Quotes About Theorems

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means....[A] machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.

Obviously, the final goal of scientists and mathematicians is not simply the accumulation of facts and lists of formulas, but rather they seek to understand the patterns, organizing principles, and relationships between these facts to form theorems and entirely new branches of human thought. For me, mathematics cultivates a perpetual state of wonder about the nature of mind, the limits of thoughts, and our place in this vast cosmos.

Many Rationals are obsessed with speculative enquiry, so their speech tends to be laced with assumptions and presuppositions, probabilities and possibilities, postulates and premises, hypotheses and theorems.

The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular.

MATHEMATICIAN

Negative numbers, equations involving unknowns, formulas, derivatives, integrals, and other concepts we shall encounter are abstractions built upon abstractions.

Godel continued drawing conclusions beyond the point where Einstein stopped.

A mathematician is a device for turning coffee into theorems.