Mathematics is the science which uses easy words for hard ideas.

Mathematics is the science which uses easy words for hard ideas.

Mathematics and the Imagination, New York: Simon and Schuster, 1940.

[W]e have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed.

Mathematics and the
Imagination, New
York: Simon and
Schuster, 1940.

Mathematics is man's own handiwork, subject only to the limitations imposed by the laws of thought.

Mathematics and the Imagination, New York: Simon and Schuster, 1940.

The purpose of models is not to fit the data but to sharpen the questions.

11th R. A. Fisher
Memorial Lecture,
Royal Society, 20
April 1983.

We [he and Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury.

Paul Halmos:
Celebrating 50 Years
of Mathematics.

All human knowledge thus begins with intuitions, proceeds thence to concepts, and ends with ideas.

Quoted in Hilbert's Foundations of Geometry.

Mathematics is not yet capable of coping with the naivete of the mathematician himself.

Sociology Learns the Language of Mathematics.

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.

The Mathematical Intelligencer, v. 13, no. 1, Winter 1991.

It is true that a mathematician, who is not somewhat of a poet, will never be a perfect mathematician.

Karl Weierstrass

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