A metric ranks mathematical theorems by proof difficulty versus statement length

What's this about?

The authors define intrinsic interestingness as proof length relative to statement length, train a 27B model to predict proof difficulty and use it to select new formal conjectures.

What exactly is a self-expanding theorem library?

Instead of waiting for a human to nominate every goal, the system proposes statements, proves them, ranks which results may unlock future work and adds useful ones as premises for the next round.

Why does this matter?

1. The metric correlates with one downstream-utility measure in the tested formal setting.
2. Optimisation reduces substantial or complete Mathlib overlap from 91.9% to 30.6%.
3. Elegance, surprise and importance are richer than a single length ratio, so mathematician evaluation remains essential.