Hermann Weyl 
Profession: mathematician.
Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
‘Mathematizing’ may well be a creative activity of man, like language or music, of primary originality . . .
My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful.
Nobody can say what a variable is.
The universe is an enormous direct product of representations of symmetry groups.
We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.
W. J. White Alfred North Whitehead Profession: mathematician.
Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.
I regret that it has been necessary for me in this lecture to administer such a large dose of four-dimensional geometry. I do not apologize, because I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. Things are what they are.
Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings.
The science of Pure Mathematics, in its modern developments, may claim to be the most original creation of the human spirit.
The study of mathematics is apt to commence in disappointment ... we are told that by its aid the stars are weighed and the billion of molecules in a drop of water are counted. Yet, like the ghost of Hamlet’s father, this great science eludes the efforts of our mental weapons to grasp it.
There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.
We think of the number “five” as applying to appropriate groups of any entities whatsoever – to five fishes, five children, five apples, five days ... We are merely thinking of those relationships between those two groups which are entirely independent of the individual essences of any of the members of either group. This is a very remarkable feat of abstraction; and it must have taken ages for the human race to rise to it.
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