Hermann Weyl Quotes

Calculus is the outcome of a dramatic intellectual struggle which has lasted for twenty-five hundred years.

Taking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half.

With an absurd oversimplification, the 'invention' of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part.

The story of pi has been extensively told, no doubt because its history goes back to ancient times, but also because much of it can be grasped without a knowledge of advanced mathematics.

Though determinants and matrices received a great deal of attention in the nineteenth century and thousands of papers were written on these subjects, they do not constitute great innovations in mathematics.... Neither determinants nor matrices have influenced deeply the course of mathematics despite their utility as compact expressions and despite the suggestiveness of matrices as concrete groups for the discernment of general theorems of group theory.

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

All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.

The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future.

I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about.

Let no man who is not a Mathematician read the elements of my work.

The advancement and perfection of mathematics are intimately connected with the prosperity of the State.

As one who has taught mathematics at all levels of university instruction, I am well aware of the negative attitude of so many students toward the subject. There are many reasons for this, one of them no doubt being the esoteric, dry way in which we teach the subject. We tend to overwhelm our students with formulas, definitions, theorems, and proofs, but we seldom mention the historical evolution of these facts, leaving the impression that these facts were handed to us, like the Ten Commandments, by some divine authority.

There's substance to the point that sociological information is new. We have five years of information to weigh against 2,000 years of history or more.

I used my history degree about twice a year whether I needed to or not.

The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.

At first critics classified authors as Ancients, that is to say, Greek and Latin authors, and Moderns, that is to say, every post-Classical Author. Then they classified them by eras, the Augustans, the Victorians, etc., and now they classify them by decades, the writers of the '30's, '40's, etc. Very soon, it seems, they will be labeling authors, like automobiles, by the year.

Taste for things of the past evolves, doesn't it? What was a masterpiece a hundred years ago is no longer so today.

On the basis of my historical experience, I fully believe that mathematics of the 25th century will be as different from that of today as the latter is from that of the 16th century.

I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.

The world operates by number, by physical laws, expressed mathematically. If you know these, you will have a better grasp of things. And some possible job skills.

No artist knows in his own lifetime whether what he does will be the slightest good, because it takes at least seventy-five to a hundred years before the thing begins to sort itself out.

Arithmetic is a kind of knowledge in which the best natures should be trained, and which must not be given up.

The regret on our side is, they used to say years ago, we are reading about you in science class. Now they say, we are reading about you in history class.

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

The important thing to remember about mathematics is not to be frightened