You can surf the wave, but sooner or later, the wave will come crashing down.
Can you share more about your architecture & process? Also a researcher involved in math research (though not strictly speaking a mathematician, but I digress). I've often thought about using AI on my notes, but they are messy and even then I can't quite figure out what to ask: prioritization, connecting ideas, lit search, etc.
I'd love to hear what you do.
There is definitely a gap in academic tooling, where an "association engine" would be very useful for a variety of fields (and for encouraging cross-pollination of ideas between fields), but I don't think LLMs are anywhere near the frontier of what can be accomplished with a given amount of computing power. I would expect simpler algorithms operating over more explicit ontologies to be much more useful. (The main issue is that people haven't made those yet, whereas people have made LLMs.) That said, there's still a lot of credit due to the unreasonable effectiveness of literature searches: it only usually takes me 10 minutes a day for a couple of days to find the appropriate jargon, at which point I gain access to more papers than I know what to do with. LLM sessions that substitute for literature review tend to take more than 20 minutes: the main advantage is that people actually engage with (addictive, gambling-like) LLMs in a way that they don't with (boring, database-like) literature searches.
I think developing the habit of "I'm at a loose end, so I'll idly type queries into my literature search engine" would produce much better outcomes than developing the habit of "I'm at a loose end, so I'll idly type queries into ChatGPT", and that's despite the state-of-the-art of literature search engines being extremely naïve, compared to what we can accomplish with modern technology.
I also agree that neural net LLMs are not the inevitable way to implement AI. I'm most intrigued by the theoretical underpinnings of mathematical proof assistants such as Lean 4. Computer scientists understand the word problem for strings as undecidable. The word problem for typed trees with an intrinsic notion of induction is harder, but constructing proofs is finding paths in this tree space. Just as mechanical computers failed in base ten while at the same time Boole had already developed base two logic, I see these efforts merging. Neural nets struggle to simulate recursion; for proof assistants recursion is baked in. Stare at these tree paths and one sees thought at the atomic level, begging to be incorporated into AI. For now the river runs the other way, using AI to find proofs. That river will reverse flow.
While CoIC has recursion "baked in", HOL does not. It turns out that we can treat structural recursion as a derived property, even over coinductively-defined types. We don't even need a notion of ordinals for this! (See https://www.tcs.ifi.lmu.de/staff/jasmin-blanchette/card.pdf and https://matryoshka-project.github.io/pubs/bindings.pdf.)
Lean 2 used HoTT, which was theoretically interesting, but not enough was known about HoTT at the time (in particular, whether it was a constructive logic – I think we have all the pieces for an explicit construction via cubical type theory now, but I don't know that anyone's put the pieces together), so that direction has been mostly abandoned. I think there's useful work to be done in that direction, but with the current state of HoTT pedagogy, I doubt I'd ever be able to keep on top of it enough to contribute; and with Lean 4 taking so much of the funding, I don't think we'll see much work in this direction until HoTT is easier to learn.
I still think you're overgeneralising. What actual thing does your poetic tree / thought / river analogy correspond to?
"Throw a massive neural network at it" is an extremely inefficient way to get results, and doesn't generalise well – for instance, there's no easy way to get online learning for a transformer model, whereas that capability just falls out of most search engine database systems. (The underlying relational database engines had a lot of work put in to make online CRUD work reliably, but that work has been done now, and we can all build on top of it without a second thought.)