Philosophy
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I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. . . But after some twenty years of arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.

Bertrand Russell

In the late 1800’s mathematicians embarked en masse on a program to do for arithmetic what Euclid had done for geometry 2000 years before. They decided it was about time to systemically lay out and prove all the theorems of mathematics which had grown up haphazardly over the centuries. Many of these theorems had never been properly proved, often because they seemed self-evident. They expected that ahead of them lay a short and rather routine quest. Actually, it was the beginning of a futile hunt for a nonexistent treasure.

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