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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.

— George Pólya How to Solve It (1945)

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More quotes by George Pólya

Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements.

How to Solve It (1945)

The best of ideas is hurt by uncritical acceptance and thrives on critical examination.

How to Solve It (1945)

As for the human race, so for the human child.

Mathematical Methods in Science (1977)

We need heuristic reasoning when we construct a strict proof as we need scaffolding when we erect a building.

How to Solve It (1945)

People tell you that wishful thinking is bad. Do not believe it, this is just one of those generally accepted errors.

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Quote text and notes from Wikiquote: George Pólya (page history), available under CC BY-SA 4.0. Source quality and labels are our own summary of what Wikiquote records.