There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.

The deepest definition of youth is life as yet untouched by tragedy.

Not ignorance, but ignorance of ignorance, is the death of knowledge.

Life is complex in its expression, involving more than percipience, namely desire, emotion, will, and feeling.

Education with inert ideas is not only useless; it is above all things harmful.

It is a profoundly erroneous truism, repeated by all copy books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.

The true method of discovery is like the flight of an aeroplane. It starts from the ground of particular observation; it makes a flight in the thin air of imaginative generalization; and it again lands for renewed observation rendered acute by rational interpretation.