Terence Tao

He just computed the first 100,000 prime numbers or so, hoping to find patterns.

And he did find a pattern, but maybe not the pattern he was expecting.

He found a statistical pattern in the primes that if you count how many primes there are, up to 100, 1,000,

they get sparser and sparser, but the drop-off in the density was inversely proportional to the natural logarithm of the range of numbers.

So he conjectured what we now call the prime number theorem.

The number of primes up to x is like x divided by the natural log of x. And he had no way to prove this.

It was data-driven.

So this was a conjecture.

It was revolutionary for its time because it was maybe the first really important conjecture of math that was statistical in nature.

So normally you talk about patterns like maybe the spacing between the primes has a certain regularity or something, but this was really something which it didn't tell you exactly how many primes there were in any given range.

It just gave you an approximation that got better and better as you...

went further and further out.

But it started the field of what we call analytic number theory.

But it was the first in many conjectures like this, many of which got proved, which sort of started consolidating the idea that the prime numbers actually didn't really have a pattern, that they behaved like random

random sets of numbers with a certain density.

I mean, they had some patterns, like they're almost all odd.

And they're not actually random.

They're what's called pseudo-random.

I mean, there's no random number generation involved in creating the prime numbers.

But