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Morris Kline on Mathematics

1908–1992 United States

← All quotes by Morris Kline

7 quotes

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)

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)

The history of arithmetic and algebra illustrates one of the striking and curious features of the history of mathematics. Ideas that seem remarkably simple once explained were thousands of years in the making.

Mathematics for the Nonmathematician (1967)

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.

Mathematical Thought from Ancient to Modern Times (1972)

The concept of the infinitely small is involved in the relation of points to a line or the relation of the discrete to the continuous, and Zeno's paradoxes may have caused the Greeks to shy away from this subject.

Mathematical Thought from Ancient to Modern Times (1972)

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.

Mathematical Thought from Ancient to Modern Times (1972)

Attribution

Quotes and notes from Wikiquote: Morris Kline (page history), available under CC BY-SA 4.0.