On July 23, 2026, Terence Tao — Fields Medalist and widely regarded as the world’s greatest living mathematician — shared a conversation he’d had with ChatGPT on social media. The topic: a potential counterexample to the Jacobian Conjecture, an open problem that has stumped mathematicians for nearly a century. The conversation was pushed to the front page of Hacker News, earning over 540 upvotes and 333 comments, drawing widespread attention from both the tech and mathematics communities.
Caption: Terence Tao is one of the most influential figures in contemporary mathematics. Image source: Wikipedia.
Who Is Terence Tao?
If you’re not familiar with the math world, here’s a quick introduction to a legendary figure. Terence Tao was born in Australia in 1975. He began teaching himself calculus at age 7, won an International Mathematical Olympiad gold medal at age 12 — still the youngest gold medalist in the competition’s history. He earned his Ph.D. from Princeton at 20, became a full professor at UCLA at 24, and won the Fields Medal — mathematics’ highest honor — at 31.
In mathematical circles, Tao is renowned not just for solving hard problems, but for his extraordinary versatility. He has made groundbreaking contributions across harmonic analysis, partial differential equations, combinatorics, number theory, and more. If any living mathematician comes closest to being a “universal genius,” it’s Terence Tao.
And yet, this mathematician — standing at the very peak of human mathematical ability — chose to ask ChatGPT for help. That fact alone is worth pondering.
The Jacobian Conjecture: A “Simple” Problem No One Can Solve
To understand this conversation, you need to know what the Jacobian Conjecture is. Let me try to explain in the simplest terms possible.
Imagine you have a map where every point has a formula telling you how to move. The Jacobian Conjecture asks: if this formula is always invertible near your starting point (you can always find your way back from any nearby position), is it also invertible across the entire map (you can find your way back from anywhere)?
The problem was first posed by mathematician Ott-Heinrich Keller in 1939 and was systematically formulated as the “Jacobian Conjecture” by Shreeram Abhyankar in the 1950s. It sounds intuitive enough, but mathematicians have been wrestling with it for nearly a century without a complete solution. Over the decades, countless partial results and near-proofs have been produced, but the full answer remains elusive.
What Tao discussed with ChatGPT was an analysis of a potential counterexample to the Jacobian Conjecture — if validated, it would directly disprove the conjecture altogether.
The Conversation: Human Intelligence Meets Machine Computation
In the publicly shared ChatGPT conversation, Tao used precise mathematical language to pose questions to the model, step by step guiding it through an analysis of whether a specific polynomial mapping constituted a counterexample to the Jacobian Conjecture.
Caption: Tao’s ChatGPT conversation page, titled “Jacobian Conjecture Counterexample.” The dialogue illustrates how a domain expert guides an AI through deep mathematical reasoning.
What makes the conversation remarkable: Tao wasn’t using ChatGPT as an “answer machine.” Instead, he treated it as a thinking partner — he’d pose directional questions, then follow up based on ChatGPT’s responses, drilling deeper, correcting, refining. The whole exchange felt like a professor mentoring a graduate student, except the “student” was a large language model.
HN user napoleoncomplex commented: “This is the second genuinely fascinating ChatGPT shared conversation I’ve seen today. The first was someone who falsified another conjecture by just repeatedly telling ChatGPT ‘continue.’ What an incredible time we live in.”
Another user, minimaxir, added: “For problems where most LLMs would give up, saying ‘continue’ actually works. The LLM fundamentally doesn’t know that something is impossible.”
The HN Reaction: Struck by the Density of Mathematical Terminology
The conversation sparked an intense discussion on Hacker News, and the most striking observation wasn’t about AI capabilities at all — it was a profound reflection on the barrier of mathematical language.
User WarmWash’s comment received widespread agreement:
“Mathematics has the most insane, impenetrable terminology system. I can usually keep my head above water in most STEM fields with some Googling and Wikipedia, but math… it just veers away from comprehensibility so fast. It’s insane.”
