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Mathematics succeeds in dealing with tangible reality by being conceptual. We cannot cope with the full physical complexity; we must idealize.

— George Pólya Mathematical Methods in Science (1977)

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Mathematics

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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Anyone who believes exponential growth can go on forever in a finite world is either a madman or an economist.

Kenneth Boulding to Kenneth Boulding in: United States. Congress. House (1973)

If the doors of perception were cleansed, everything would appear to man as it is: infinite.

William Blake The Marriage of Heaven and Hell (1790)

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing.

Bertrand Russell

The land of easy mathematics where he who works adds up and he who retires subtracts.

Núria Añó

Attribution

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.