Hermann Weyl Quotes

Still more astonishing is that world of rigorous fantasy which we call mathematics.

Our account does not rob the mathematicians of their science... In point of fact they do not need the infinite and do not use it.

Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.

The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms.

Axiomatization is what one does last, it's rubbish. It's the hygiene of mathematics, axiomatization.

Goals and objectives are based on theories and foundations.

Mathematics is a place where you can do things which you can't do in the real world.

Math is sometimes called the science of patterns.

The universe is governed by science. But science tells us that we can't solve the equations, directly in the abstract.

The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.

One of the strangest features of string theory is that it requires more than the three spatial dimensions that we see directly in the world around us. That sounds like science fiction, but it is an indisputable outcome of the mathematics of string theory.

The essence of mathematics lies precisely in its freedom.

It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it.

I can see that, without being excited, mathematics can look pointless and cold.

We do not master a scientific theory until we have shelled and completely prised free its mathematical kernel.

Our mathematics of the last few decades has wallowed in generalities and formalizations.

The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.

Mathematics commands all my respect, but I have no use for engines.

The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used, but these have no more real bearing on the matter than those employed in genealogical tables have in explaining the laws of procreation.

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.

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

Where there is matter, there is geometry.

Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.

I assert that, in any particular natural science, one encounters genuine scientific substance only to the extent that mathematics is present.

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