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

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

'Facts, facts, facts,' cries the scientist if he wants to emphasize the necessity of a firm foundation for science. What is a fact? A fact is a thought that is true. But the scientist will surely not recognize something which depends on men's varying states of mind to be the firm foundation of science.

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.

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

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

The thought: A logical inquiry