Theorems Quotes

“We often hear that mathematics consists mainly of 'proving theorems.' Is a writer's job mainly that of 'writing sentences?”

“Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems—general and specific statements—can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.”

“Economists often like startling theorems, results which seem to run counter to conventional wisdom.”

“The fundamental laws of the universe which correspond to the two fundamental theorems of the mechanical theory of heat.1. The energy of the universe is constant.2. The entropy of the universe tends to a maximum.”

“The third and, given due consideration, most probable of all my theorems, is that life is ordered by the principles of some religion so peculiar and obscure it has no followers, and none may fathom it, nor know the rituals by which to court its favor.”

“A dozen more questions occurred to me. Not to mention twenty-two possible solutions to each one, sixteen resulting hypotheses and counter-theorems, eight abstract speculations, a quadrilateral equation, two axioms, and a limerick. That's raw intelligence for you.”

“I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations’, are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards.”

“One can be enlightened about proofs as well as theorems. Without enlightenment, one is merely reduced to memorizing proofs. With enlightenment about a proof, its flow becomes clear and it can become an item of astonishing beauty. In addition, the need to memorize disappears because the proof has become part of your soul.”

“In the Principia Mathematica, Bertrand Russell and Alfred Whitehead attempted to give a rigorous foundation to mathematics using formal logic as their basis. They began with what they considered to be axioms, and used those to derive theorems of increasing complexity. By page 362, they had established enough to prove "1 + 1 = 2.”