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I finally reached the conclusion that mathematics was the study I was best fitted to follow, though I did not clearly see in what way I should turn the subject to account.

I was a mathematics major and really into math.

Regardless of any deviations, it was clear I was supposed to end up in math and physics.

Without troublesome work, no one can have any concrete, full idea of what pure mathematical research is like or of the profusion of insights that can be obtained from it.

I locate that special problem in a character and then try to understand it. That's the genesis of all my work.

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

Thus, the more succinctly a train of thought was expounded, and the more comprehensive the unity of its basic idea, the closer it would approximate to the prerequisites of the mathematical way of thinking.

A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.