Hermann Weyl Quotes

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

Geometry is the art of correct reasoning from incorrectly drawn figures.

Mostly, I try to take a rational approach to life.

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

What I knew was I liked math and science, and I never wanted to memorize everything. I wanted to understand where it came from.

The main functions of intelligence, that of inventing solutions and that of verifying them, do not necessarily involve one another. The first partakes of imagination; the second alone is properly logical.

Definitions are the foundation of reason. You can't reason without them.

It's a simple exercise; a little logic, a little taste, and the will to cooperate.

Talk about rationality can get very confusing unless the things with which rationality deals are also included.

Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.

If a man's wit be wandering, let him study the mathematics; for in demonstrations, if his wit be called away never so little, he must begin again.

Thinking. A process by which I use my brain to make a rational decision.

Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.

You don't learn algebra with your blessed soul. Can't you look at it with your clear simple wits?

I agree that it's important to be of a virtuous nature, but I would also contend that if you had to choose between giving a man a noble disposition or teaching him to think clearly, you'd do better to teach him to think clearly. Too many problems in this world are caused by men with noble dispositions and clouded minds.

Logic is a large drawer, containing some useful instruments, and many more that are superfluous. A wise man will look into it for two purposes, to avail himself of those instruments that are really useful, and to admire the ingenuity with which those that are not so, are assorted and arranged.

With method and logic one can accomplish anything.

When I come upon anything-in Logic or in any other hard subject-that entirely puzzles me, I find it a capital plan to talk it over, aloud, even when I am all alone. One can explain things so clearly to one's self! And then, you know, one is so patient with one's self: one never gets irritated at one's own stupidity!

Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.

We can't avoid reasoning; we can only avoid doing it well.

Crime is common. Logic is rare. Therefore it is upon the logic rather than upon the crime that you should dwell.

The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.

That is the first thing I know for sure: (1.) If the questions don't make sense, neither will the answers.

We seem to have trouble with [critical thinking]. And our political system doesn't help.

I think it's important to reason from first principles rather than by analogy. The normal way we conduct our lives is we reason by analogy. [With analogy] we are doing this because it's like something else that was done, or it is like what other people are doing. [With first principles] you boil things down to the most fundamental truths…and then reason up from there.