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

What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?

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?

Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.

But for harmony beautiful to contemplate, science would not be worth following.

. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.

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.