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Episode Notes
Researchers at OpenAI gave an AI model Erdős’ conjecture and walked away. When they returned, they discovered a breakthrough: The model had disproved the conjecture in a mathematical proof posted May 20 on OpenAI.com. “It’s a beautiful piece of mathematics that has been discovered,” says Melanie Matchett Wood of Harvard University, who contributed remarks to an accompanying paper in which outside experts reviewed the AI’s result . The discovery bolsters hopes that AI can contribute to scientific understanding. But the AI proof relied on perseverance rather than creative insight and has raised concerns about how mathematics will be done going forward.
On June 2 a group of experts published a declaration calling for tight guardrails around AI in mathematical research . As of June 5, the declaration has 1,590 signatures.
Reader Version
In a recent development, researchers at OpenAI tasked an AI model with addressing a longstanding mathematical question known as the Erdős unit distance problem. This problem, posed by the mathematician Paul Erdős in 1946, asks for the maximum number of pairs of points that can be placed on a plane such that each pair is exactly one unit apart. Despite decades of effort, no one had been able to prove or disprove Erdős’s conjecture, until now. The AI model produced a mathematical proof that disproved the conjecture, a result published on May 20 on OpenAI’s website.
Melanie Matchett Wood of Harvard University, who reviewed the AI’s work, described the proof as a “beautiful piece of mathematics” and saw it as a significant breakthrough for the field. The AI’s approach combined tools from algebra and number theory, two foundational areas of mathematics not typically associated with this geometric problem. Wood believes this cross application of mathematical tools could inspire new directions in research. However, she expressed skepticism about the AI’s role as a true breakthrough in artificial intelligence, suggesting that existing publicly available models might have been capable of producing the same result.
The AI’s proof relied more on perseverance, systematically exploring possibilities, rather than creative insight, which has sparked debate about the future of mathematical research. Some experts worry about how AI generated proofs might affect trust, credit, and access in the scientific community. In response, a group of mathematicians and researchers published a declaration on June 2 calling for strict guardrails around the use of AI in mathematical research. By June 5, this declaration had gathered nearly 1,600 signatures, reflecting widespread concern.
The host of Project Scientist, who shared their perspective on this news, welcomed the AI’s achievement as a positive step forward for humanity and scientific progress. They questioned the rationale behind calls for guardrails, suggesting that resistance to AI’s role in discovery might stem from ego or fear of losing credit rather than genuine issues. The host emphasized the importance of embracing AI’s ability to handle vast amounts of data and complex problems, arguing that such tools can accelerate understanding and benefit society. OpenAI clarified that the model used was a general purpose large language model trained for reasoning, without specialized mathematical software or guidance.
The model was prompted simply to either prove or disprove Erdős’s conjecture, and it chose to disprove it by finding a counterexample. This choice surprised some, as mathematicians had long believed the conjecture to be true, highlighting how AI might challenge established assumptions. While the AI’s proof marks a milestone, it also raises questions about the nature of mathematical creativity and the evolving role of human mathematicians. The host and experts alike recognize the potential for AI to transform research but also acknowledge the need for thoughtful discussion about how to integrate these tools responsibly.
The debate continues as the mathematical community grapples with balancing innovation, trust, and the human element in discovery.
Automatic Transcript
Welcome back to Project Scientist, where I, your host, will be attempting to become an independent scientist through documenting my own journey. Now, in this video, we will be talking more about AI, because that's what the news is about, but how AI is figuring out mathematics in fields where we have been trying to figure out the answers to the solutions for a very long time. Okay, in this article, it's figured out an Erdos quiz slash question, and AI has found that out. It seems as though people do not like the idea that AI is doing these things.
I think it's a great thing because it pushes humanity forward and further along the journey of living and helping others, but it seems as though now, people want guardrails for these exact things. I don't know what the problem is or the issue, but we're just going to read the article and see where the problem is, if there is an actual problem. If you're new here, please follow the podcast. Okay, follow the YouTube channel. As you can tell, it's on the YouTube. And yeah, let's just go ahead and make this into an interesting read. Sweet. All right, the problem here is that it says AI cracked an Erdos math problem. Sorry, not Ergos, Erdos. Now, experts want guardrails. All right, should be interesting to read.
