To be humane, we must ever be ready to pronounce that wise, ingenious and modest statement 'I do not know'.

They who depend upon manifest observations will philosophize better than those who persist in opinions repugnant to the senses.

And believe me, if I were again beginning my studies, I should follow the advice of Plato and start with the mathematical sciences, which proceed very cautiously and admit nothing as established until it has been rigorously demonstrated.

Philosophy itself cannot but benefit from our disputes, for if our conceptions prove true, new achievements will be made; if false, their refutation will further confirm the original doctrines.

The greatest wisdom is to get to know oneself.

I, Galileo, son of the late Vicenzo Galilei, swear that I never said that the prime numbers are useless. What I said was that you cannot count lunar craters by counting 2, 3, 5, 7.

One can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are methematical figures.