IMO problems are specifically selected to be non-standard. For the previous 10 years, I served as the national coach of the USA International Math Olympiad team ( https://www.quantamagazine.org/po-shen-loh-led-the-u-s-math-team-back-to-first-place-20210216 ). During the IMO itself, the national coaches meet to select the problems that will appear on the exam paper. One of the most important tasks of that group is to avoid problems that have similarity to problems that have appeared anywhere before. During those meetings, national coaches would often dig up an old obscure math competition, on which a similar problem had appeared, and show it to the group, after which the proposed problem would be struck down.
So, this AI breakthrough is totally different from #GPT being able to do standardized tests through pattern-matching. It strikes at the heart of discovery. It’s very common for students to hit a wall the first time they try IMO-style problems, because they are accustomed to learning from example, remembering, and executing similar steps.
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
I saw someone claiming the opposite:
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