Mathematics is the key and door to the sciences.

You cannot teach a person something he does not already know, you can only bring what he does know to his awareness.

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.

You may force me to say what you wish; you may revile me for saying what I do. But it moves.

Alas! Your dear friend and servant Galileo has been for the last month hopelessly blind; so that this heaven, this earth, this universe, which I by my marvelous discoveries and clear demonstrations had enlarged a hundred thousand times beyond the belief of the wise men of bygone ages, henceforward for me is shrunk into such a small space as is filled by my own bodily sensations.

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.

Vision, I say, is related to light itself. But of this sensation and the things pertaining to it, I pretend to understand but little; and since even a long time would not suffice to explain that trifle, or even to hint at an explanation, I pass over this in silence.