"Gauss... created one of the first mathematical data sets. He computed the first [~]100,000 prime numbers. ...He found a statistical pattern ...they get sparser and sparser, but the drop-off in the density was inversely proportional to the of the range of numbers. So he conjectured... the the number of primes up to x is... x divided by the natural log of x, and he had no way to prove this. It was a conjecture. It was revolutionary because it was maybe the first important conjecture of math that was statistical in nature. ...It just gave you an approximation that got better... as you went further... out. ...It started the field of... . ...[I]t was the first of many ...which ...started consolidating the idea that the prime numbers ...really didn't have a pattern, that they behaved like random sets of numbers with a certain density. They have some patterns. They're almost all odd. ...They're not actually random. They're... pseudorandom."
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Educators from the United StatesBloggers from the United StatesMathematicians from the United StatesMathematicians from ChinaMathematicians from Australia
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Terence Tao
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