Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.

...one can hardly deny that mankind has a common store of thoughts which is transmitted from one generation to another.

A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press.

It is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot: but that hardly deserves the names of thought. It only becomes possible at all after the mathematical notation has, as a result of genuine thought, been so developed that it does the thinking for us, so to speak.

Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.

Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.

The thought: A logical inquiry