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.

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.

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.

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

The aim of scientific work is truth. While we internally recognise something as true, we judge, and while we utter judgements, we assert.

Having visual impressions is, of course, necessary for seeing things, but it is not sufficient. What must be added is not anything sensible. And it is precisely this that unlocks the outer world for us; for without this non-sensible something, each of us would remain locked up in his inner world.

There is more danger of numerical sequences continued indefinitely than of trees growing up to heaven. Each will some time reach its greatest height.