algebra

geometry

logic

Rene Descartes

statistics

occupation / innovator as

mathematician

nationality

American

historian of mathematics

innovator in the field of

philosophy of mathematics

mathematics

is a method that enables man to reason efficiently. It mechanizes thought, and hence produces almost automatically results that may otherwise be difficult to establish. While geometry contained the truth about the universe, algebra offered the science of method.

Descartes... complained that Greek geometry was so much tied to figures "that is can exercise the understanding only on condition of greatly fatiguing the imagination." Descartes also deplored that the methods of Euclidean geometry were exceedingly diverse and specialized and did not allow for general applicability. Each theorem required a new kind of proof... What impressed Descartes especially was that algebra enables man to reason efficiently. It mechanizes thought, and hence produces almost automatically results that may otherwise be difficult to establish. ...historically it was Descartes who clearly perceived and called attention to this feature. Whereas geometry contained the truth about the universe, algebra offered the science of method. It is... paradoxical that great thinkers should be enamored with ideas that mechanize thought. Of course, their goal is to get at more difficult problems, as indeed they do.

is the truth about the universe, but algebra offers the science of method.

is the art of going wrong with confidence.

is responsible for recognizing and calling attention to the fact that algebra enables man to reason efficiently. It mechanizes thought, and hence produces almost automatically results that may otherwise be difficult to establish. Whereas geometry contained the truth about the universe, algebra offered the science of method.

Morris Kline

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Morris Kline