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

— 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)

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)

For these proofs Heron gave new proofs that avoided extending the lines, in order to meet the objection of anyone who would deny that the space was available for the extension.

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.

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

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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.

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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.