“By refraining from reducing multiplication to addition we are enabled through these axioms to banish continuity, which is so difficult to fix precisely, from the logical structure of geometry.” — Hermann Weyl Copy Share Image
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… — Hermann Weyl Copy Share Image
For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number. — Hermann Weyl Copy Share
Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold. — Hermann Weyl Copy Share
The introduction of numbers as coordinates by reference to the particular division scheme of the open one-dimensional continuum is an act of violence whose… — Hermann Weyl Copy Share
“Our generation is witness to a development of physical knowledge such as has not been seen since the days of Kepler, Galileo and Newton,… — Hermann Weyl Copy Share
“the problem is then to develop a theory of invariance with respect to arbitrary linear transformations, in which, however, in contra-distinction to the case… — Hermann Weyl Copy Share
Before you generalize, formalize, and axiomatize there must be mathematical substance. — Hermann Weyl Copy Share
The whole is always more, is more capable of a much greater variety of wave states, than the combination of its parts. ... In… — Hermann Weyl Copy Share
Not only in geometry, but to a still more astonishing degree in physics, has it become more and more evident that as soon as… — Hermann Weyl Copy Share
“The goal of mathematics is the symbolic comprehension of the infinite with human, that is finite, means.” — Hermann Weyl Copy Share
God exists because arithmetic is consistent - the Devil exists because we can't prove it! — Hermann Weyl Copy Share
Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or… — Hermann Weyl Copy Share
Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind. — Hermann Weyl Copy Share
Our mathematics of the last few decades has wallowed in generalities and formalizations. — Hermann Weyl Copy Share
