While large language models have made it possible for anyone to generate code, mathematics, or writing by simply asking, a popular belief that LLM skill is universal misses a crucial reality: domain expertise remains the most important factor in getting value from these tools.
According to Sean Goedecke, a software engineer and writer, the pattern is clear in how experts use LLMs versus novices. The difference is illustrated through mathematician Terence Tao’s interaction with ChatGPT about a recently discovered counterexample to the Jacobian Conjecture. Tao’s approach reveals several key practices: his prompts are concise and focused on the essential gist rather than point-by-point responses; he steers the model toward “talking-to-mathematicians mode” rather than explanatory mode simply by signaling his expertise; he pushes back when outputs seem unnecessarily complex, using phrases like “this looks more complex than I was hoping for” rather than direct contradiction; and he rarely accepts the model’s suggestions for where to go next, instead making his own leaps.
But these techniques alone don’t explain Tao’s success. The fundamental skill enabling his approach is actual mathematical understanding—the ability to extract relevant ideas from lengthy outputs, suggest alternative formulations, and identify what seems incorrect.
Goedecke observes the same principle applies to his own programming work. Developers with deep familiarity of their codebase can push LLMs much harder than those without it. With genuine knowledge of how systems work, users can reject suggestions as too complex, point out existing solutions, or reframe problems in familiar terms. Someone without domain knowledge can still get something useful from an LLM, but they’re capped at a lower ceiling.
This dynamic suggests that concrete specificity and familiarity matter more than generic principles. Tao asks detailed questions like “does X work here?” or “given Y and Z, why A?”—questions only answerable by someone with deep knowledge of the domain. Similarly, programmers who understand their own systems can ask these kinds of specific, steering questions.
The implication is significant: as language models become more powerful, human expertise will likely remain valuable rather than obsolete. For many tasks, the human becomes the bottleneck, not the model. The difficult part is communicating to the model exactly what solution is needed. As Goedecke puts it, “The information is ‘in the model’ already, but it takes a very smart human to pull it out.”
Key facts
- LLMs have made generalist-level output accessible to everyone, but this doesn’t mean prompting requires no skill
- Domain expertise is the most important skill in prompting, not prompting technique alone
- Mathematician Terence Tao’s ChatGPT conversations demonstrate how expert users steer models toward better, more concise outputs by signaling their knowledge
- Deep familiarity with a specific domain—like a codebase or field of mathematics—allows users to identify flawed suggestions and redirect the model more effectively
- As models improve, humans will remain valuable because the bottleneck is in communicating what kind of solution is desired, not in the model’s capabilities