Twenty-Five Thousand Groups, and the Ones Nobody Can Reach
There is a question in mathematics that has been open since the 1800s, and for one slice of it you can now attack it by search. I built a factory that produced degree-24 polynomials, submitted ten thousand scoreable pairs to a competition organised with the LMFDB and Terence Tao, and finished 54th of 256 with a score of 2.36. The interesting part is not the rank. It is that I can prove, with numbers, exactly why the score was small, and the answer says something about how these searches should be run.