QWE AI Academy Everyone keeps asking the same thing: if Terence Tao – a Fields medalist – needs ChatGPT to understand a math paper, what am I supposed to do with it? That’s the wrong question. The right one is: how did he use it, and can I copy that?
Tao’s ChatGPT conversation about the Jacobian Conjecture counterexample dropped on July 21, 2026, linked from his blog post “A digestion of the Jacobian conjecture counterexample.” Within hours it was all over X and Hacker News. The math is hard. The technique isn’t. This post walks you through what he actually did with ChatGPT, why the usual “prompt engineering” advice misses the point, and how to run the same workflow on any paper that’s too hard for you.
The question people are actually asking
The share link shows Tao asking ChatGPT to help him digest an explicit polynomial map that Anthropic researcher Levent Alpöge found using the model Fable 5 in July 2026. It’s a three-variable polynomial whose Jacobian determinant is identically -2, yet the map is three-to-one – which shouldn’t be possible if the Jacobian Conjecture (posed by Ott-Heinrich Keller in 1939) were true.
So the question people keep asking: “Can I just paste hard papers into ChatGPT and get Tao-level understanding?” No. But you can get closer than you think if you copy his method instead of his vocabulary.
Why the standard “summarize this paper” prompt fails
Most people paste a hard PDF in, ask “explain this to me,” get a bland summary, close the tab. The summary feels informative. You learned nothing – because you never hit the actual obstruction, the specific step where the paper stops making sense for you.
Tao doesn’t do that. His chat reads like a mathematician talking to a well-read colleague: he proposes a reformulation, checks whether it’s equivalent, asks about a specific geometric object, pushes back when the reply doesn’t quite fit. It’s a dialogue about one specific stuck point. Not a request for a summary.
The evidence this matters: a separate mathematician, Andy Jiang, prompted ChatGPT independently and – per commenters on Secret Blogging Seminar – got “almost an elegant geometric construction” (a P¹ × Sym²(P¹) → Sym³(P¹) formulation) that was cleaner than what Tao’s own chat produced. Same model. Different prompt. Very different output. The prompt phrasing mattered more than who was typing.
The workflow to actually copy
Extracted from the shared chat – a checklist you can run on any paper:
- Read the paper first. Get stuck. Note the exact sentence where you stopped. Not the whole section – the sentence.
- State the setup back to ChatGPT in your own words. Definitions included. This exposes your misunderstanding before you ask anything.
- Propose a reformulation. Even a wrong one. “Isn’t this equivalent to saying X?” Tao does this constantly.
- Ask ChatGPT to verify or break your reformulation. This gives the model something concrete to check instead of a vague “explain.”
- When it hand-waves, call it out. “That step feels magical. What’s the underlying reason?” – this is where Tao repeatedly pulls out real substance.
- Recontextualize. Ask what standard object or construction this resembles. This is how you build the mental library that makes the next paper faster.
No “act as a math professor,” no role prompt, no elaborate system message. Direct back-and-forth on one specific technical obstruction.
There’s something worth sitting with here. Tao has spent decades building the pattern recognition that tells him which reformulations are worth trying. The chat looks effortless because of everything that isn’t in the chat. What you’re actually copying is a shape – a questioning posture – not a shortcut. That shape can scale down to wherever you are right now. It’s the same shape whether the paper is algebraic geometry or intro real analysis.
A worked example on the Jacobian chat itself
Open the share link in one tab. Before reading ChatGPT’s reply to any of Tao’s questions, try to answer it yourself. Then compare.
The setup: the counterexample is a polynomial map from C³ to C³ with constant Jacobian -2, but it collapses three distinct points to the same output. The “stabilization” trick extends this to every dimension n ≥ 3 by adjoining identity coordinates. The n = 2 case (the plane) is still open as of July 2026. The n = 1 case is trivial.
Ask yourself before ChatGPT tells you:
1. Why does the stabilization trick preserve the Jacobian being -2?
2. Why can't you run stabilization in reverse to shrink C³ down to C²?
3. What's the geometric meaning of "three points map to the same output"?Now scroll to ChatGPT’s replies. The model’s answers are only useful because Tao’s questions were specific. Change the question and the reply changes. The lesson is in the question shape, not the model output.
One more thing: keep a scratchpad open next to the shared chat. Every time Tao asks a question, pause. Write your guess. Then read the reply. That gap – between your guess and the answer – is where the learning actually happens.
Three things about ChatGPT shared links that nobody mentioned
The link is frozen.Per OpenAI’s Shared Links FAQ: “Messages you add to the original chat after creating or updating the link are not automatically added.” So if Tao continues the conversation privately, you’ll never see it unless he creates a new link. Save a local copy if you care.
You can adopt it. Any ChatGPT account (free tier works) lets you continue a shared chat as your own private thread – all of Tao’s context preserved, your questions added on top. The best study aid nobody mentions: you inherit a Fields medalist’s setup and run your own experiments from there.
Images break sharing on Enterprise. The Enterprise Shared Links FAQ is blunt about it: uploaded or generated images make the share fail entirely. Text-only chats work fine. For math specifically, paste LaTeX text rather than formula screenshots if you want the chat to be shareable.
And one catch worth flagging: the share link is a snapshot of a snapshot. If Tao ever deletes the share – not the blog post, just the share permission – the URL goes dark. That’s not hypothetical; it’s how OpenAI’s sharing model works. Bookmark it, but also copy the raw text somewhere.
Pro tips for using this the way Tao did
- Don’t paste the whole paper. Paste the exact paragraph you’re stuck on plus one sentence of context. Long inputs push the model toward summarizing rather than engaging – you get Wikipedia, not a collaborator.
- Prefer “why is this true” over “explain this.” The first is a technical question. The second is an invitation to bullet points.
- Cross-check against your own reasoning. Tao catches ChatGPT’s small errors mid-conversation. If you can’t spot them, you’re not ready to learn from that specific chat – try an easier paper first.
- Try the same question with different framing. Jiang’s cleaner answer came from a different prompt entirely. Reroll with new phrasing before concluding the model doesn’t know.
FAQ
Do I need ChatGPT Plus to open Tao’s shared conversation?
No. Anyone can view it in a browser without logging in at all.
Did ChatGPT find the Jacobian counterexample?
No – and this is the mix-up most news coverage made. The counterexample was found by Anthropic researcher Levent Alpöge using Fable 5. Tao’s ChatGPT chat came later; he used it to understand the already-published counterexample, not to discover it. Two separate AI stories that happened to land the same week, and they’ve been conflated ever since.
Is copying Tao’s exact prompts going to make me better at math?
Probably not on its own. The prompts work because Tao already knows which reformulations are worth trying, which objects to name-drop, which hand-waves deserve a follow-up. What you can copy is the shape of the interaction: specific stuck point → proposed reformulation → request for verification → pushback on vague answers. That shape scales down to whatever level you’re actually at. One practical constraint: start with a paper one notch harder than what you can read comfortably, not ten notches. Jumping to the Jacobian chat cold, without the background, is like watching a grandmaster’s game replay and expecting to understand every move – the moves are all there, but the reasons behind them aren’t.
Next step: open chatgpt.com, grab a paper or textbook chapter you got stuck on last month, and run the six-step workflow above on the exact sentence where you stopped. Don’t summarize. Interrogate.