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, s….

In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer..

Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination..

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all….

Every phenomenon, however trifling it be, has a cause, and a mind infinitely powerful, and infinitely well-informed concerning the laws of nature cou….

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..

Intuition is more important to discovery than logic..

The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the conti….

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a ph….

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

I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with ….

A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it ….

What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only ….

Guessing before proving! Need I remind you that it is so that all important discoveries have been made?.

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

Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and,….

Experiment is the sole source of truth..

Hypotheses are what we lack the least..

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

It is not order only, but unexpected order, that has value..

It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that pe….