Quotes About Theorems

A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories.

How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!

You can learn to find unknowns in equations, draw equidistant lines and demonstrate theorems, but in real life there's nothing to position, calculate, or guess.

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.

We can think of the difference between math and science in terms of possible worlds. Math is concerned with truths that would hold in any possible world: given these axioms, these theorems will follow. Science is all about discovering the actual world in which we live.

The glacierscape called it up, the silent, shining tulle, the dreaming hats and cubes, the theorems and corollaries, that girl who had thought a wedding promise was binding as a law of physics.

ANALYTIC GEOMETRY (1637)

Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius.

The mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity.

I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths.

A mathematician is a machine for turning coffee into theorems.

Abstract ideas like equality and liberty have a spurious transparency, and can be used to derive pleasing theorems in the manner of Jean-Jacques Rousseau or John Rawls.

A mathematician is a person who can find analogies between theorems a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories.

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, and I shall use the language which is natural to a man who holds it.

he had made such and such a move, then I had such and such a winning combination in mind.' But the 'great game' of chess is primarily psychological, a conflict between one trained intelligence and another, and not a mere collection of small mathematical theorems.

Now we can see what makes mathematics unique. Only in mathematics is there no significant correction—only extension. Once the Greeks had developed the deductive method, they were correct in what they did, correct for all time. Euclid was incomplete and his work has been extended enormously, but it has not had to be corrected. His theorems are, every one of them, valid to this day.

Torricelli fully realized the advantages and disadvantages of the method of indivisibles; and he suspected that the ancients possessed some such method for discovering difficult theorems, the proofs of which they cast in another form either "to hide the secret of their method or to avoid giving occasion for contradiction to jealous detractors.

A mathematician is a device for turning coffee into theorems.

Plane geometry is sort of the key course where you learn about proving things and abstraction.

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.

He had abundant free time, which he spent working on a series of new theorems in the field of information theory.

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

The job of economic theorists is to prove theorems. The job of policy economists is to figure out which theorems to apply.

To a person of analytical ability, perceptive enough to realise that mathematical equipment was a powerful sword in economics, the world of economics was his or her oyster in 1935. The terrain was strewn with beautiful theorems begging to be picked up and arranged in unified order.