Quotes on Mathematics

In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.

If a man's wit be wandering, let him study the mathematics; for in demonstrations, if his wit be called away never so little, he must begin again.

In mathematics there are no true controversies.

I confess, that very different from you, I do find sometimes scientific inspiration in mysticism ... but this is counterbalanced by an immediate sense for mathematics.

If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

I am interested in mathematics only as a creative art.

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?

Having been the discoverer of many splendid things, he is said to have asked his friends and relations that, after his death, they should place on his tomb a cylinder enclosing a sphere, writing on it the proportion of the containing solid to that which is contained.

I also ask you my friends not to condemn me entirely to the mill of mathematical calculations, and allow me time for philosophical speculations, my only pleasures.

As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

A great deal of my work is just playing with equations and seeing what they give.

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

[I]f in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics, in so far as disposed through it we are able to reach certainty in other sciences and truth by the exclusion of error.

[In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory.

Science attempts to find logic and simplicity in nature. Mathematics attempts to establish order and simplicity in human thought.

Mathematics is an obscure field, an abstruse science, complicated and exact; yet so many have attained perfection in it that we might conclude almost anyone who seriously applied himself would achieve a measure of success.

Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don't look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.

The mere man of pleasure is miserable in old age, and the mere drudge in business is but little better, whereas, natural philosophy, mathematical and mechanical science, are a continual source of tranquil pleasure, and in spite of the gloomy dogmas of priests and of superstition, the study of these things is the true theology; it teaches man to know and admire the Creator, for the principles of science are in the creation, and are unchangeable and of divine origin.

The life and soul of science is its practical application, and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in the earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind.

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.