The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.

A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.

Mathematicians do not study objects, but the relations between objects.

It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, example, use language, and our language is necessarily steeped in preconceived ideas. Only they are unconscious preconceived ideas, which are a thousand times the most dangerous of all.

Intuition is more important to discovery than logic.

Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.

If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science is feared, it is above all because it can give no happiness? Man, then, can not be happy through science but today he can much less be happy without it.