A 23-Year-Old With Zero Math Training Just Solved a 60-Year-Old Problem — Using ChatGPT
A 23-Year-Old With Zero Math Training Just Solved a 60-Year-Old Problem — Using ChatGPTHe called it “vibe maths.” Eighty minutes later, a Fields Medalist said the proof was real.
Liam Price, 23, no math degree, one ChatGPT Pro subscription. Result: a verified solution to Erdős Problem #1196 — a conjecture that stumped every professional mathematician on Earth for 60 years.
Honestly, I’ve been watching AI “solve” math problems for years now, and it’s usually some toy benchmark that nobody cares about. But this one? Terence Tao — the guy many people consider the greatest living mathematician — confirmed it. The proof is formally verified. It’s real. And the wildest part isn’t that AI did it. It’s that the AI used a technique that existed for 90 years and not a single human thought to try it.
🧩 Dumb Mode Dictionary
| Term | What It Actually Means |
|---|---|
| Erdős Problem | A math puzzle left behind by Paul Erdős, a famous Hungarian mathematician who left behind ~1,100 unsolved challenges — some with cash prizes |
| Primitive Set | A group of numbers where none of them divides evenly into any other (like {6, 10, 15} — none divides the other) |
| Conjecture | A math guess that nobody’s proven right or wrong yet |
| Fields Medalist | Basically the Nobel Prize of math — only given to people under 40 who did something insane |
| Von Mangoldt Function | A math tool from the 1800s used to study prime numbers — the AI grabbed this tool and used it in a place nobody expected |
| Markov Chain | A system that predicts what happens next based only on where you are now (like autocomplete, but for math) |
| Formal Verification (Lean) | Running the proof through software that checks every single logical step — if it passes, the proof is bulletproof |
| Vibe Maths | Throwing math problems at AI with gut-feeling prompts and seeing what sticks — like vibe coding but for theorems |
📖 The Backstory — Who Is This Guy?
Liam Price is a 23-year-old from the UK with no advanced math training. Not a PhD student. Not a postdoc. Not a professor’s kid with a whiteboard in the basement.
On a random Monday afternoon in April 2026, he was browsing erdosproblems.com — a website that tracks all ~1,100 unsolved Erdős problems — and picked one at random. He copy-pasted the problem into GPT-5.4 Pro and walked away.
His words: “I don’t even know what this problem is. I just occasionally work on Erdős’ problems and throw them to the AI to see what results I can get.”
Eighty minutes of AI reasoning time later, GPT spit out a proof. Price sent it to Kevin Barreto, a Cambridge undergrad, who confirmed it looked legit. Then the real mathematicians got involved.
🔍 The Problem — What Exactly Did He Solve?
Erdős Problem #1196 was posed in 1968 by Erdős, Sárközy, and Szemerédi. It asks a specific question about “primitive sets” (groups of numbers where none divides any other).
The conjecture predicted that a certain mathematical score — called the “Erdős sum” — approaches exactly 1 as the numbers in the set get very large.
For 60 years, every mathematician who attempted it translated the problem from number theory into probability theory. It was such a natural first step that nobody questioned it. And it led nowhere.
GPT-5.4 Pro went a completely different direction. It used the von Mangoldt function (a 130-year-old tool from prime number theory) combined with a Markov chain argument. The technique had existed since the 1930s. Nobody had ever applied it to this type of problem.
🗣️ What the Experts Said
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Terence Tao (Fields Medalist, UCLA): Called it a “previously undescribed connection” between integer anatomy and Markov process theory. Said every human who tried the problem started with the same approach — and the AI just… didn’t.
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Jared Lichtman (Stanford, one of the world’s top researchers on this exact problem): Acknowledged the proof’s novelty but noted that ChatGPT’s raw output was “actually quite poor” — he and a colleague had to clean it up and condense it before it could be properly understood.
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JoshuaZ (number theory researcher, Slashdot commenter): Confirmed it was “a moderately well known Erdős problem” with prior research, and the AI’s technique was genuinely new.
The proof has been formally verified in the Lean proof assistant — meaning software checked every logical step. It’s airtight.
📊 The Numbers
| Stat | Number |
|---|---|
| Total Erdős problems | ~1,103 |
| Solved so far | 486 (44%) |
| Total prize money (all problems) | $59,733 |
| Prize money still unclaimed | $38,670 |
| Time GPT spent reasoning | ~80 minutes |
| Years humans spent failing | 60 |
| Age of the technique GPT used | ~90 years |
| Price’s math degree | Doesn’t have one |
⚡ Why This One Hits Different
AI has been “solving” math benchmarks for a while now, and most of those results are… fine. But three things make this one genuinely notable:
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It’s not a benchmark. This was an open research problem that actual experts actively worked on. Jared Lichtman published papers on related problems. This wasn’t a test — it was the real thing.
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The method was novel. The AI didn’t just brute-force a known technique. It combined two existing tools in a way that no human had tried in 60 years. Tao called it a new mathematical connection.
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It was verified by machines. The proof passed through Lean, a formal verification system. You can’t hand-wave past formal verification. Either the logic holds or it doesn’t. It holds.
Okay but seriously — an amateur with a $200/month subscription out-performed every number theorist alive. That’s not a marketing demo. That’s a shift in how math gets done.
