Erdos Problem 1196: Can AI now solve maths that no human can?

Summary

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More or Less – Erdos Problem 1196: Can AI now solve maths that no human can?

Podcast: More or Less
Host: Charlotte MacDonald (BBC Radio 4)
Date: May 16, 2026
Episode Theme: Can artificial intelligence solve mathematical problems previously unsolved by humans, and what does this new capability mean for mathematics and mathematicians?

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Episode Overview

This episode dives into the fascinating story of how artificial intelligence (AI)—specifically OpenAI’s GPT-5.4—has solved Erdos Problem 1196, a mathematical challenge that stumped human mathematicians for years. Host Charlotte MacDonald speaks with mathematicians Katie Steckles and Jared Duker Lichtman, as well as Liam Price, the amateur mathematician who prompted the AI into generating the solution. The episode explores the implications for the future of mathematics, collaboration between humans and AI, and how mathematicians themselves feel about these advances.

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Key Discussion Points and Insights

The Mystique of Unsolved Problems (01:42 – 04:33)

• Maths and Mystique: Charlotte MacDonald introduces the world of unsolved mathematical puzzles, highlighting their long-standing mystique in academia. Cites Fermat's Last Theorem as an example which was famously unsolved for centuries.
  • Notable quote: “Fermat’s Last Theorem… it was several hundred years before we actually got a resolution to this. And the mathematician that proved it was using areas of maths that didn't even exist in Fermat's time.”
    — Katie Steckles (03:26)
• Erdos and His Problems: The episode introduces Paul Erdos, a prolific, itinerant mathematician whose open problems have spanned all mathematical fields. His wandering, collaborative style set the scene for modern mathematical culture.
  • Over 1,200 Erdos problems exist, collected online as of 2023.

Primitive Sets & Erdos Problem 1196 (04:44 – 06:26)

• Primitive Sets Explained: Jared Duker Lichtman explains primitive sets as sets of numbers where no number divides another, a slightly more general concept than prime numbers.
  • “The numbers 4, 5, and 6 considered in isolation are a primitive set. You can’t divide four by five or six and get a whole number. And the same’s true for five and six.”
    — Charlotte MacDonald (05:26)
• The Elusiveness of Problem 1196: For years, mathematicians including Lichtman have puzzled over problem 1196—a specific question about primitive sets and how large their sums can be as numbers get big.

The AI Breakthrough (06:36 – 08:03)

• Liam Price's Role: Without formal training, British amateur mathematician Liam Price used GPT-5.4 Pro to attack problem 1196 with a carefully crafted prompt. After 80 minutes, the AI “spit out” a raw and unstructured—but apparently correct—proof.
  • “I used an AI from OpenAI to solve ERDOS problem 1196. So I came up with a clever prompt… and after about 80 minutes of thinking, it came out with a solution.”
    — Liam Price (07:05)
  • “After maybe about an hour or so of just kind of reading it through… it was pretty clear that it was correct and the idea was very nice.”
    — Jared Duker Lichtman (07:46)
• Verification: Price had GPT run its own solution through a separate instance for error checking, then passed it to mathematician friends who confirmed its validity.

The Significance of the Solution (08:03 – 08:50)

• A Milestone in AI Mathematics: While AIs have solved other Erdos problems before, problem 1196 was considered especially challenging, and the solution was celebrated by prominent mathematicians.
• Emotional Response: Rather than feeling upset at being “beaten” to the solution, Jared saw it as a cause for excitement and further research.
  • “Instantly I was very happy and actually started working on these other clusters of problems to use this idea.”
    — Jared Duker Lichtman (08:43)

What Does This Mean for Mathematicians? (08:50 – 10:06)

• AI as Colleague: Lichtman analogizes today’s AI to a “trusted colleague”—someone down the hall who sometimes comes up with wild yet valuable insights.
  • “I think right now we're in a position where AI can actually provide intuitions like a trusted colleague could…”
    — Jared Duker Lichtman (09:41)
• Human Expertise is Still Essential: Charlotte emphasizes that, unlike journalism or photography, only expert mathematicians are equipped to interpret and verify AI-generated proofs. AI can’t do it all alone.

