[empath75]

I've been spending 3 weeks, as a non mathemetician, chasing down a particular, very simply-stated, but secretly quite complex problem, and AI has been _so incredibly helpful_, not just in making progress on it, and doing obvious stuff like formalizing in lean, doing literature searches, reading through 10 or 15 papers and summarizing the results for me and how they apply to what I'm doing, giving me enough of an introduction to _entire fields_, that I can talk intelligently about it (I've had email correspondence with a couple of professional mathematicians in a few different fields about it, who agreed that it's an interesting, simple, but difficult problem). I've gone from "this should be easy", to "okay, I've almost got a proof", to "this is impossible", to literally just nailing down a few remaining sub-cases out of an infinite family.

I don't want to call anyone out, but I emailed one fairly famous mathemetician, and he literally said: "This is very interesting, I thought about it for a while, couldn't figure it out, but I thought ChatGPT had an interesting response..." and he linked me to his chatgpt transcript... (which, was actually helpful, because he asked it a better question than I was asking).

I have a suspicion that math will quite soon be exactly like programming and fall to the same machinery that coding is.

One thing that I noticed is that a common workflow I had was isolating hard subquestions in a self contained way and then "surveying" multiple different LLMs in a totally clean context. They would often say: "Oh, this is a obvious example of such-and-such" and immediately clear the barrier.

[losvedir]

I'd be very cautious about "AI psychosis" here, or at the very least becoming a "crank". I've read too many stories of people convincing themselves they're on the verge of some great discovery to not hear "3 weeks to become conversational in mathematical fields" and not see all kinds of red flags.

I studied math at MIT and have several friends who are professors now and they deal with cranks all the time and since they're very kind and conflict averse people they tend to respond with perfunctory emails when they get inbounds like that.

So just be wary. Your external validation may not be as strong as you think it is, though kudos to you for at least trying to step out of the AI vortex to attempt to ground yourself.

[empath75]

> I'd be very cautious about "AI psychosis" here, or at the very least becoming a "crank". I've read too many stories of people convincing themselves they're on the verge of some great discovery to not hear "3 weeks to become conversational in mathematical fields" and not see all kinds of red flags.

---

it's not a great discovery, it's a pretty minor question, that I thought would be easy and it's not -- i've just been poking off and on at it for weeks, and I'm relying on lean to verify everything. It's actually a quite specific CS-adjacent problem that I came up with trying to write code, that just is hard to solve, and nobody in the literature that I could find has looked at directly. The end result of it will have exactly zero consequences other than proving an interesting lower bound for a question that as far as i can tell, nobody has bothered even looking at but me. The reason it touches on multiple fields is that it's sort of both an algebra problem and a CS problem, so i keep having to flip between them to understand what I'm looking at, and there are a lot of sub-fields that span both that have different tools, and it took me a while to find the right one.

[handle584]

Having been in academia for a bit, I find it somewhat hard to believe multiple professional mathematicians in different fields give meaningful reply to a random email solicitation from an internet stranger within three weeks, simply because those people's inboxes are absolutely bombarded every minute.

In reality people would be thrilled to have such response even with a finished preprint on arXiv. Anyway if you really hit the jackpot hope it will be smooth working out the details and get it published!

[empath75]

Well, I was emailing specific people who were working on very closely related things, and had recently published papers about it and I had very small, concrete questions about their results and not much about my question, except for context.