1. “A scientist can hardly encounter anything more desirable than, just as a work is completed, to have its foundation give way.”
2. “The aim of scientific work is truth. While we internally recognise something as true, we judge, and while we utter judgements, we assert.”
3. “I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorem while the root dries into the depths.”
4. “Every good mathematician is at least half a philosopher and every good philosopher is at least half a mathematician.”
5. “Arithmetic has began to totter.”
6. “There is more danger of numerical sequences continued indefinitely than of trees growing up to heaven. Each will some time reach its greatest height.”
7. “Without some affinity in human ideas art would certainly be impossible; but it can never be exactly determined how far the intentions of the poet are realized.”
8. “Your discovery of the contradiction cause me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build arithmetic.”
9. “A philosopher who has no connection to geometry is only half a philosopher and a mathematician who has no philosophical vein is only half a mathematician.”
10. “A judgement, for me is not mere grasping of a thought, but the admission of its truth.”
