A lot of excitement about AI in Math

Yesterday, someone found a small elliptic curve with rank >=30

y² + xy = x³ − 201769035260418549083594900060734240952308696994802735114305555 x + 1151107939141058565733479426024323225135665982951300586808823640527729578307228357301072889377

The idea:

- There is a nerd competition to find the smallest elliptic curve (y^2+axy = x^3 + bx) with the highest rank
- Elliptic curve rank = how many independent points you need to generate all its rational points
- Generating a rational point means there is a “sum” function on the elliptic curve that generates new points using existing ones

So basically, it’s like a competition for “how to write a program using the least amount of code,” but for mathematicians.

The result itself is completely pointless, because no one cares about high ranks, and it has no practical applications.

But it feels like a great example of the kind of research AI should eat alive.

Our brain is great at summing numbers (2+2=4), but bad at summing numbers on elliptic curves.

However, the problem is extremely formalizable

We can brute force and verify using AI because it’s all verifiable objects: the sum on curves is well defined

Rank 30 itself probably doesn’t matter