Terence Tao's ChatGPT chats show why domain expertise wins
The essay opens with a contrast: in the 2010s, a technical gap like not knowing CSS meant relying on a skilled colleague or hoping the internet already had the answer. Today anyone can get sort-of-okay CSS out of an LLM, and because everyone is talking to the same models, many people conclude that prompting skill does not really exist and 'skilled prompters' get the same results as first-time users. The author calls this wrong: the most important skill in prompting is expertise in the domain you are prompting for.
The central illustration is Terence Tao's conversation with ChatGPT about the recently discovered counterexample to the Jacobian Conjecture. The author says flatly that this is not the same ChatGPT he talks to, and that he could not reach where Tao gets even with unlimited tokens to spend. He draws four observations from the conversation: Tao's messages are short and address only the gist rather than responding point by point; the model's outputs are far more concise with Tao than when the author himself discusses mathematics with GPT-5.6 Sol, because signaling expertise shunts the model into a 'talking to mathematicians' mode instead of an 'explaining to amateurs' one; Tao pushes back on weak answers without directly contradicting the model, using phrasing like 'this looks more complex than I was hoping for'; and Tao supplies most of the leaps and suggestions himself, rarely taking the model's advice on where to go next.
The author stresses that none of this is copyable as a checklist: you cannot prompt like Tao on mathematics just by imitating his style, because his technique depends on actually understanding the mathematics well enough to pull the relevant idea out of a multi-paragraph response, propose alternate formulations, and spot what looks wrong. Tao is a better mathematician than the author is a programmer, but he says the same pattern shows up in his own coding work: a good mental model of a codebase lets him push an LLM much harder than he could with no familiarity, saying things like 'no, I think it could be simpler here' or 'but don't we already do X?' He links this to an earlier idea of his that system design problems are dominated by concrete specifics rather than generic principles, and says he would rather have familiarity with a codebase than a general understanding of software systems. Just as Tao asks pointed questions like 'does X work here?' about the Jacobian Conjecture, the author asks equivalent specific questions about the systems he owns at GitHub.
His conclusion: without domain knowledge, an LLM still gets you something, which is not bad, but with domain knowledge you can wring far more value out of the same model by steering it hard toward what you want. Most people will mix both modes, since everyone has expertise in some areas and not others. He extends this into a broader claim: human expertise stays useful as models get stronger, because for many tasks the human, not the model, is the bottleneck. The needed information is already 'in the model,' but it takes a smart, knowledgeable human to pull it out through precise communication of exactly what solution is wanted.
In a later edit responding to Hacker News discussion, the author notes that commenters shared anecdotes on both sides, some describing expertise helping and its absence hurting, while others called the thesis plausible but flagged the obvious suspicion that it is a reassuring view for experts to hold about their own continued value, a point he says he agrees with, adding that he expects the picture to shift again by the time anyone studies it rigorously. He also addresses commenters who argued that OpenAI's own math prompts were themselves inexpert, which they took as evidence against the expertise thesis: he responds that OpenAI has a team of expert mathematicians who check and filter the model's suggested discoveries, and that this filtering step cannot currently be skipped.
Key facts
- The author argues the key skill in prompting an LLM is domain expertise, not a generic prompting technique, against the view that identical models make 'skilled prompters' pointless.
- The proof case is Terence Tao's ChatGPT conversation about the recently discovered counterexample to the Jacobian Conjecture; the author says he could not reach that quality even with unlimited tokens.
- Tao's pattern: short messages aimed at the gist, indirect pushback ('this looks more complex than I was hoping for'), and Tao supplying his own next steps rather than following the model's suggestions.
- The author applies the same logic to his own programming work at GitHub, where a solid mental model of the codebase lets him push an LLM harder, for example objecting 'no, I think it could be simpler here.'
- Responding to Hacker News commenters who said OpenAI's own math prompts looked inexpert, the author counters that OpenAI's expert mathematicians check and filter the model's suggested discoveries, a step he says currently cannot be skipped.
Why it matters
The essay pushes back on a common reading of the LLM era: that since everyone talks to the same models, prompting skill has been leveled away. Reframing the deciding factor as domain expertise rather than prompt technique changes what is worth investing time in. It also supports a broader claim the author makes explicitly: human expertise keeps its value as models get stronger, because the bottleneck on many tasks shifts from the model's capability to a human's ability to communicate precisely what solution they actually want.
Who it affects
Anyone using LLMs for professional or specialist work, illustrated through two very different fields: mathematics, via Terence Tao's public conversation with ChatGPT, and software engineering, via the author's own experience pushing an LLM on codebases he knows well at GitHub. The argument is aimed at people deciding whether deepening domain skill still pays off, or whether LLMs have made specialist knowledge redundant.
How to use it
Drawn from Tao's observed pattern: keep messages short and aimed at the gist rather than responding point by point; push back on weak outputs indirectly, for instance flagging that a proposed answer 'looks more complex than I was hoping for' rather than simply overruling the model; contribute your own next steps and formulations instead of defaulting to the model's suggestions; and use your own sense of the problem to identify what looks wrong in a response. The author is explicit that these are symptoms of expertise, not a checklist that substitutes for it.
How solid is it
This is a personal essay on a single author's blog, not a study: it rests on close reading of one public conversation (Tao's) plus the author's own subjective experience prompting LLMs about his GitHub codebases, with no numeric data behind the claim. The author himself flags the weak point in a follow-up edit: several Hacker News commenters noted the thesis is a conveniently reassuring one for people with expertise to hold about their own continued value, and he says he agrees with that suspicion.
Risks and caveats
The central case is an exceptional one: Terence Tao is a globally recognized mathematician, and the author admits he cannot replicate Tao's prompting style on mathematics himself because he lacks the underlying math knowledge, meaning the pattern may not generalize cleanly to less expert users. The essay also acknowledges a counterargument raised by commenters, that OpenAI's own math prompts read as inexpert, which some took as evidence against the expertise thesis; the author's rebuttal leans on OpenAI's in-house expert mathematicians filtering the model's output afterward, which is itself a caveat on how independently reliable the model's raw suggestions are.
“this looks more complex than I was hoping for”
— Terence Tao, as quoted in the essay