When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole; it is to intuition that we must look for it.

So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality.

Point set topology is a disease from which the human race will soon recover.

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

Geometry is not true, it is advantageous.

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

[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.