Mathematician solves algebra's oldest problem using intriguing number sequences

This has been discussed before. I understand that it is not a new result and also not an exact result: A method for constructing an infinite sequence of approximations to the exact solution. It has been long proven that exact solutions do not exist above a certain degree.

Interesting, but I wish they went deeper into the geodes and how it all actually works. ACM might do a more technical writeup.