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.

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.

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.

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

How is error possible in mathematics?

Hypotheses are what we lack the least.

One does not ask whether a scientific theory is true, but only whether it is convenient.