> The model outputs are much more concise than when I try and talk to GPT-5.6 Sol about mathematics. By signalling expertise, Tao shunts the model into “talking-to-mathematicians” mode, not “explaining-to-amateurs” mode

I believe this works in two different ways.

First, information compression. The use of professional language helps describe problems more densely with minimal information loss/distortions. Verbose output by LLMs (e.g. ELI5) tend to incorporate local chat context, which can destabilize the context (e.g. out-of-topic, irrelevant nitpicking on writing style and wordings) and lead to faulty logic and even hallucination. LLMs are not good enough to look through all the noise, so, sometimes, it's helpful to refine the input data before performing actual tasks.

Second, boosting logical pattern-matching. Using professional language helps drive logical reasoning through simpler pattern-matching b/w texts. This is not about whether LLMs can reason or not; it's about how high-level reasoning is guided by preconception. Even humans tend to consume only textual surface of highly complicated theories (e.g. Adam Smith's "invisible hand"), and use them casually during conversation. It's similar for LLMs: if the conversation is conducted entirely in professional language, LLMs can easily incorporate external professional information into its reasoning. If the text is written in amateurish tongue, translating it into professional language can introduce errors and distortions.

So, yeah, keep your conversation professional, tidy and tight. A large volume of unprofessional text helps no one.