Big advance on simple-sounding math problem was a century in the making

I wish the math was explained better . I know the format is limited ands it will go over most people's heads but it does not do the matter justice.

I have an MSc in math but haven't managed to grasp modular forms, which is needed for the proof.

If anybody has a learning path or a primer recommendation for modular forms (assuming formal math education), I'd be very interested in reading more about it.

But as such I doubt it can be more accessible to everybody.