https://files.catbox.moe/qgy1ni.pdf
Perhaps it's a bit silly but I show here the full conversation I had yesterday with Claude, in which I asked it to teach me Groth16 (the most famous ZKP system). It's a little cheat-y in that I had already "overview" studied it, more than once, but I always found the existing explanatory materials difficult to work though and lost track at some point. This time, with Claude actively teaching me, I can confidently say I have a solid understanding of the whole system, after one single day.
In my opinion LLMs are great for these things: Search, learning and language (incl. code). They can seem ludicrously brilliant at all of these, but in each case you have to be wary of different variants of the same flaw: their inability to notice their weakspots. In learning Spanish I get 97% perfect explanations/answers/translations, but with certain obscure slang it might resolutely refuse to accept the existence of the phrase I'm referring to. In this Groth16 conversation it slips up with a specific equation/algebraic notation (it says it was 'sloppy'; I'd say it was wrong) halfway through, in a way a human professor wouldn't. In search I'm not as sure as I don't use it as much, you could argue semantics and say it's not really the one doing the search, but I bet it slips up in a similar way there too.
I don't think this kind of flaw is the real story, though. The real story is that if you frame your request properly, and you engage seriously and reflectively, you have access to a teacher that a decent simulation of a high-level expert, in a one-on-one session. If you actually want to learn something, I do think you should do as I did here and ask it to "teach me X based on the fact that my background is roughly Y (so it can pitch at the right level), and ask concept-checking questions along the way".
(btw this is not a commentary about claude vs others .. i think this kind of job can be done ~ equally by all the latest models).
I have to emphasize how natural this felt. I really felt like I was talking to a teacher that was listening carefully to my responses and engaging with them. Among a number of notable moments in the conversation, this one in particular, after the aforementioned algebra screwup, stood out to me: I asked "yes. back to Q13. rewrite it if necessary, otherwise I'll just keep thinking." and it responded after a few seconds: "{Claude:} The question stands as is. Take your time."
A reasonable push-back on this example is that I chose something that has been described and discussed on the 'net a lot over the last 8+ years - certainly no other ZKP system has as much material. So it's showing the best it can be. If you discuss cutting-edge research with it, you're in *much* more dangerous territory.