Hermann Weyl Math Quotations

Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.

For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.

The introduction of numbers as coordinates is an act of violence.

The constructs of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow mathematician interested in the constructs of his imagination. We cannot help the feeling that certain mathematical structures which have evolved through the combined efforts of the mathematical community bear the stamp of a necessity not affected by the accidents of their historical birth.

You can not apply mathematics as long as words still becloud reality.

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

Before you generalize, formalize, and axiomatize there must be mathematical substance.

Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind.

Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.

Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the universal organ for world understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation.