Some years ago I was struck by the large number of falsehoods that I had accepted as true in my childhood, and by the highly doubtful nature of the whole edifice that I had subsequently based on them. I realized that it was necessary, once in the course of my life, to demolish everything completely and start again right from the foundations if I wanted to establish anything at all in the sciences that was stable and likely to last.

Nothing is more fairly distributed than common sense: no one thinks he needs more of it than he already has.

Thus each truth discovered was a rule available in the discovery of subsequent ones.

For each of us there is a set limit to our intellectual powers which we cannot pass.

Reason is nothing without imagination.

Archimedes, that he might transport the entire globe ... demanded only a point that was firm and immovable; so also, I shall be entitled to entertain the highest expectations, if I am fortunate enough to discover only one thing that is certain and indubitable.

Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.