Ludwig Wittgenstein Quotes

I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.

I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.

A elegantly executed proof is a poem in all but the form in which it is written.

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

Proof is an idol before whom the pure mathematician tortures himself.

A proof is a proof. What kind of a proof? It's a proof. A proof is a proof. And when you have a good proof, it's because it's proven.

It is hard to know what you are talking about in mathematics, yet no one questions the validity of what you say. There is no other realm of discourse half so queer.

Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.

I would prefer to just continue to speak about truth and to speak about what makes sense.

What is required of a working hypothesis is a fine capacity for discrimination.

The American public's a lot more sophisticated than we all give them credit for. And on complicated issues, I'm going to give them straight answers. And if it takes more than three minutes, I'm going to do it.

The wonderful thing about maths is it's a totally logical subject, and a pathway has been marked out. I think a lot of these things can be crystallised in something quite essential, that people can get. If I can't explain it, I realise that's probably because I don't completely understand it myself.

A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.

Don't leave inferences to be drawn when evidence can be presented.

if you do not appreciate the mathematics, you cannot see, among the great variety of facts, that logic permits you to go from one to the other

A mathematical theorem can be true whether or not it is realized in the world.

An ounce of algebra is worth of a ton of verbal argument.

… mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

In practical life we are compelled to follow what is most probable ; in speculative thought we are compelled to follow truth. A man would perish of hunger and thirst, if he refused to eat or drink, till he had obtained positive proof that food and drink would be good for him. But in philosophic reflection this is not so. On the contrary, we must take care not to admit as true anything, which is only probable. For when one falsity has been let in, infinite others follow.

I believe only in the mathematics.

Mathematics is the queen of the sciences.

Irrefragability, thy name is mathematics.

You could probably prove, by judicious use of logarithms and congruent triangles, that real life is a lot more like soap opera than most people will admit.

To be sure, mathematics can be extended to any branch of knowledge, including economics, provided the concepts are so clearly defined as to permit accurate symbolic representation. That is only another way of saying that in some branches of discourse it is desirable to know what you are talking about.