Imagine Claude coming up with a solution to the Grand Unified Theory and also proved that P = NP, would we see physicist write an angry letter saying that we should ignore these results because they weren't derived by artesian hands? Give me a break.
Mathematicians issue warning as AI rapidly gains ground
311–320 of 366 posts
Re: Mathematicians issue warning as AI rapidly gains ground
#312Earlier quoted context omitted.
> In the past "computer" was a job description and mechanical power came from serfs. Serfs, all right, but in what world do you live where "computers", people who did manual computing (i.e. mechanical additions/multiplications/... with very large numbers) are the same as actual research mathematicians, who are basically pure logicians? The only perspective where it makes sense to root for mathematicians to go away is…
I don't think that "root[ing] for mathematicians to go away" is the problem. The problem (if there is one) is that the process by which that occurs is economically determined. No amount of complaining will stop AI from being useful in mathematics or erase the incentives to make it better. It's automatic process, like photography sidelining painting or shoe factories sidelining cobblers. We go through this with every…
Nothing in history is inevitable.
Re: Mathematicians issue warning as AI rapidly gains ground
#313Much of math (or science) research has the strange quality of being mostly curiosity-driven, but having giant benefits that occasionally spin out to the public. Some questions are more urgent and practical. My feeling is that the more directly practical a question is, the more likely the research community is to support AI usage in that question. The annoying thing about recent AI advances is that they target questio…
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 intr…
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.
Re: Mathematicians issue warning as AI rapidly gains ground
#314> Mathematics produces not only a body of results, but also understanding, clarity, and judgment among the communities of mathematicians who have shaped them, often in the context of their own autonomously guided research. This expert knowledge is essential, both to effectively use mathematics, and to continue to articulate new and significant research questions. In a word, the job of the mathematics department is no…
> Outsourcing the work deprives you of who you become by writing it. Just because AI can do something that resembles work should not mean outsourcing work to it. Mathematicians should not outsource their work to AI just like programmers should not outsource programming to AI. Humans working with AIs in a tight loop means intellectual work becomes more high-level and creative, but a human should always own the work, v…
> Mathematicians should not outsource their work to AI just like programmers should not outsource programming to AI.
There is a huge difference between the two. Mathematicians work on discovering fundamental truths of the universe that go into the corpus of human knowledge forever. Programmers create utilities.
Re: Mathematicians issue warning as AI rapidly gains ground
#315Earlier quoted context omitted.
Do AIs produce answers whose work is incomprehensible to humans? It seems like you could just have the AI elaborate multiple times until you were satisfied with the explanation and documentation of what went into figuring out the answer. It’s not like the AI is one shotting the answer in a single opaque query anyways.
Like other commenters, I think you’re also underestimating the complexity of esoteric higher level math. Consider the “Magnus Carlsen” of mathematics, who is more capable of understanding mathematics than any other human. But then also realize that that individual has probably devoted their entire career into a specific subdomain of mathematics. Within other deep recesses of mathematics, this Magnus equivalent will b…
> “speak the language” of the concepts the LLMs have produced
LLMs don't produce concepts, they just predict next tokens; they can't invent new concepts, only synthesize what is in their probability distribution already. They can mix/fuse vast areas of math together that are inaccessible to individual mathematicians, but can't create new concepts not present in their probability distribution.
Re: Mathematicians issue warning as AI rapidly gains ground
#316Much of math (or science) research has the strange quality of being mostly curiosity-driven, but having giant benefits that occasionally spin out to the public. Some questions are more urgent and practical. My feeling is that the more directly practical a question is, the more likely the research community is to support AI usage in that question. The annoying thing about recent AI advances is that they target questio…
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 intr…
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!
Re: Mathematicians issue warning as AI rapidly gains ground
#317Earlier quoted context omitted.
Much like for many the point of chess is that it's played by humans, with truly superhuman AI relegated to a training aid, mathematics is in many ways about human comprehension. You can use AI to find and proof new theorems. But if you get to the point where humans can't understand it, is it even still math?
Is it still chess, if humans cannot understand it? Because that's the point we are at in chess. Engines making moves, that humans cannot understand, but somehow they work out to be best or seemingly best. Look at the Leela Zero games, when it came out. These engines play kind of other-worldly chess.
Exactly. If we wanted "the best chess" we'd watch Stockfish against Leela Zero. Far better mechanically than human chess. But people are much more interested in Magnus Carlsen playing Gukesh. Both train with chess engines, but the thing that makes the chess game interesting are the human beings that understand their own moves and try to understand those of their opponent
Re: Mathematicians issue warning as AI rapidly gains ground
#318Earlier quoted context omitted.
> Outsourcing the work deprives you of who you become by writing it. Just because AI can do something that resembles work should not mean outsourcing work to it. Mathematicians should not outsource their work to AI just like programmers should not outsource programming to AI. Humans working with AIs in a tight loop means intellectual work becomes more high-level and creative, but a human should always own the work, v…
> Mathematicians should not outsource their work to AI just like programmers should not outsource programming to AI. There is a huge difference between the two. Mathematicians work on discovering fundamental truths of the universe that go into the corpus of human knowledge forever. Programmers create utilities.
I know a PHD in math that claims math is invented by ourselves and not any universal true. So well, depends who you ask.
Also some of these programming utilities may outlive some math proof. Time will tell
Re: Mathematicians issue warning as AI rapidly gains ground
#319Earlier quoted context omitted.
I see that point of view but there's another that I've recently been thinking about. Many of the fields that were traditionally considered for "smart" people (STEM etc.) are the ones that are being really hammered by AI. Whereas, things which people considered lightweight often involving social relationships and interpersonal skills are still beyond the scope of AI (much of it even theoretically beyond the scope alth…
This is actually a very old AI insight, acknowledged at least as early as the 80s, let me see if I can find the quote. Found it: > Rodney Brooks explains that, according to early AI research, intelligence was "best characterized as the things that highly educated male scientists found challenging", such as chess, symbolic integration, proving mathematical theorems and solving complicated word algebra problems. "The t…
Brooks is weirdly sexist, but it's unsurprising that (higher) "intelligence" should mean things that are hard, not things that are easy.
Re: Mathematicians issue warning as AI rapidly gains ground
#320Earlier quoted context omitted.
While you are right in a way, I think you miss the point. In the past "computer" was a job description and mechanical power came from serfs. They surely developed skills we are lacking today but I'd argue that overall the world is a better place with digital computers and electrical motors. It frees up these people to do something else, something of higher value.
When I was a child, I lived in a neighborhood. Every week a garbage truck picked up the house hold trash. 5 guys were on that truck. 1 driver and 4 guys that actually lifted up various shaped trash cans and dumped them into the truck. Today I live in an apartment complex. 100 families take their trash to the compactor. 1 guy in a garbage truck comes once a week to collect the compacted refuse. I wonder what happened…
They were already available to do something of higher value. Automation frees them up to do something of lower value.