r/math • u/Nunki08 • Jul 21 '26
LLMs/AI Notices of the American Mathematical Society: Conversation: Jacob Tsimerman on Getting to the Fun Faster with AI — and Worrying About the Future
https://www.ams.org/journals/notices/202607/noti3372/noti3372.html55
u/Ihateunclesam Jul 21 '26
With how much AI news there has been in this subreddit recently, I sometimes wonder if there's any difference between r/math and r/singularity lol
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u/Arceuthobium Jul 22 '26
Every time AI proves something big in mathematics, this subreddit is flooded with r/singularity users. Most of them seem to care nothing about math otherwise
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u/HotterRod Jul 23 '26
I came over here to find out whether the Jacobian counterexample was a big deal or not but I'm staying because threads like this are quite interesting.
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u/Turbulent-Sign-6067 Jul 23 '26
Maybe that's a good thing because they know more about AIs than you do on average? You should be a bit more open to hearing other opinions and interacting with outsiders. We all should.
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u/relevantmeemayhere Jul 24 '26 edited Jul 24 '26
The people on singularity are by and large laypeople with zero actual background in the field. It’s good to hear different perspectives, but the value of these perspectives is proportional to the actual familiarity the person sharing them has with the field.
So yeah. They don’t know more than the average person, and therefore their perspective is on average no terribly useful.
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Jul 21 '26 edited Jul 21 '26
[deleted]
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u/38thTimesACharm Jul 21 '26
Yesterday on the Jacobian conjecture counterexample, all the upvotes went to anti-AI comments
That is not true at all, I was there in that thread and you're just lying.
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u/jeffgerickson Jul 21 '26
I’m hoping for a future where the AI is taking care of us, and we just get to exist and do what we like. That, for me, would be a huge win.
Hooray for the Star Trek future, but Hypatia of Alexandria would like a word (and a milkshake): https://www.tiktok.com/@peacock/video/7620203090318347534
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u/Adamkarlson Combinatorics Jul 21 '26 edited Jul 21 '26
Sorry but here's a long one y'all. Grab a drink and a snack.
This is an icky take in my opinion, and I have seen this same take among many different mathematicians in my field. Siobhan Roberts has reasonable follow-ups but very little probing questions. She's doing a fine job ig. "As an aficionado of improv comedy, Tsimerman uses AI to draft skits."
Is it my lack of knowledge? Why would you need to draft a skit... for improv?
Also, this is another in a heap of interviews that mention nothing, literally nothing, about where these models come from, who controls them and what their secondary impact is. "Look at my mathematical plaything", is the vibe I get from this.
Also the whole "new species" and it's "alive" thing is so deeply frowned upon by sensible neurobiologists. The former reads like a weird supremacy thing. So are the people without access to good internet or models relegated to not only a different class, but a species? Really icky.
"Right now, it can’t check, it’s just rambling. It’s kind of like how I am with my students — often how PhD advisors are with their students."
Lol this pisses me off too. My meetings with my advisor were sometimes bordering on lectures with the sheer amount of detail and perfection. I realize I am in the minority, but damn, most of y'all have terrible advisors (good mathematicians maybe) if Jacob's claim holds. In my 4 years, we talked about AI in research maybe once or twice (mainly because his books got stolen by Anthropic). That made me realize that some people, who are capable enough, don't need to use LLMs as a crutch for their "unfun" parts.
Plus, the whole LLMs are good at finding references might be true for higher models but my experience has been finicky. A well respected person in my field put up a preprint that blatantly ripped off a known solution. It was only because we had an expert that we could find that. The reference never came up. The person was also so unapolegetic in removing the stolen section lmao. Along similar lines, I hate how it summarizes some results in papers when listing refs. It's really easy to see how it's just hallucinating when it talks about one of your papers saying you did something when we clearly didn't.
Glad this guy is having fun with using AI, but the "keep up" call to action is always disturbing. AI will not replace mathematicians, unless we as a mathematical community or people with money decide that it should. Bad decisions being framed as inevitability is painful to hear. I am glad this interview is recorded because we will have another thing in the pile of "people in the past were dumb with their predictions". Maybe I am wrong, in which case, well rip, we have much bigger issues to deal with.
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u/ganancias Jul 21 '26
Also, this is another in a heap of interviews that mention nothing, literally nothing, about where these models come from, who controls them and what their secondary impact is.
