Science is what we understand well enough to explain to a computer. Art is everything else we do.

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.

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

Mathematics is as much an aspect of culture as it is a collection of algorithms.

The man ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization.

Mathematics are well and good but Nature keeps dragging us around by the nose.

The shortest path between two truths in the real domain passes through the complex domain.

The purpose of computing is insight, not numbers.

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

The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry.

As long as algebra is taught in school, there will be prayer in school.

No human investigation can be called real science if it cannot be demonstrated mathematically.

Although he may not always recognize his bondage, modern man lives under a tyranny of numbers.

The mathematics are distinguished by a particular privilege, that is, in the course of ages, they may always advance and can never recede.

Mighty is geometry; joined with art, resistless.

One can't believe impossible things.

Nixon's motto was, if two wrongs don't make a right, try three.

There still remain three studies suitable for free man. Arithmetic is one of them.

But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not.

Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof.

A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence.

Now I feel as if I should succeed in doing something in mathematics, although I cannot see why it is so very important. . . The knowledge doesn't make life any sweeter or happier, does it?

A GREAT discovery solves a great problem but there is a grain of discovery in any problem.

It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.

It is clear that economics, if it is to be a science at all, must be a mathematical science.

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