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Because they [the ancient Greeks] feared infinite processes they missed the limit process. In approximating a circle by a polygon they were content to make the difference smaller than any given quantity, but something positive was always left over. Thus the process remained clear to the intuition; the limit process, on the other hand, would have involved the infinitely small.

— 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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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.