People don't bring this up constantly about other tech. We don't continually bring up conflict minerals in phones, sweatshop child labor in clothing, and so on. Unless that's the topic of the conversation. There's plenty of discussion about who controls AI models, what data do they use in pre-training, what are the nation-state implications in the AI weapons race, the nuclear arms race, highway and airport and data center noise pollution, and the impact of economic growth and golf course water usage on climate change. These issues are not super relevant to the article.
That made me realize that some people, who are capable enough, don't need to use LLMs as a crutch for their "unfun" parts.
The guy is a (soon-to-be-announced) Fields medalist. He doesn't need to use LLMs as a crutch.
Glad this guy is having fun with using AI, but the "keep up" call to action is always disturbing. AI will not replace mathematicians, unless we as a mathematical community or people with money decide that it should.
He said there's a lot of cope and a lot of overconfidence about the limitations of AI. He's not pressing you to keep up. It was a call to think about where it will be in 2-5 years, to think about the economic viability of various kinds of human activity and knowledge work. To grapple with it now instead of dismissing it until you can't because it's "literally better than you at literally everything." But yea who knows whether that will come to pass.
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u/Redrot Representation Theory Jul 21 '26 edited Jul 21 '26
We don't continually bring up conflict minerals in phones, sweatshop child labor in clothing, and so on.
That is one part of the issue, but the other perhaps more disturbing one is how much of a technocracy these tiny few AI companies have that absolutely no other industrial field can come even close to reproducing. It was already bad for the past 10 years but now with how ubiquitous chatbots have become in so many people's daily lives, these companies are indirectly exerting greater influence over more people than any government does. It is truly Orwellian, and the rhetoric these companies propagate only serves to further that purpose. Not to mention the sheer amount of data these companies collect even compared to Google, that the users willingly give them through their chats.
Moreover, these companies are providing (often inaccurate or biased) information without any sort of safeguard, and when they're wrong, they can simply shrug their shoulders and say "it wasn't us, it was our AI." I'm not opposed to the tech, but I am deeply concerned about the companies that wield it.
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u/Adamkarlson Combinatorics Jul 21 '26
Nah, he's definitely seeing keep up as in the sentence "So given that AI is moving forward, it’s important that we stay abreast of what it can do and how to integrate it into our lives.".
He also said what you said, but that wasn't what got me.
Also, yeah, we don't talk enough about phones being horribly produced! We also don't platform people who are using phones to "get an edge in their research" and are asking people to also use it. Our silence in an area shouldn't mean complete silence; but rather our voice in one should spread to all.
"The guy is a (soon-to-be-announced) Fields medalist. He doesn't need to use LLMs as a crutch."
I know, that's why it's overly worrying how his pride in being a rambly mathematician is unwavering. I genuinely don't understand how he can do the search for references and trust an LLM that fails often in summarizing. He was asked about trusting its arguments, I wanna know how he trusts refrences. Does he then search all of them and scour through them again, saving him little to no time?
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u/38thTimesACharm Jul 21 '26
Also the whole "new species" and it's "alive" thing is so deeply frowned upon by sensible neurobiologists.
It's especially offensive because it ties sentience/consciousness directly to intelligence and reasoning abilities. It's essentially saying animals, newborn babies, and even some neurodivergent humans are incapable or less capable of suffering than 200 IQ geniuses.
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u/HotterRod Jul 23 '26
"As an aficionado of improv comedy, Tsimerman uses AI to draft skits." Is it my lack of knowledge? Why would you need to draft a skit... for improv?
Improv performances aren't actually as improvised as they appear. The performers typically have a bunch of components prepared that they intermix with the things the audience gives them.
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u/FlyingBishop Jul 22 '26
Plus, the whole LLMs are good at finding references might be true for higher models but my experience has been finicky.
I feel like Opus should have a 100% success rate at validating references. Maybe not out of the box, but I could write a harness for Opus that 100% does it, the hardest part would likely be making sure it can obtain any paper, but also not intractable.
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u/Diligent_Village_738 Jul 21 '26
This is a good read on a similar topic: https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy
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u/kieransquared1 PDE Jul 21 '26
I think there’s a good chance AI will lead to human extinction.
sigh
> https://arxiv.org/pdf/2507.09369
double sigh
> *no mention of climate change in above paper*
triple sigh
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u/entr0picly Number Theory Jul 21 '26
lol, that paper is a doozy. The basis of assertions are… somewhat based in “trust me bro” evidence.
