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Aristotle had considered the question of whether space is infinite and gave six nonmathematical arguments to prove that it is finite; he foresaw that this question would be troublesome.

— Morris Kline Mathematical Thought from Ancient to Modern Times (1972)

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Mathematics

More quotes by Morris Kline

The Pythagoreans associated good and evil with the limited and unlimited, respectively.

Mathematical Thought from Ancient to Modern Times (1972)

The Greeks failed to comprehend the infinitely large, the infinitely small, and infinite processes. They "shrank before the silence of the infinite spaces."

Mathematical Thought from Ancient to Modern Times (1972)

Fermat applied his method of tangents to many difficult problems. The method has the form of the now-standard method of differential calculus, though it begs entirely the difficult theory of limits.

Mathematical Thought from Ancient to Modern Times (1972)

Aristotle says the infinite is imperfect, unfinished, and therefore unthinkable; it is formless and confused. Only as objects are delimited and distinct do they have a nature.

Mathematical Thought from Ancient to Modern Times (1972)

Laplace created a number of new mathematical methods that were subsequently expanded into branches of mathematics, but he never cared for mathematics except as it helped him to study nature.

Mathematical Thought from Ancient to Modern Times (1972)

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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: Morris Kline (page history), available under CC BY-SA 4.0. Source quality and labels are our own summary of what Wikiquote records.