The plain man is familiar with blindness and deafness, and knows from his everyday experience that the look of things is influenced by his senses; but it never occurs to him to regard the whole world as the creation of his senses.

Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.

Strange as it may sound, the power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.

Many an article that I myself penned twenty years ago impresses me now as something quite foreign to myself.

The biological task of science is to provide the fully developed human individual with as perfect a means of orientating himself as possible. No other scientific ideal can be realised, and any other must be meaningless.

I once knew an otherwise excellent teacher who compelled his students to perform all their demonstrations with incorrect figures, on the theory that it was the logical connection of the concepts, not the figure, that was essential.

Everyone is free to set up an opinion and to adduce proofs in support of it. Whether, though, a scientist shall find it worth his while to enter into serious investigations of opinions so advanced is a question which his reason and instinct alone can decide. If these things, in the end, should turn out to be true, I shall not be ashamed of being the last to believe them.