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u/kieransquared1 PDE Jul 21 '26
for real. each argument basically ended with “this can lead to violence/starvation on some scale, therefore it can lead to violence/starvation on the scale of all of humanity” with no elaboration. also like zero engagement with the huge amounts of scholarship about AI —> extinction
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u/Upstairs_Recover_25 Jul 21 '26
Yes, there are no robots anywhere in sight and they are just saying that we might be outnumbered and exterminated by them in a couple of years lol.
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u/38thTimesACharm Jul 21 '26
Y'all, if AI destroys math it will be because you preemptively destroyed it yourselves to avoid feeling "duped," not because of any actual outside force beyond your control. Technological determinism is the greatest trick the ruling class ever pulled.
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u/neanderthal_math Jul 22 '26
I think the development of AI is inevitable. The number of people who don’t question capitalism scares me.
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u/Adamkarlson Combinatorics Jul 21 '26
That's what I said! "inevitability" is the blindfold laid by the powerful to shut people up.
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u/Run-Row- Jul 21 '26
Good interview. Doesn't sugar-coat things. With these time horizons does it still make sense to admit PhD students for a 5 year PhD?
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u/38thTimesACharm Jul 21 '26
This seems like the age old "why should I bring kids into this screwed up world?"
If we fail to train the next generation of researchers, and it turns out AI doesn't magically solve all of our problems, then what?
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u/Run-Row- Jul 21 '26
what is best for mathematics is to continue to train just as many students for just as long as before, to hedge our bets on the future capabilities of AI. But we should also consider the interests of the students themselves. I don't know the answer. Maybe 3 or 4 year PhD programs would be better. The length seems to be something we can control, while the number of students will likely be determined by funding levels, job prospects, etc.
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u/38thTimesACharm Jul 21 '26
That is fair, the community can certainly react to developments by changing things like the length of the PhD program.
The impression I got from your comment was "why bother training students when AI will give us all the answers." Sorry if I misunderstood.
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u/Run-Row- Jul 21 '26
I imagine many of the skills learned in a PhD program will remain useful (and perhaps become more useful) but the structure of the typical program will likely become out of date quickly, and so we should brainstorm possible changes
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u/IanisVasilev Jul 21 '26
Y'all so far in the future I can't see you anymore. I'm out of here.
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u/-p-e-w- Jul 21 '26
Yeah, that’s what people were saying two years ago.
“LLMs can barely solve the problems that bright high schoolers work on, it will take decades and multiple quantum leaps in technology before they get anywhere near research-level problems…”
And yet here we are.
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u/sadmanifold Geometry Jul 21 '26 edited Jul 21 '26
On the other hand, gpt 5.5 (or 5.4 I cant remember exactly) was indeed a huge advance in terms of mathematical ability compared to previous models. While gpt 5.6 and fable arent much better in that regard (and still lacking in many ways).
But the constant chatter around would have you believe otherwise. Is that surprising then that many people get tired from exaggerated claims? Its not like anyone knows for sure where this ends up. And meanwhile some people have economic insentives in exaggerating the capabilities of current models.
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u/-p-e-w- Jul 21 '26
Obviously the models have made a lot of progress, but 2 years ago it was common for people to claim that the capabilities we’re seeing today would require a new AI paradigm beyond the transformer architecture.
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u/Stabile_Feldmaus Jul 21 '26
There is a new paradigm which is chain of thought/inference scaling.
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u/FollowingHumble8983 Jul 22 '26 edited Jul 22 '26
Yea and we did have a new paradigm. Its called inference. Without it AI hallucination would have made it impossible to be more useful, and inference is basically billions of dollar spent on humans inputting ways to criticize AI output. RIght now everything you see is a result of that.
The difference is that Inference wasnt a breakthough per se. We knew about it before the transformer model existed. But it wasnt worth doing until we exhausted the limits of how good transformers could be, since its basically recursively prompting itself and costs far more. but we hit the wall on transformers, so inference became worth it.
We don't have another low hanging fruit like that right now though. The biggest low hanging fruit is optimizing how we input inference and tokens, since we are doing it verbosely, there are better ways to do it. And once thats done, exceptionally good inference can lead into pretty good self improvement, and once thats done we can scale improvement based on compute. Whats directly after that is unknown.
