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

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.

You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.

With a thousand joys I would accept a nonacademic job for which industriousness, accuracy, loyalty, and such are sufficient without specialized knowledge, and which would give a comfortable living and sufficient leisure, in order to sacrifice to my gods [mathematical research]. For example, I hope to get the editting of the census, the birth and death lists in local districts, not as a job, but for my pleasure and satisfaction.

I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.

The higher arithmetic presents us with an inexhaustible store of interesting truths - of truths, too, which are not isolated, but stand in a close internal connection, and between which, as our knowledge increases, we are continually discovering new and sometimes wholly unexpected ties.

The Infinite is only a manner of speaking.