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, I daresay, an aesthetic purpose.

There are no solved problems; there are only problems that are more or less solved.

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, I daresay, an aesthetic purpose.

Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.

Geometry is not true, it is advantageous.

When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks.

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