Hermann Weyl

“In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual mathematical domain.”

“A mathematician is a master of the art of changing the question.”

“The question of the ultimate foundations and the ultimate meaning of mathematics remains open; we do not know in which direction it will find its final solution.”

“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.”

“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.”

“My work has always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful.”

“Mathematics is the science of the infinite.”

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

“The objective world simply *is*, it does not *happen*. Only to the gaze of my consciousness, crawling upward along the life line of my body, does a section of this world come to life as a fleeting image in space which continuously changes in time.”

“A modern mathematical proof is not very different from a modern symphony.”

“It is the unity of logic and intuition which lifts mathematics to the level of art and brings it so close to philosophy.”

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