Whoever wishes to acquire a deep acquaintance with Nature must observe that there are analogies which connect whole branches of science in a parallel manner, and enable us to infer of one class of phenomena what we know of another. It has thus happened on several occasions that the discovery of an unsuspected analogy between two branches of knowledge has been the starting point for a rapid course of discovery.

Value is the most invincible and impalpable of ghosts, and comes and goes unthought of, while the visible and dense matter remains as it was.

The child which overbalances itself in learning to walk is experimenting on the law of gravity.

In matters of philosophy and science authority has ever been the great opponent of truth. A despotic calm is usually the triumph of error. In the republic of the sciences sedition and even anarchy are beneficial in the long run to the greatest happiness of the greatest number.

Charles Babbage proposed to make an automaton chess-player which should register mechanically the number of games lost and gained in consequence of every sort of move. Thus, the longer the automaton went on playing game, the more experienced it would become by the accumulation of experimental results. Such a machine precisely represents the acquirement of experience by our nervous organization.

Many persons entertain a prejudice against mathematical language, arising out of a confusion between the ideas of a mathematical science and an exact science. ...in reality, there is no such thing as an exact science.

As a general rule, it is foolish to do just what other people are doing, because there are almost sure to be too many people doing the same thing.