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?

In the old days when people invented a new function they had something useful in mind. Now, they invent them deliberately just to invalidate our ancestors' reasoning, and that is all they are ever going to get out of them.

How is error possible in mathematics?

A small error in the former will produce an enormous error in the latter.

One geometry cannot be more true than another; it can only be more convenient.

Every good mathematician should also be a good chess player and vice versa.

This harmony that human intelligence believes it discovers in nature - does it exist apart from that intelligence? No, without doubt, a reality completely independent of the spirit which conceives it, sees it or feels it, is an impossibility. A world so exterior as that, even if it existed, would be forever inaccessible to us. But what we call objective reality is, in the last analysis, that which is common to several thinking beings, and could be common to all; this common part, we will see, can be nothing but the harmony expressed by mathematical laws.