To kick things off: what is ζ(s)? It’s a function from the complex plane to itself, defined as follows:

ζ(s) = 1/1^s + 1/2^s + 1/3^s + …

This might look like some kind of crazy math formula, but trust me it’s actually pretty cool. The reason why is because this function has a bunch of interesting properties that we can use to study the distribution of prime numbers and other arithmetic phenomena.
So let’s dive right in! One of the most famous results in number theory is the Riemann hypothesis, which states that all the zeros of ζ(s) (except for the trivial ones at -2, -4, …) lie on a certain line called the critical strip. This line runs from s = 1/2 + iT to s = 1/2 iT, where T is some large number that we’re not going to worry about right now (we can always come back and fill in those details later).
Now you might be wondering: why should we care about this critical strip? Well, for starters it turns out that the distribution of zeros on this line has a lot to do with the behavior of prime numbers. In fact, if we could somehow figure out exactly how many zeros there are in each small region of the critical strip (known as a “striplet”), then we would be able to make some pretty amazing predictions about the distribution of primes!
But here’s where things get tricky: calculating the number of zeros inside a given striplet is notoriously difficult. In fact, it’s one of the biggest unsolved problems in all of mathematics (and has been for over 150 years). So instead of trying to solve this problem directly, we’re going to take a more indirect approach and use some clever tricks to get around it.
One such trick is called “geometric deep learning,” which involves using neural networks to learn the distribution of zeros in the critical strip. This might sound crazy at first (and trust me I was skeptical too), but believe me when I say that this stuff actually works! In fact, some researchers have been able to achieve state-of-the-art results on this problem using deep learning techniques.
And if you want to learn more about this topic, I highly recommend checking out some of the resources listed below!