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Memorable Quotes & Moments

• “You just want to know something is true… For certain problems, one really just wants to know the answer and have access to it, regardless of how it is obtained.”
  — Jared Duker Lichtman (08:56)
• “AI may not be turning up at your house in the middle of the night like Erdos and asking you to do its laundry, but it could still facilitate the kind of manic collaboration that the great man once did.”
  — Charlotte MacDonald (10:06)
• “It’s very strange. I mean, it's very strange. You know, I'd just kind of be sat here at my computer trying these problems, not really expecting anything to come of it. And having all of this kind of attention was unexpected, but I'm happy about it.”
  — Liam Price (08:03)

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Timestamps for Key Segments

• 01:42 – 04:33: Intro to famous unsolved math problems; Erdos’s biography and open problems
• 04:44 – 06:26: Explanation of primitive sets and Erdos Problem 1196
• 06:36 – 07:55: How AI solved Problem 1196; Liam Price’s process
• 07:55 – 08:50: Verification and significance of the breakthrough
• 08:50 – 10:06: Mathematicians’ reactions; collaboration between AI and humans

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Episode Tone & Final Thoughts

The conversation is friendly, accessible, and occasionally whimsical, with a sense of awe at both mathematical tradition and technological progress. Rather than pitting AI against mathematicians, the episode emphasizes potential for collaboration—framing AI as the latest in a long line of eager, eccentric collaborators in the grand tradition of Paul Erdos.

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Contributors:

• Charlotte MacDonald (Host, BBC Radio 4)
• Katie Steckles (Mathematician)
• Jared Duker Lichtman (Mathematician, Stanford)
• Liam Price (Amateur mathematician; AI enthusiast)

Contact:
Send number suggestions to [e-mail].

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Transcript

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[Charlotte MacDonald]

Hello and thanks for downloading the More or less podcast with a program that looks at the numbers in the news and in Life and in 50 year old maths puzzles. I'm Charlotte MacDonald. Ever since AI started creeping into our lives, people in certain professions have been worrying that it's come to steal their jobs. Software coders, insurance analysts and junior lawyers are all watching AI unfold with understandable trepidation. But recent events mean we might need to spare a thought for the select few whose job sits at the very pinnacle of academia. The brave souls who study pure mathematics. For hundreds of years, mathematicians have been straining their gigantic brains against fiendish maths problems that no one has yet been able to figure out. They ponder them, debate them, publish papers on them. Solving them can be a life's work. Then, on 13 April this year, AI appeared to solve a mathematical problem that has so far eluded mere human thinkers, known as ERDS problem 1196. Experts in the field were surprised, to say the least. But what is this problem has AI really solved It. And what does it mean for mathematics if it has unsolved maths problems have a certain mystique. The one you might have heard of is Fermat's last theorem, which was discovered in a handwritten note on the edge of a page in a textbook written by the 17th century mathematician.

[Katie Steckles]

He'd written, I have a solution, but it's too big to fit in the margin.

[Charlotte MacDonald]

That's mathematician Katie Steckels. And it wasn't solved until 1994.

[Katie Steckles]

It was several hundred years before we actually got a resolution to this. And the mathematician that proved it was using areas of maths that didn't even exist in Fermat's time.

[Charlotte MacDonald]

And while you might have only heard of one, there are plenty more with all kinds of strange names. The Collatz conjecture, the Riemann hypothesis.

[Katie Steckles]

Oh, there's loads. And we're finding more every day. Every area of maths has its sort of big questions.

[Charlotte MacDonald]

There are the Hilbert problems and the Millennium problems. But more recently another larger set of maths problems has been put together. These are known as the Erds problems and they were first posed by one of maths most frenziedly productive minds.

[Katie Steckles]

So Paul Erds was one of the most famous mathematicians in terms of being a story, right? He's a story to tell. He was what people call an itinerant mathematician. So he would spend almost all of his time traveling around, visiting conferences, going to maths events and he would stay at the houses of other mathematicians. I think there's an implication that he just kind of turned up and was like, here's my laundry, please feed me some food, etc. People were quite happy to host him and to talk to him.

[Charlotte MacDonald]

There are over 1200 ERDS problems and in 2023 they were collected together on a website so mathematicians could see which needed solving and share their proofs.

[Jared Duker Lichtman]

I first heard about this one particular Erds problem called the Erds primitive set conjecture when I was a senior in my undergraduate.

[Charlotte MacDonald]

That's Jared Duker Lichtman, mathematician and number theorist at Stanford University and kind of

[Jared Duker Lichtman]

completely fell in love with the problem.

