Stanford University. His work on heuristics and pedagogy has had substantial and lasting influence on mathematical education, and has also been influential in artificial intelligence.
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The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. … Mathematics cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information.