Quotes About Theorems

The academy is the architectural equivalent of what Husserl apostrophized as epoché—a building for shutting out the world and bracketing in concern, an asylum for the mysterious guests that we call ideas and theorems. In today's parlance, we would call it a retreat or a hideaway.

Everything is physics and math.

Mathematicians have, according to Wright, been "unreasonably successful" in finding applications to apparently useless theorems, and often years after the theorems were first discovered.

In particular the rules of logic tell us how to create, from the opening arrangement (the list of axioms), new arrangements (called "theorems").

A topologist enters a coffee shop, orders coffee and a doughnut, and is served. Preoccupied with topological theorems, he takes a bite out of his coffee cup and has to finish his thoughts in a nearby emergency ward. His mistake is somewhat understandable as a doughnut and coffee cup are topologically equivalent

If Nietzsche's existential relativism be accepted, then there will always be true things that do not fit any existing reality-tunnel, just as in mathematics Godel demonstrated that there will always be true theorems not deducible from any set of axioms. (See Chapter Two.)

myths are not just stories: they are narrative hypotheses, personified theorems that address the very nature of the world... Myths are really about the nature of nature...

Theorems are fun especially when you are the prover, but then the pleasure fades. What keeps us going are the unsolved problems.

There are no creeds in mathematics.

Geometry is the most complete science.

Without computers we will be stuck only proving theorems that have short proofs.

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

One may characterize physics as the doctrine of the repeatable, be it a succession in time or the co-existence in space. The validity of physical theorems is founded on this repeatability.

the 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 favour.

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.

Gödel's incompleteness theorems brought the second ending of the Grundlagenstreit. Where Hilbert had won the conflict in the social sense, he had lost it in the scientific sense.

In real life a right-angled triangle is very unlikely to have a square on its hypotenuse.

OS AXIOMAS, EMBORA BÁSICOS PARA TODAS AS PROVAS, SÃO ELES MESMOS NÃO-PROVADOS OU ATÉ MESMO NÃO PROVÁVEIS... SE OS AXIOMAS SÃO NEGADOS, AS PROPOSIÇÕES DEDUZIDAS A PARTIR DOS AXIOMAS NÃO EXISTEM, VISTO QUE NÃO HÁ NADA A PARTIR DO QUE ELAS POSSAM SER DERIVADAS; A VALIDADE DO SISTEMA INTEIRO TORNA-SE SUSPEITO... OS AXIOMAS DE UMA PESSOA DETERMINAM OS SEUS TEOREMAS.

mathematics as a tree with strong roots (the Axioms), a solid trunk (Rigorous Proof) and ever growing branches blooming with wondrous flowers (the Theorems).

Either of my contemporaries or of my successors, will, by means of the method when once established, be able to discover other theorems in addition, which have not yet occurred to me.

Projective geometry is all geometry.

I have found a very great number of exceedingly beautiful theorems.

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

Math does come easily to me, but I was always much more interested in what theorems imply about the world than in proving them.