[gus_massa]

From a comment by j2kun https://news.ycombinator.com/item?id=49000833 , someone asked Fable and there was an almost counterexample in 2d but it uses division too. [Instead of f=x^2+7xy they have something like f=x^2+7x/y so it's not a polynomial.] As far as I know, nobody know what trick to make to avoid that division. It looks like the new trick was to use a third variable to avoid the division. Note that the implementation of the trick is not straightforward. The almost counterexample was sitting around for almost 30 years, and nobody knew how to fix it.

From another old comment, someone else was trying to find a counterexample with 16 variables using a computer to make thousands of attempts and failed. So it's far from obvious that the trick to add a variable solves the problems.

[dumpstate]

Right. Nothing obvious in public. Where I'm heading is that all labs pay for solutions to software engineering task and never publicize those, I assume they do the same with maths?

[gus_massa]

>>> What’s a chance the counterexample was in the training?

My guess is it was not in the training. Only the 2D "almost" countraexample was in the training, but it was not clear how to fix it.

It's not clear how much steering Levent Alpöge did to get the result. He said he did during the final match of the World Cup, but he is from Turkey and living in USA and the game sadly was quite one sided, so I guess he does not care too much. So my guess is that he had a long chat with Fable.

I'm guessing too much, but if I can guess one more time the problem was probably too difficult to get solved by Levent Alpöge alone and by Fable alone, and it's a genuine Centaur solution.