Knowledge Quotes

"To know oneself is the beginning of wisdom."

"The art of doing mathematics consists in finding that special case which contains all the germs of generality."

"We must know. We will know."

"In mathematics you don't understand things. You just get used to them."

"A new field opens itself to a close study of any questions of absolute importance."

"Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts."

"I have always thought that the greatest danger comes from underestimating the vastness and subtlety of mathematical ideas."

"We want mathematics to be a unified edifice, not a collection of scattered facts."

"The abstract and the concrete are always intertwined in the mathematical process."

"The aim of mathematics is to understand the hidden harmony in all things."

"Mathematics is the gateway to all sciences."

"Every mathematical truth, once discovered, becomes part of the eternal heritage of mankind."

"A set is a Many that allows itself to be thought of as a One."

"What distinguishes the mathematician is the ability to think abstractly."

"Pure mathematics is the judge of its own creations."

"The concept of number is the obvious invariant suggested by the recognition of the identity that the given enumerates."

"A collection is a Many out of which nothing is selected."

"The infinite is not a number, but a concept."

"The mathematician creates not the truth, but the form of truth."

"Every discovery reveals ten new mysteries."

"I have shown that the infinite admits of different degrees."

"I don't believe in empiricism. I believe in the power of thought."

"Every logical system has its limits; this is the essence of my life's work."

"The mind sees what it is prepared to see."

"In every formal system, there are truths that cannot be spoken."

"To abandon the search for certainty is to begin genuine understanding."

"The incompleteness of any system reflects the incompleteness of human knowledge."

"Every answer generates new questions of equal complexity."

"In every proof lies an unproven assumption waiting to be discovered."

"The demand for certainty is one which is natural to man, but is nevertheless an intellectual vice."