When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false.

Mathematics is the queen of science, and arithmetic the queen of mathematics.

In the last two months I have been very busy with my own mathematical speculations, which have cost me much time, without my having reached my original goal. Again and again I was enticed by the frequently interesting prospects from one direction to the other, sometimes even by will-o'-the-wisps, as is not rare in mathematic speculations.

Life stands before me like an eternal spring with new and brilliant clothes.

I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.

When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false.

We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.