Hacker News new | ask | show | jobs
by dwrensha 937 days ago
The IMO Grand Challenge is "formal to formal" -- a solver is given the problem specified in the Lean programming language, and must produce a solution in Lean. To see more concretely what this setup might look like, check out https://github.com/dwrensha/compfiles.

The AI MO prize is "informal to informal" -- a solver is given a problem in natural language and must produce a solution in natural language.

My belief is that the best way to get to "informal to informal" is to first solve "formal to formal", but not everyone thinks so.
1 comments
lupire 937 days ago
"Informal to formal" is harder than "formal to formal". These puzzle problems are quite simple (for computers) if you have a formalization.

"Informal to informal" is so far snake oil.

link
dwrensha 937 days ago
> These puzzle problems are quite simple (for computers) if you have a formalization.

That may be true someday, but it's not yet! That's exactly what the IMO Grand Challenge is about, and nobody has gotten close to solving it.

link
lupire 937 days ago
Do you have formal problems with formal solutions (so, you know the formalization is sufficiently complete) that cannot be found by existing (powerful) computer search techniques?
link
dwrensha 937 days ago
About half of the problems in Compfiles have complete solutions. They are marked by the checkmarks in the list at https://dwrensha.github.io/compfiles/index.html .

As far as I know, based on published systems like LeanDojo [1] and Magnushammer [2], computers today can only solve a small handful of the very easiest of these problems (like maybe Imo1959P1).

[1] https://leandojo.org/

[2] https://arxiv.org/abs/2303.04488

link