There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.

When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again.

His second motto: Thou, nature, art my goddess; to thy laws my services are bound.

Theory attracts practice as the magnet attracts iron.

By explanation the scientist understands nothing except the reduction to the least and simplest basic laws possible, beyond which he cannot go, but must plainly demand them; from them however he deduces the phenomena absolutely completely as necessary.

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

Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.