The methods used to solve these “new” problems are, as I’ve already stated, highly amenable to brute-force approaches. It’s more of a computation problem [BitterLesson](http://www.incompleteideas.net/IncIdeas/BitterLesson.html). I’m again not surprised these kinds of problems got solved.
While these problems may be new, they employ very similar methods to those definitely used in previous competitive programming and Math Olympiad problems. I don’t think the author has really looked into the specifics of how AlphaGeometry and AlphaProof have come up with these solutions. It’s honestly disappointing to see that they were able to mislead such people (if he truly hasn’t looked into the specifics). It seems more like he wants to use his status to push a particular narrative.
I would bet a lot that this system will fail on almost any combinatorics problem at the moment...
Since this is a point that seemingly causes a lot of confusion and misunderstanding, I’ll try to find some time to write down my reasoning and thoughts in a more exhaustive post.
I would bet a lot that this system will fail on almost any combinatorics problem at the moment...
I don’t know if you guessed this prior to reading the post, but if so good guess:
AlphaProof solved two algebra problems and one number theory problem by determining the answer and proving it was correct. This included the hardest problem in the competition, solved by only five contestants at this year’s IMO. AlphaGeometry 2 proved the geometry problem, while the two combinatorics problems remained unsolved.
I’ve been wondering about this ever since I saw that sentence, so now I’m curious to see your post explaining your reasoning.
ETA: I just saw sunwillrise’s great comment on this and am now wondering how your reasoning compares
The methods used to solve these “new” problems are, as I’ve already stated, highly amenable to brute-force approaches. It’s more of a computation problem [BitterLesson](http://www.incompleteideas.net/IncIdeas/BitterLesson.html). I’m again not surprised these kinds of problems got solved.
While these problems may be new, they employ very similar methods to those definitely used in previous competitive programming and Math Olympiad problems. I don’t think the author has really looked into the specifics of how AlphaGeometry and AlphaProof have come up with these solutions. It’s honestly disappointing to see that they were able to mislead such people (if he truly hasn’t looked into the specifics). It seems more like he wants to use his status to push a particular narrative.
I would bet a lot that this system will fail on almost any combinatorics problem at the moment...
Since this is a point that seemingly causes a lot of confusion and misunderstanding, I’ll try to find some time to write down my reasoning and thoughts in a more exhaustive post.
I don’t know if you guessed this prior to reading the post, but if so good guess:
I’ve been wondering about this ever since I saw that sentence, so now I’m curious to see your post explaining your reasoning.
ETA: I just saw sunwillrise’s great comment on this and am now wondering how your reasoning compares