David Hilbert Quotes

Science is curiosity, testing and experimenting.

I am never satisfied until I can make a mathematical model of what I am studying. If I succeed in making one, I understand. If I cannot, I do not understand.

Science is facts.

Science is knowledge arranged and classified according to truth, facts, and the general laws of nature.

Take the situation of a scientist solving a problem, where he has certain data, which call for certain responses. Some of this set of data call for his applying such and such a law, while others call for another law.

I'm a mathematician, basically. What I do is look around for problems where I can find useful applications for mathematics. All I do, really, is the math, and other people have the ideas.

… new concepts arise from experiments and observations, and … the new concepts in turn lead to further experiments and observations.

Maths is the language of science.

Reason and science allow us to properly think about the necessary data that are required in order to answer a given question. This is precisely why the scientific method is the most powerful framework for understanding the world.

As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.

Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

Theory and fact are equally strong and utterly interdependent; one has no meaning without the other. We need theory to organize and interpret facts, even to know what we can or might observe. And we need facts to validate theories and give them substance.

It is a fatal fault to reason whilst observing, though so necessary beforehand and so useful afterwards.

Thus you see, most noble Sir, how this type of solution to the Königsberg bridge problem bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle.

In every department of physical science there is only so much science, properly so-called, as there is mathematics.

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

Our account does not rob the mathematicians of their science... In point of fact they do not need the infinite and do not use it.

I assert that, in any particular natural science, one encounters genuine scientific substance only to the extent that mathematics is present.

Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.

Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.

By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics. Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.

Theory can leave questions unanswered, but practice has to come up with something.

Mathematics is the gate and key to science.

By the help of God and with His precious assistance, I say that Algebra is a scientific art. The objects with which it deals are absolute numbers and measurable quantities which, though themselves unknown, are related to "things" which are known, whereby the determination of the unknown quantities is possible.

With me, everything turns into mathematics.