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.

I would say here something that was heard from an ecclesiastic of the most eminent degree: The intention of the Holy Spirit is to teach us how one goes to heaven, not how the heavens go.

Mathematics is the key and door to the sciences.

I wish, my dear Kepler, that we could have a good laugh together at the extraordinary stupidity of the mob. What do you think of the foremost philosophers of this University? In spite of my oft-repeated efforts and invitations, they have refused, with the obstinacy of a glutted adder, to look at the planets or the Moon or my glass [telescope].

The difficulties in the study of the infinite arise because we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this... is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.

Nature...does not act by means of many things when it can do so by means of a few.

If experiments are performed thousands of times at all seasons and in every place without once producing the effects mentioned by your philosophers, poets, and historians, this will mean nothing and we must believe their words rather than our own eyes?