QWE AI Academy Two ways to read Terence Tao’s ChatGPT conversation about the Jacobian conjecture counterexample that dropped on July 21, 2026. Option one: skim the transcript, nod at the LaTeX, close the tab, post something. Option two: treat it as a free apprenticeship in how a Fields medalist prompts an LLM, and copy the moves. Option two is better – the math is above most of us, but the workflow is imitable.
That’s what this piece is about. Not a news recap of what Alpöge and Fable did. A hands-on read of how Tao used ChatGPT to digest something he didn’t immediately understand – and how you can do the same tomorrow morning on any hard paper.
The scenario: you saw the tweet, now what?
Picture the situation. On July 20, 2026, mathematician Levent Alpöge posted an X thread announcing an explicit polynomial map – the algebra world lit up. The next day, Tao published a blog post and – this is the unusual part – linked to his ChatGPT session where he worked through it.
Suddenly you have a shared URL sitting in front of you. It’s a read-only snapshot of one of the sharpest mathematicians alive doing something you’re about to do this week: reading unfamiliar material with an AI beside him. The question isn’t “what did he learn.” It’s “what pattern is he using that I’m not?”
What a ChatGPT share link actually is (and what it isn’t)
Before the workflow, the mechanics – because most readers get this wrong. Per OpenAI’s help docs, a shared link creates a unique URL for a conversation. Anyone with it can view the full transcript in a browser without logging in. It’s a snapshot – frozen at the moment of creation.
That frozen part matters. Messages added to the original chat after the link is generated don’t automatically appear in the shared link – that’s straight from OpenAI’s documentation (as of July 2026). To share later messages, a new link would need to be created. So if Tao kept asking questions after clicking “Share,” those exchanges aren’t visible to anyone.
One commenter on X noted the “main takeaway” was Tao’s habit of typing double spaces after periods. That’s the level of scrutiny these transcripts now get – endearingly human for a document about a 40-year unsolved problem.
How to use Tao’s chat as a template
The setup. None of this requires understanding a single line of algebraic geometry.
- Open the shared link. Read it once end-to-end without stopping. Don’t try to follow the math – watch the shape of the prompts. How long are they? Where does he break?
- Fork it. Click into any message and start a follow-up – this opens a fresh private conversation on your account, seeded with everything above. Your additions don’t touch the original. Turns out you can ask “explain this like I’m a first-year undergrad” without breaking anything.
- Note the rhythm. Tao doesn’t dump the whole problem in one prompt. He lets ChatGPT respond, then narrows: “Now show me why this term vanishes.” That compression move – response, then drill – is the thing worth stealing.
- Reproduce with your own paper. Grab a preprint you’ve been putting off. Paste one paragraph. Ask ChatGPT to explain the setup. Then keep drilling.
Fifteen minutes, start to finish. What you’re really clocking is that even Tao doesn’t read hard papers linearly – he reads them conversationally, using the AI as a stand-in for the colleague who’d normally sit across from him.
The prompting patterns worth stealing
Tao’s blog post frames the counterexample construction as looking like “a massive miracle” before he decomposes it geometrically. That framing – naming the confusion out loud – carries into the chat. He tells ChatGPT what feels miraculous, then asks it to remove the miracle.
The move: If a paper’s result feels like magic, don’t ask the AI “explain this.” Ask: “Which step in this construction feels arbitrary to you, and why isn’t it?” That pulls out the actual structural insight instead of a restated summary.
Second pattern: Tao was working in a live-browsing mode. An X user noted their own explainer page appeared among the model’s retrieved sources during Tao’s session – meaning ChatGPT was actively pulling documents, not riffing from training memory. That matters because the counterexample was announced on July 20, 2026, after most models’ knowledge cutoffs; a browsing-enabled session bypasses the stale-knowledge problem.
Third: he corrects the model in-line rather than restarting. When ChatGPT drifts, one-line correction, continue. That habit alone will save you hours.
Honest limitations
Tao’s chat is not the discovery session. Alpöge credited Fable – not ChatGPT – for producing the counterexample. Paul Lezeau then formalized it in Lean and submitted it to Google DeepMind’s Formal Conjectures repo. Tao’s ChatGPT session came after – as digestion of an already-announced result. Mixing these up is the single most common mistake in threads about this.
You can’t tell which model version he used. The public share view doesn’t display the model name. If you’re trying to replicate his exact prompting rhythm, you’re guessing at a variable that matters.
Same map, different chatbot, different behavior. Multiple users reported pasting the polynomial map into other assistants and watching them reject it – those models were trained before July 20, 2026, and “know” the conjecture is still open. It’s a small comedy of knowledge cutoffs, per explainx’s writeup. If you fork Tao’s chat and push into newer questions, don’t be shocked if a later message hits an outdated cached belief.
Why this specific transcript matters more than the last ten
Tao’s view of AI tools has shifted publicly and on a documented timeline. September 2024: “a mediocre, but not completely incompetent, graduate student.” March 2026: “ready for primetime” in math and theoretical physics. That’s an 18-month arc from skepticism to endorsement – and this transcript is the artifact sitting at the endorsement end.
The Jacobian chat is the first widely-shared transcript showing him in learning mode, not proving mode. Most of us aren’t proving new theorems. We’re trying to understand something someone else did. Watching him do exactly that, in public, with a tool most of us have open in another tab – that’s the tutorial.
FAQ
Can I continue Tao’s ChatGPT conversation myself?
Sort of, but not the way you’d hope. Clicking into the link starts a fresh private conversation on your own account – you can ask follow-up questions, but anything Tao added after generating the share link is invisible to you, and he won’t see what you ask. It’s a fork, not a continuation.
Do I need to understand the Jacobian conjecture to learn from this?
No. Here’s a concrete way to approach it: pretend the math is a foreign language and watch only the English scaffolding – how Tao asks, how he pushes back, when he lets the model wander, when he reels it in. That skill transfers to any domain. For context: the conjecture held that a polynomial map with a nonzero constant Jacobian determinant must be invertible. As of July 2026, that’s false in three or more complex dimensions (Alpöge’s counterexample), and still open in two dimensions. Background scenery.
Is it safe to share my own ChatGPT chats like this?
The link is fully public – anyone who has it can read the full conversation. No login required, no access controls. Your name is removed by default, but everything you typed is visible. Fine for a math digestion session. A bad idea for anything with client data, API keys, or half-formed ideas you’d rather not have indexed.
Next step: open Tao’s shared link, pick one prompt you find surprising, and rewrite it in your own words for a paper you’ve been avoiding. That’s the whole exercise.