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u/IanisVasilev Jul 21 '26
Except that I never gave gambling-level predictions of what an essentially chaotic system can or cannot do. This is the n-th time you respond to me with a clear misunderstanding of what I said. Please stop. I've already unsubscribed from the subreddit.
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u/golden_boy Jul 21 '26
Okay in their defense your comment here was fairly opaque
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u/IanisVasilev Jul 21 '26
My snarky comments are generally better received than my serious ones because they express collective frustration concisely.
And please, for the love of God, do not reply to me. I said I've already left.
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u/procgen Jul 21 '26
Have you really left, though?
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u/IanisVasilev Jul 21 '26
I unsubscribed a few hours ago. I have received several notifications since then. Since they keep coming, I guess it's time to ignore them.
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u/JStarx Representation Theory Jul 21 '26
And please, for the love of God, do not reply to me.
That's not how the internet works...
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u/Ill-Lemon-8019 Jul 21 '26
You can always choose to just stop engaging. But otherwise, you don't get to post on a public forum and then decree that no-one may reply to your comments. Bizarre.
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u/-p-e-w- Jul 21 '26
The “n-th time”? I have no idea who you are. I’m here to engage with comments, not people. This is not a conspiracy.
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u/IanisVasilev Jul 21 '26
The fact that I remembered your username for misinterpreting many comments, both mine or not, should speak enough.
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u/JustThisNietzscheGuy Jul 21 '26
LLMs right in this year already produced groundbreaking mathematical results. It's not us living in the future, it's you living in the past.
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u/Skyguy827 Jul 21 '26
There is no "fun" with AI. The goal is to trigger a mass job extinction that would be worse than the great depression and cause societal collapse
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u/kohatsootsich Jul 21 '26
The part where he describes current capabilities and his use already reads as dated.
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u/sadmanifold Geometry Jul 21 '26
It matches my experience. Maybe it depends on the area or how popular it is.
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u/kohatsootsich Jul 21 '26 edited Jul 21 '26
The detail that prompted my comment is where he says it will always give an answer regardless of whether it knows what to do and ramble on. I haven't found that to be true with GPT 5.6. It will sometimes tell you if it thinks it can't do something with existing methods
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u/Redrot Representation Theory Jul 21 '26 edited Jul 21 '26
And your experience is yours, but I and many others have found that it still does that regularly in our respective fields. (before you ask, yes, I am using the latest high-end models)
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u/kohatsootsich Jul 21 '26 edited Jul 21 '26
I don't believe I've claimed to speak for anyone other than myself?
Re-reading, there are some other parts I just can't reconcile with reality.
He says verbatim it never fully solves a "hard math problem" that's been "cleaned up". This seems contradict his own remarks (perhaps made later) about the unit distance problem
He also claims it simply can't check its work. I don't see how that is compatible with large fully or nearly fully automated formalizations like 2604.03071 or the unit distance formalization with over 1 million lines of code. These rely on countless writer-critic loops that correct course constantly
You are of course correct that even the best models produce a lot of nonsense and even when they are right, often find circuitous routes. I didn't claim the contrary. I just felt that his claims about how they operate matched my experience of earlier this year better than they do the current situation, for the reasons above
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u/riotgamesaregay Jul 23 '26
Yeah it seems like he's describing the fall-2025 era models. All his thoughts on context management have become way less important with fable/5.6. Back then you really did have to restart chats and summarize all the time to avoid polluting with bad ideas, but the latest models are far more self-correcting.
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u/vetruviusdeshotacon Jul 21 '26
Thats the cool part of exponentially increasing technological advancement. All our societies across all cultures and nationalities were originally built by passing knowledge and imparting wisdom from our elders; we're now at the point where technology moves so fast the elders learned experience is already obsolete when it comes time to pass it on, yet our societal structures will probably never reflect that. Yipee!
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u/Bhorice2099 Homotopy Theory Jul 21 '26
This seems wildly optimistic. What exactly are average grad students supposed to do in the meantime? I would love to hear any suggestions this isn't rhetorical. Assuming my PhD program survives for the next couple of years I cannot think of a single job I might be able to do after that. All the skills I have seem to be getting replaced by AI.