George Pólya - Reasoning Quotes

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The efficient use of plausible reasoning is a practical skill and it is learned... by imitation and practice.... what I can offer are only examples for imitation and opportunity for practice.

George Pólya
Everyone knows that mathematics offers an excellent opportunity to learn demonstrative reasoning, but I contend also that there is no other subject in the usual curricula of the schools that affords a comparable opportunity to learn plausible reasoning.... let us learn proving, but also let us learn guessing.

George Pólya
Demonstrative reasoning penetrates the sciences just as far as mathematics does, but it is in itself (as mathematics is in itself) incapable of yielding essentially new knowledge about the world around us. Anything new that we learn about the world involves plausible reasoning, which is the only kind of reasoning for which we care in everyday affairs.

George Pólya
The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference.

George Pólya
The general or amateur student should also get a taste of demonstrative reasoning... he should acquire a standard with which he can compare alleged evidence of all sorts aimed at him in modern life.

George Pólya
In plausible reasoning the principal thing is to distinguish... a more reasonable guess from a less reasonable guess.

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

George Pólya
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
Geometry is the art of correct reasoning on incorrect figures.

George Pólya