He went on to illustrate:
“Just one line from the conversation: ‘the special fiber is the associated graded ring… and this filtration admits three generators with sufficiently simple homogeneous lifts, then one can prove’ — in any other context I’d at least have some intuition about what’s being discussed, but math? No clue whatsoever.”
This comment highlights a fact often overlooked in tech circles: the language barrier in mathematics is far higher than in other scientific fields. A competent software engineer can quickly grasp the basics of TCP/IP, but faced with concepts like “graded ring,” “filtration,” and “homogeneous lifts” from algebraic geometry, even someone with a solid STEM background can feel completely lost.
AI as a “Thinking Partner,” Not an “Answer Machine”
A recurring theme throughout the HN discussion was this: the way Tao used ChatGPT represents the right approach to AI in high-level knowledge work.
User layer_x wrote: “Tao’s questions are extremely specific, guiding the AI in useful ways… this ‘symbiotic relationship’ (for lack of a better term) seems to be an emerging value proposition for AI.”
Another user, guywithabike, said: “What blows me away is that one of the smartest people on earth keeps asking questions, and the LLM keeps responding in that ‘yes, and if you think about it, it’s actually quite simple’ tone, like a professor mentoring a gifted student.”
But note a critical point: Tao knows exactly what he’s doing. The reason he can use ChatGPT effectively is his unparalleled depth of understanding in his field — this has nothing to do with “prompt engineering” tricks. As HN user bubblymagic put it: “The art of using AI is first and foremost mastery of the subject matter. I can use AI to write code because I have decades of programming experience. But I can’t use it for theoretical physics research because I can’t evaluate whether its answers are correct.”
This is the most thought-provoking aspect of Tao’s conversation — the AI didn’t “do” his math research for him. It became an efficient amplifier for his own thinking process.
The Other Side: Where Does AI Hit Its Limits?
Of course, the discussion also included sober voices.
Several commenters pointed out that ChatGPT showed clear limitations in the conversation — it would confidently produce partially incorrect derivations, sometimes requiring Tao to correct it multiple times. One anonymous user commented: “Even the most cutting-edge model is fully capable of getting lost in complex reasoning. You have to constantly intervene to stop it from charging down stupid paths.”
This raises a central question: if even Tao needs to repeatedly correct the model, how risky is it for ordinary users applying AI to specialized problems?
Furthermore, some noted that the conversation is “interesting” primarily because of Tao’s exceptional guidance skills. With an average person, the same conversation could veer entirely off course — the LLM would politely generate a bunch of plausible-looking but actually wrong “mathematical garbage.”
Caption: The lively Hacker News discussion about Tao’s ChatGPT conversation. The community engaged in deep exploration of AI’s role in mathematical research.
Conclusion: Genius’s Tool or Tool’s Pride?
Looking back at the entire episode, the most nuanced observation to me is this: the way Tao uses ChatGPT is fundamentally the same as how millions of programmers use Copilot or Cursor — guided by professional intuition, letting the AI handle information retrieval, initial screening, and derivation assistance, while the human expert always steers the ship.
HN user mnky9800nz put it well: “What surprised me most about seeing Tao’s conversation is that even he interacts with AI the same way I do in my own field — asking questions, following up, asking for clarification, asking for simplification. It’s almost identical.”
This might be the real definition of “expert” in the age of AI: someone who knows what questions to ask and how to tell whether an answer is trustworthy — that matters far more than “knowing all the answers.”
As for the Jacobian Conjecture itself — does this conversation ultimately lead to a verified counterexample? There’s no conclusion yet. But whatever the outcome, this experiment in “the world’s smartest human + the most advanced AI” has already shown us an intriguing glimpse of what the future could look like.
Reference Links
- Terence Tao’s Hacker News post sharing the ChatGPT conversation that sparked widespread discussion
- ChatGPT Shared Conversation Page: Jacobian Conjecture Counterexample
- Wikipedia: Jacobian Conjecture
- Wikipedia: Terence Tao biography
- Hacker News Community Discussion: Multi-angle debate on mathematical terminology density and AI as a thinking partner
- Fields Medal Foundation: Terence Tao award profile
