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.

I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths.

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

The thought: A logical inquiry

Arithmetic has began to totter.

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

What are numbers? What is the nature of arithmetical truth?