– Can anyone describe Riemann hypothesis? You can ELI15 also. I am okay with it. I know it’s kind of impossible but still asking the question. So any mathematician here.
In: Mathematics
First, let’s talk a bit about the motivation. Prime numbers are really important in math. They’re the building blocks that make up all the other whole numbers. A natural question you might ask is, “How many prime numbers are there?” A few thousand years ago, the Greeks figured out there are infinitely many. The next question you might ask is, “How many are there below 100? Or 1000? Or 1000000? Or more generally, how many primes are there below x?”
The answer, it turns out, is pretty close (in a very precise sense) to x/log(x). And we can do better than that. If you play some tricks with integrals, you can come up with the Li(x) function, which is an even better approximation. If we play with these approximations, a certain function, known as the Riemann zeta function, shows up a lot. And so to really understand the prime numbers, we want to understand the zeta function.
One of the best ways to understand a function is to know where it evaluates to 0. It’s not too hard to show zeta(x) is 0 when x is a negative even number. But if we allow for complex numbers as inputs, there are other places where zeta(x) is 0. In particular, the Riemann Hypothesis says that all of those are complex numbers with real part 1/2.
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