Current LLMs are far from Terence Tao but Tao himself wrote this:
“The 2023-level AI can already generate suggestive hints and promising leads to a working mathematician and participate actively in the decision-making process. When integrated with tools such as formal proof verifiers, internet search, and symbolic math packages, I expect, say, 2026-level AI, when used properly, will be a trustworthy co-author in mathematical research, and in many other fields as well.”
What Tao does when proposing an idea most likely encapsulates much more than what a current LLM does. I’m no Terence Tao but I sometimes come up with useful ideas. In a more complex case, I revise those ideas in my head and sometimes on paper several times before they become useful (analogous to using evolutionary algorithms).
However, it is impractical to think consciously of all possible variations. So the brain only surfaces ones likely to be useful. This is the role an LLM plays here.
An expert or an LLM with more relevant experiences would be better at suggesting these variations to try. Chess grandmasters often don’t consciously simulate more possibilities than novices.
Critically, though, the LLM is not acting as a domain expert here. It's acting as a code mutator. The expertise it brings to the table is not mathematical - Codey doesn't have any special insight into bin packing heuristics. It's not generating "suggestive hints and promising leads", it's just help the evolutionary search avoid nonsense code mutations.
An LLM serves as a sort of “expert” programmer here. Programming itself is a pretty complex domain in which a purely evolutionary algorithm isn’t efficient.
We can imagine LLMs trained in mathematical programming or a different domain playing the same role more effectively in this framework.
I disagree that the type of coding the LLM is doing here is "expert" level in any meaningful sense. Look for example at the code for the bin-packing heuristics:
These aren't complex or insightful programs - they're pretty short simple functions, of the sort you typically get from program evolution. The LLM's role here is just proposing edits, not leveraging specialized knowledge or even really exercising the limits of existing LLMs' coding capabilities.
To be clearer, the word “expert” in my comment above is in quotation marks because an LLM has more programming expertise than a non-programmer or an evolutionary algorithm, but not anywhere near a true expert programmer.
A fun story from a UCLA math PhD: “terry tao was on both my and my brother's committee.
he solved both our dissertation problems before we were done talking, each of us got "wouldn't it have been easier to...outline of entire proof"”
https://twitter.com/AAAzzam/status/1735070386792825334
Current LLMs are far from Terence Tao but Tao himself wrote this:
“The 2023-level AI can already generate suggestive hints and promising leads to a working mathematician and participate actively in the decision-making process. When integrated with tools such as formal proof verifiers, internet search, and symbolic math packages, I expect, say, 2026-level AI, when used properly, will be a trustworthy co-author in mathematical research, and in many other fields as well.”
https://unlocked.microsoft.com/ai-anthology/terence-tao/