[Charlotte MacDonald]

The Erdos problems we're talking about today are to do with primitive sets. You probably know about prime numbers, whole numbers which only divide by themselves and one, well, a primitive set's a bit like that, but where you pick out the numbers specifically so that the rule still works even though the numbers aren't necessarily prime. So for example, the numbers 4, 5 and 6 considered in isolation are a primitive set. You can't divide four by five or six and get a whole number. And the same's true for five and six. And that's all we're going to tell you about the maths in these Erdos problems. There's something to do with permitted sets. Everything else is way too complicated. Back to Jared.

[Jared Duker Lichtman]

You know, kind of on my own time and at nights I would still think about this problem and couldn't put it down. And I ended up solving it after four years of kind of never giving up on the problem.

[Charlotte MacDonald]

What Jarrod solved in four years was Erds problem 164, which he went on to use in his doctorate. But that wasn't the only problem he was interested in. There was a cluster of other related ERDS problems, including problem 1196. And he'd been thinking about that one too for all that time.

[Jared Duker Lichtman]

What happens if the numbers in a primitive set are all larger than X and you want to understand how the score can grow as X tends to infinity?

[Charlotte MacDonald]

And he kept on thinking about it and working on it for another three years, until last month he woke up to find an email on his computer.

[Jared Duker Lichtman]

I received a message saying that this essentially amateur mathematician had run GPT 5.4 pro on this problem and received output that that he thought could be a candidate solution to this problem. And when I received the message I was immediately very skeptical and I started reading through the output and again the output looked very, very raw and very unstructured.

[Charlotte MacDonald]

This raw and unstructured proof had been teased from AI chatbot ChatGPT by a 23 year old Brit without a maths degree.

[Liam Price]

My name's Liam Price and I used an AI from OpenAI to solve ERDS problem 1196. So I came up with a clever prompt and I gave it to the AI and after about 80 minutes of thinking, it came out with a solution. So I then passed it to another version of the model to say, here's the solution, please can you look at it and verify that it's correct of which it came out. And saying that it essentially couldn't find any errors in the argument, Liam sent

[Charlotte MacDonald]

the solution to his mathematician friend Kevin, who then sent it on to Jared to look over. Let's get back to Jarrod to see how he got on with it.

[Jared Duker Lichtman]

After maybe about an hour or so of just kind of reading it through and kind of sifting through what the raw output looked like, yeah, it was pretty clear that it was correct and the idea was very nice.

[Charlotte MacDonald]

The problem that Jared had been thinking about for seven years had been solved in one prompt by AI in under 80 minutes.

[Liam Price]

It's very strange. I mean, it's very strange. You know, I'd just kind of be sat here at my computer trying these problems, not really expecting anything to come of it. And having all of this kind of attention was unexpected, but I'm happy about it. Yes,

[Charlotte MacDonald]

AI has solved Erdos problems before, dozens of them, in fact. But problem 1196 is different. Mathematicians have been working on it for decades, and the proof that AI came up with has been celebrated by some of the greatest minds in the business. So was Jarrod upset that a chatbot had beat him to the punch?

[Jared Duker Lichtman]

You know, instantly I was very happy and actually started working on these other clusters of problems to use this idea.

[Charlotte MacDonald]

Jared is completely relaxed about the fact that AI is solving these difficult problems.

[Jared Duker Lichtman]

As a mathematician, you just, you just want to know something is true. If someone else solves a problem like a human solves a problem that you cared about, I don't think people would necessarily be also asking, you know, did your colleague solving the problem, like, are you upset that there's a solution? So for certain problems, one really just wants to know the answer and have access to it, regardless of how it is obtained.

[Charlotte MacDonald]

At the same time, what's very clear from this story is that AI could only work because there are people like Jarrod who actually understand pure mathematics and, and care about the solutions. It's not like photography or journalism where the public can make sense of the output themselves. You're always going to need mathematicians, even if AI keeps getting better at the solutions.

[Jared Duker Lichtman]

I think right now we're in a position where AI can actually provide intuitions like a trusted colleague could. So maybe you have someone down the hall who is coming up with crazy ideas. And I think we're at the stage now that for some part of the time, the output is going to actually bear fruit. And at the moment, right now, in 2026, we're at a point where we're kind of at a collaborator, kind of feedback.

[Charlotte MacDonald]

AI may not be turning up at your house in the middle of the night like Erdos and asking you to do its laundry, but it could still facilitate the kind of manic collaboration that the great man once did. That's it for this week. Thanks to Katie Steckles, Jared Duka Lichtman and Liam Price. If you've seen a number you think we should take a look at, email us on more or lessbc.co.uk until next time. Goodbye.

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