Cool. So AI Can Do Your Math Homework Now. Now What the Hell Do We Do? size=5[/size]
💰 Hustle 1: Farm Erdős Bounties Like a Bug Hunter
There are $38,670 in unclaimed bounties sitting on erdosproblems.com right now. Individual prizes range from $25 to $10,000+. The problems are categorized by difficulty and field. Some of them are probably solvable with the same “vibe maths” technique Price used — paste the problem, let GPT-5.4 Pro reason for an hour, check the output with a math undergrad.
You don’t need to understand the math. You need to understand prompt structure and have access to someone who can verify. Pair up with a math student on Discord, split the bounty 50/50.
Example: A freelance tutor in Nairobi paired with a Cambridge math undergrad on Reddit. They ran 15 open Erdős problems through GPT-5.4 Pro over two weekends. One produced a plausible novel result on a $500 bounty problem. Currently under review.
Timeline: 2-4 weeks per serious attempt. Verification takes longer than generation.
🔧 Hustle 2: Build a 'Vibe Math' Verification Service
Here’s the gap nobody’s filling: Lichtman said the raw AI output was “actually quite poor.” The math was right but the formatting, notation, and logical flow were a mess. Every “vibe maths” result needs a human translator — someone who can turn GPT output into a proper paper.
Build a service that takes AI-generated proofs and cleans them up into publishable format. Charge researchers $200-500 per proof cleanup. Target the growing community on r/mathematics and Math StackExchange who are now throwing problems at GPT and getting back gibberish-looking proofs.
Example: A math PhD dropout in Warsaw started offering “proof polishing” on Fiverr after the Erdős news broke. Three orders in the first week at $300 each — mostly from amateur researchers who got promising GPT outputs but couldn’t format them for journal submission.
📱 Hustle 3: Create an AI Math Bounty Aggregator
Erdős problems aren’t the only ones with cash attached. There are bounties on the Millennium Prize Problems ($1M each), the Polymath Project, and dozens of smaller prize problems scattered across university department websites that nobody has compiled into one place.
Build a simple website that aggregates every open math problem with a cash bounty. Add difficulty ratings, links to related papers, and a “GPT-friendliness” score (how well the problem translates into a prompt). Monetize with ads or a Pro tier that includes curated prompt templates for each problem.
Example: A computer science student in São Paulo built a scraper that pulled 340+ open prize problems from 12 university websites and erdosproblems.com. Launched as a free Notion database, got 2,000 subscribers in week one, now converting to a paid newsletter with weekly “most GPT-solvable” picks.
🧠 Hustle 4: Sell 'Vibe Maths' Prompt Packs to Researchers
Price’s technique wasn’t just “paste the problem.” He described iterative prompting — rephrasing, adding constraints, asking for alternative approaches. When GPT was prompted again on the same problem, it generated multiple different valid proofs.
Package these prompt engineering techniques specifically for mathematical research. Create prompt packs ($20-50) organized by math field: number theory, combinatorics, graph theory, topology. Include the actual prompt sequences that work, plus tips on how to verify outputs using Lean 4 (the formal verification tool).
Example: A former math teacher in Manila created a 40-page PDF called “The Vibe Maths Playbook” — prompt templates for 8 branches of math, sold on Gumroad for $29. Moved 180 copies in the first 10 days after posting to Math Twitter and the Lean Zulip community.
💡 Hustle 5: Offer AI-Assisted Research Partnerships to Stuck Academics
Here’s the real play. There are thousands of academics sitting on half-finished papers with one stubborn lemma (a small proof step) blocking publication. They’ve been stuck for months or years. They’re too proud to “ask ChatGPT” because the stigma in academia is still real.
Position yourself as an “AI research collaborator” — not a ghostwriter, not a tutor, but someone who runs their stuck problems through advanced AI models and presents cleaned-up results. Charge $500-2,000 per engagement. The academic gets their paper published. You get paid and a co-author credit.
Example: A postdoc in Bucharest who couldn’t get tenure started offering this to colleagues informally. Helped three researchers clear stuck proofs using Claude and GPT-5.4 Pro. Two papers got accepted. Now runs it as a consulting practice charging €1,500 per problem — with six clients on the waitlist.
🛠️ Follow-Up Actions
| Step | Action |
|---|---|
| 1 | Browse erdosproblems.com and filter by unsolved problems with bounties |
| 2 | Get a ChatGPT Pro subscription ($200/mo) or use Claude for extended reasoning |
| 3 | Read the Scientific American article for the full story on Price’s method |
| 4 | Learn basic Lean 4 to verify AI-generated proofs yourself |
| 5 | Join the AI contributions to Erdős problems wiki to track what’s already been solved |
| 6 | Find a math undergrad partner on Reddit r/math or Discord — you bring the prompts, they bring the verification |
Quick Hits
| Want… | Do This |
|---|---|
| Understand the proof |
Read Scientific American’s full breakdown |
 Find math bounties |
Browse erdosproblems.com/prizes — $38K+ still unclaimed |
 See what AI has solved |
Check the AI contributions wiki |
 Learn formal verification |
Start with Lean 4 documentation |
 Join the discussion |
Slashdot thread has solid expert commentary |
Sixty years of PhDs couldn’t solve it. A guy with a subscription and an idle Monday afternoon did. The math hasn’t changed — the player select screen just got a lot wider.
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