I am always interested in the development of AI within mathematics, particularly in number theory. I read on this website that AI has achieved a silver-medal level in solving IMO problems, which has caused quite a stir on social media. However, I need to know if this news is true. I am aware that some mathematicians are disappointed with AI's contributions to number theory. Is it true that AI achieves a silver-medal standard in solving International Mathematical Olympiad problems (IMO 2024UK)? I may ask also about Deepmind trustworthy as a source as @Federico Poloni commented below
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$\begingroup$ The link you report is from the website of Deepmind, the AI's creator. Are you asking for further confirmation? Do you wish to ask if Deepmind is trustworthy as a source? $\endgroup$– Federico PoloniCommented Jul 26 at 15:19
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11$\begingroup$ It depends on what you mean by silver medal! The website points out that the AI took more time to solve the problem than the human competitors had. Beyond that, there's not much to say. $\endgroup$– Will SawinCommented Jul 26 at 15:23
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$\begingroup$ @WillSawin, have you checked the AI solution to P1, P2, and P3 which is generated on their website using AlphaGeometry and AlphaProof? $\endgroup$– zeraoulia rafikCommented Jul 26 at 15:26
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3$\begingroup$ Also: Gowers notes that humans converted the questions into the form needed by the computer. $\endgroup$– Gerald EdgarCommented Jul 26 at 16:16
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3$\begingroup$ Separate from your concerns, I couldn't help but notice this statement at the webpage you linked to: "The IMO is the oldest, largest and most prestigious competition for young mathematicians, held annually since 1959." It only took a few seconds of googling to find a counterexample to the 1st claim (Eötvös-Kürschák competition) and the 2nd claim is ridiculous (each year only about $600$ people participate in the IMO). Maybe with appropriate qualifiers and context made explicit the sentence is true, but written as it is raises red flags for me that otherwise would not have been raised. $\endgroup$– Dave L RenfroCommented Jul 26 at 17:27
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The website says that the AI's "solutions were scored according to the IMO's point-awarding rules by prominent mathematicians Prof Sir Timothy Gowers, an IMO gold medalist and Fields Medal winner, and Dr Joseph Myers, a two-time IMO gold medalist and Chair of the IMO 2024 Problem Selection Committee."
The website also quotes Gowers: "The fact that the program can come up with a non-obvious construction like this is very impressive, and well beyond what I thought was state of the art."
There is no need to check the solutions that were verified by Gowers and Myers. Apart from the time control, AI can now solve IMO problems at silver medal level.
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10$\begingroup$ @zeraouliarafik I think there are two reasons why the question is downvoted. First, the question is not a mathematical one but a technological one. Second, the answer to the question is in the link you provided. $\endgroup$ Commented Jul 26 at 15:43
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5$\begingroup$ @zeraouliarafik I voted to close the question as opinion-based since the aspect of "is Deep Mind trustworthy" is pretty clearly a question of opinion. $\endgroup$ Commented Jul 26 at 15:49
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11$\begingroup$ @zeraouliarafik I haven't checked the proofs, but I am pretty sure people have. If someone was going to concoct a devious scheme to pretend to earn an IMO silver medal with AI when they really didn't, it wouldn't be by submitting invalid solutions but rather simply having humans come up with valid solutions and pretending their AI found them, which would be much harder to detect. The expertise of mathematicians would not be very valuable for determining if this happened, and MO is certainly not the right forum to discuss this. $\endgroup$ Commented Jul 26 at 15:59