Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure.

Wir mussen wissen. Wir werden wissen. We must know. We will know. Inscribed on his tomb in Gilttingen.

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?

Mathematics is a game played according to certain simple rules with meaningless marks on paper.

How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.

The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms.

The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.