We must say that there are as many squares as there are numbers.

But let us remember that we are dealing with infinities and indivisibles both of which transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness.

Two truths cannot contradict one another.

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.

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

But, because my private lectures and domestic pupils are a great hinderance and intteruption of my studies, I wish to live entirely exempt from the former, and in great measure from the latter. ... in short, I should wish to gain my bread from my writings.

Take note, theologians, that in your desire to make matters of faith out of propositions relating to the fixity of sun and earth you run the risk of eventually having to condemn as heretics those who would declare the earth to stand still and the sun to change position-eventually, I say, at such a time as it might be physically or logically proved that the earth moves and the sun stands still.