If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living

Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.

All of mathematics is a tale about groups.

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

Experiment is the sole source of truth.

Tolstoi explains somewhere in his writings why, in his opinion, “Science for Science's sake” is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection. Is it not better to be guided by utility, by our practical, and more especially our moral, necessities?

It is far better to foresee even without certainty than not to foresee at all.