> AlphaZero plays games with (1) perfect information

I'm not sure why this matters? Everyone plays chess with perfect information. Both players see the entire board and all possibilities unlike, say, Scrabble or poker.

I think GP meant that in the sense of "AlphaZero can only play games that have perfect information". It's a restriction of the algorithm, not a statement about how AlphaZero approaches the games it plays.

This is why AlphaGo leveled up into AlphaZero playing Chess, and didn't learn to play Starcraft (yet).

ah yeah, i gotcha. my bad

They essentially hold for math, which is a pretty big deal.

What are the winning conditions for math?

A smaller proof using fewer axioms or other proofs than the current state-of-the-art.

Discovering new and "interesting" proofs. Don't ask me to define "interesting" in this context.

In the field of formal/machine proofs, nobody really cares about the length of the proofs because part of the point is the proofs are checked by the computer back to the basic axioms so you can trust the proofs are correct. Being able to discover long and ugly proofs to difficult theorems or coming up with new theorems would have endless applications.

It's exactly my original point that these goals are not well-defined in early 21st century maths.