(OP) The first of ten problems OpenAI solved was an improvement to the Cohn-Elkies bound. I briefly worked with Henry Cohn on sphere packing in undergrad. This topic is actually surprisingly accessible to the amateur mathematician so I thought I'd write up a primer and accessible description of the actual result.
How are they solving it? I would love to see the structuring to solve it.
There's a sketch of part of the proof in "the Mellin ansatz." I'd definitely recommend reading the sections before it, though, since they attempt to establish the more foundational connection between sphere packing and harmonic analysis (which is necessary to understand OpenAI's proof).