David Hilbert Quotes

Skepticism may undermine beliefs, but never belief.

The capacity to reason is a special sort of capacity because it can lead us to places that we did not expect to go.

No problem can withstand the assault of sustained thinking.

It is evident that one cannot say anything demonstrable about the problem before having resolved these preliminary questions, and yet we hardly possess the necessary information to solve some of them.

When I was in school, I liked math because all the problems had answers. Everything else seemed very subjective.

When you have eliminated the impossible, whatever remains, however improbable, must be the truth.

To solve a problem it is necessary to think. It is necessary to think even to decide what facts to collect.

I have had my results for a long time: but I do not yet know how I am to arrive at them.

I throw a spear into the darkness. That is intuition. Then I must send an army into the darkness to find the spear. That is intellect.

I like thinking and being able to answer questions that are tough to answer. You have to try to figure out how to get a good answer and look intelligent.

Mathematicians always like a deceptively difficult problem.

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus 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.

Then you have a big problem, because a human is a thinking animal. If you don't think, you're not really a human.

I think you have to be left-brained, to a certain extent, to understand science. I can talk about it, but I can't do it.

It's strange how few of the world's great problems are solved by people who remember their algebra.

I really kind of pride myself on figuring stuff out pretty quickly but I couldn't, couldn't. I just had no idea.

Mechanical rules are never a substitute for clarity of thought.

I May Be Wrong but I Doubt It.

Bein logical gave me a reason to doubt

Mathematical reasoning may be regarded.

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

Sherlock Holmes observed that once you have eliminated the impossible then whatever remains, however improbable, must be the answer. I, however, do not like to eliminate the impossible.

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

A scientist may not be sure of the answer, but he's often sure he can find one. And that's a condition which is clearly not enjoyed by philosophy.

We are used to dealing with problems that have a solution and that can be solved in a finite period. But we're at the beginning of a long period of adjustment that does not have a clear-cut terminal point, and in which our wisdom and sophistication and understanding has to be one of the key elements.