The model disproved a famous conjecture raising questions about trust, credit, and access. Okay, think about placing dots on a flat surface. You want as many pairs as possible to be separated by the same distance, but any amount of dots, what is the greatest possible number of pairs that can be exactly that far apart? The question, what mathematicians call the unit distance problem seems simple. The answer is tricky. 80 years ago, in 1946, the famous mathematician Paul Erdos proposed what he thought was the answer, but no one had been able to prove or disprove his conjecture, at least not until now.
So if 80 years has gone by and not one single person or professional has found out the true answer, well, I think we're going to find out if maybe he was right or no, or if the AI just corrected him and it's like, he's wrong. But this is interesting in general, because it allows us to know how much of an information in terms of now that we've gotten right and that we've gotten wrong. The amount of data that AI uses is a lot, is vastly amount. It's probably too much for us to even try and think of at once, or even as a group. We need AI, we need machines to like collect these data and make an actual algorithmic precise answer. So I think it's good in general, but we'll read on.
Researchers at OpenAI gave an AI model Erdos conjecture and walked away. When they returned, they discovered a breakthrough. The model had disproved the conjecture in a mathematical proof posted May 20 on OpenAI.com. So even though no one could have actually, you know, disproved or proved 80 years ago, even up to now, I guess now we've got our final answer. Erdos was wrong. It's a beautiful piece of mathematics that has been discovered, says Melanie Matchett Wood of Harvard University, who contributed remarks to an accompanying paper in which outside experts reviewed the AI's result. The discovery bolsters hopes that AI can contribute to scientific understanding.
But AI proof relied on perseverance rather than creative insight, and has raised concerns about how mathematics will be done going forward. On June 2, a group of experts published a declaration calling for tight guardrails around AI in mathematical research. As of June 5, the declaration has 1,590 signatures. First off, what do they mean by a declaration calling for tight guardrails? What are the guardrails they were trying to guard? Because this in of itself is amazing. Are you trying to say you want more scientists to figure out more maths, but you don't want AI to do it? So you want to guard problems that's going to last for 80 years? Like, come on, man, let's really use our brains here.
I know glory and ego wants to be the forefront of discoveries, but come on, let's actually do stuff for the humanity of the world and not think about ourselves and rewards and so on and so forth. A breakthrough for math, but maybe not for AI. The AI model that produced this result isn't publicly available yet. So, OpenAI, ChatGPT and all that stuff. So it's definitely not 5.5 on the extra high tier. So if you've got that, don't think that's what, you know, they used. But OpenAI says it is a general purpose, large language model trained for reasoning. It did not use any math specific tools or software. And we didn't guide the model in any particular way, says OpenAI researcher Sebastian Bubeck.
The original prompt composed by AI described the conjecture and instructed the model that a complete solution must either prove or disprove it. Mathematicians had believed the conjecture was true, yet the model tried to disprove it instead. I'm a bit puzzled here because it said that there was no actual answer for 80 years. So I don't know why mathematicians believe the conjecture was true. So then how many things that's informationally out there that we as citizens, normal citizens think is true when it's not really true? Is gravity really 9.8? Do you know what I'm saying? What's going on? Do you know what I'm saying? Yeah, yet the model tried to prove it instead.
Wood sees the result as a breakthrough for mathematics. The AI came up with a counter example using tools from two of the oldest and most foundational mathematical fields, algebra and number theory. It seems that these areas shouldn't have anything to do with this geometry question, Wood says. But the result, in quotations, shows that tools from one part of mathematics can be applied really fruitfully in this other area of mathematics. She thinks this result will inspire mathematicians to think of new ways to apply those same tools. I fully agree. I think it should. She's not convinced, however, that this is a breakthrough in artificial intelligence.
When she read the solution, it seemed to her that the latest publicly available AI models could have come up with it, but he didn't. Do you know what I'm saying? In fact, one researcher posted on X that he had reproduced the proof using a publicly available model.
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