David Hilbert Quotes

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

I was a mathematics major and really into math.

In math, you're either right or you're wrong.

I accept no principles of physics which are not also accepted in mathematics.

In modern times the belief that the ultimate explanation of all things was to be found in Newtonian mechanics was an adumbration of the truth that all science, as it grows towards perfection, becomes mathematical in its ideas.

Geometry will draw the soul toward truth and create the spirit of philosophy.

Just as I had long suspected, a person didn't really need math for anything anyway. Maybe some people did. Some limited people.

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience

For hundreds of pages the closely-reasoned arguments unroll, axioms and theorems interlock. And what remains with us in the end? A general sense that the world can be expressed in closely-reasoned arguments, in interlocking axioms and theorems.

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of mathematics?

Heaven often protects valuable souls charged with great secrets, great ideas, by long shutting them up with their own thoughts.

The idea [of A Period of Transition album] was to get a break from everything for a while because I've been doing it for so long. I started doing it when I was 12.

But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer.

Chemistry has the same quickening and suggestive influence upon the algebraist as a visit to the Royal Academy, or the old masters may be supposed to have on a Browning or a Tennyson. Indeed it seems to me that an exact homology exists between painting and poetry on the one hand and modem chemistry and modem algebra on the other. In poetry and algebra we have the pure idea elaborated and expressed through the vehicle of language, in painting and chemistry the idea enveloped in matter, depending in part on manual processes and the resources of art for its due manifestation.

There's math, and everything else is debatable!

The global warming is going on. These are not single cases. These are all part of a general way we've been looking at the world. As long as we look at the world that way it's going to go on. Because the idea that the important thing is for some people get rich while the rest of the people work for them is very deeply dug in...

The physicist, in his study of natural phenomena, has two methods of making progress: (1) the method of experiment and observation, and (2) the method of mathematical reasoning. The former is just the collection of selected data; the latter enables one to infer results about experiments that have not been performed. There is no logical reason why the second method should be possible at all, but one has found in practice that it does work and meets with reasonable success.

If you ever have a new idea, and it's really new, you have to expect that it won't be widely accepted immediately. It's a long hard process.

Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.

All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.

In the study of ideas, it is necessary to remember that insistence on hard-headed clarity issues from sentimental feeling, as it were a mist, cloaking the perplexities of fact. Insistence on clarity at all costs is based on sheer superstition as to the mode in which human intelligence functions. Our reasonings grasp at straws for premises and float on gossamers for deductions.

The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.

Film is very much about sitting around and talking about ideas, and that's the stuff that I love, but I haven't experienced that yet in the television that I've done so far. It makes me long for movies again because, creatively, I always have a much more fulfilling experience there.

All the best ideas come out of the process; they come out of the work itself. Things occur to you.If you're sitting around trying to dream up a great idea, you can sit there a long time before anything happens.But if you just get to work, something will occur to you and something else will occur to you and something else that you reject will push you in another direction.