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- Hacker News
- Sad to see such smart people with such small visions for the future.
Like… surely I don’t need to explain why artificial minds are a unique invention?In mathematics, it is more natural to treat AI as an assistant rather than as a competitor. As Jeremy Avigad (2026) puts it, “We should keep in mind that AI is nothing more than technology, designed to serve our purposes. It is misguided to think of mathematicians as competing with AI; when we drive a car, we aren’t competing to see who can go faster, and when we use a phone, we aren’t competing to see who can speak louder.”by bbor - >The first assumption is wrong because to really solve a mathematical problem, providing a mere answer (even if formally certified) is not sufficient. What is missing is an intelligible proof that human mathematicians can understand and use to advance the aims of mathematics.
This makes a bad assumption that humans need to be the one to advance the aims of mathematics. LLMs could be what advances the aims of mathematics and we just have to worry on making it so LLMs can digest these proofs.
>Nevertheless, if it turns out that what OpenAI has provided is a mere answer
It has a proof attached. Saying that it "doesn't provide understanding" does not invalidate that there is a formal proof. It fundamentally is trying to expand the requirements of proof to be something more than is required.
by charcircuit - The authors discuss the dual roles of proofs, and the new need to differentiate them better, clearly in the article.by anonymouz
- For the moment, AI is not capable of advancing mathematics _in the sense_ you're describing. AI is very bad at designing stuff, asking questions, etc. Maybe in the future you'll be able to ask the AI "cure cancer" and it'll do it, but for now we're very far away from that (this doesn't mean the current achievements aren't impressive).by robotpepi
- This is exactly backwards. Mathematics predates the idea of formal proof by millenia. The purpose of proofs since Euclid is to explain to your fellow human why something is true. The idea that the purpose of math is formal proof alone is a new idea that (some) computer programmers want to impose on the field (for the understandable reason that it makes computers primary).
Formal proof only emerged early in the 20th century, and the standard became that in theory a proof should be formalizable to answer any skepticism, but the real goal in Euclid's time and ours has been to communicate why a theorem is true to your fellow humans. There were a few theorems that are only known via computer proof, like the Four Color Theorem, but this has always been regarded as disappointing or even controversial, and the fact that there hasn't been any conceptual breakthrough has meant that we didn't learn anything other than the sheer fact that the Four Color Theorem is true. Theorems that produce understanding, on the other hand, typically produce many new ideas that lead to more theorems.
The purpose of scholarship is understanding. This is just as true for science as it is for math. If AI produces a unified theory of fundamental physics, but it's just an opaque blob, physicists will find it just as unsatisfying.
by QuesnayJr - Math needs its own unique type of prompt engineers who can understand the output quickly.
That’s where the future of mathematicians lies.
by brador - I'm a bit worried that this line of reasoning is assuming its conclusion, in stating that mathematics is for human understanding.
This is not something that's just true on its own; it's on us as a species to make sure that it remains that way, for the sake of our dignity.
However, this position will be extremely difficult to defend, against the economic value of not caring.
by svara - It points to a possible alignment: math helps humans to _discover_. So can AI.
You're right though; the economic and emotional impact of OpenAI's executives are much more obvious today. In comparison, the actual implications of Navier-Stokes blow-ups on the epistemological landscape will take at least two years to become obvious to any intelligence, if ever.
I'm optimistic that the Joe in the street will soon be able to make earth shattering discoveries with the help of AI, at least once a week, when universal basic tokens come to pass. Then the nihilists will also keep their existential or otherwise depression to their AI therapists. Hopefully then the puritan billionaires can only helplessly compare the profligate blooming of a thousand new avenues to unrestrained moral depravity
- I feel like, to different degrees, we’re witnessing the same effect seen in image generation or text generation. People who don’t know better about art or writing would be impressed by what gen AI can produce and will find it indistinguishable from a human-produced equivalent. This admittedly is good enough for most business endeavors that cared only about the process, and would gladly avoid the cumbersome (to them) process that leads there. But art or writing is not just about the product as much as it is about the human process itself. That is true for all creative forms, even the ones that are normalized in business. Now with the advancements of the frontier models, we’re seeing this in growingly complex fields like mathematics. It does seem to produce results, but the process is equally important. Yet we pretend to measure its ability only based on the result. It’s as if these tools grow to become better at pretending to be top of the crop in increasingly complex fields, which makes it harder and harder for people that actually have a deep grasp of those fields to explain why that’s not exactly what’s going on.
- business endeavors that cared only about the process, and would gladly avoid the [...] process
you mean they care about the product...
by em-bee - "It is not the destination, but the journey that matters"
For now, AI will be another tool in the toolbox of mathematicians. With humans driving the conversation to help understand the world better. If/when AGI is reached maybe we won’t be in the driver seat as much. I don’t think that matters. The goal of math is to achieve greater understanding of the world, regardless if humans are driving or if an AI is.
by justinparus - Why would my tax dollars go to fund someone's journey on what's essentially a hobby at this point?by moralestapia
- I appreciate the wordplay in the title.
- It's a clever pun, but it implies maths is ended, which is the exact opposite of what the article says. Given how many people responded to strawman misinterpretations of the Fields medallists' statement yesterday I don't expect that to have a positive effect on the discussion.by omnicognate
- "After Math" seems premature. Maths is probably infinite meaning there will always be more to discover.
Regarding AI getting better than humans, in some ways it may be more like the invention of the microscope - instead of worrying about it reducing demand for people with good eyes it may open up new discoveries.
One example I'm kind of excited for is that I've long suspected that the inability to combine quantum mechanics with general relativity is because the maths gets too hard for humans. I mean Navier Stokes on singularities in fluid flow in euclidean space is hard enough. Particles may be singularities in quantum fields in relativistic space time which is probably mathematically far harder. But it would be interesting to know how that works.
by tim333 - Wouldn't AI make the field of mathematics more ambitious? In software development it feels that way: there are often tasks I can take on that would have been too risky in 2025, because it was unclear if they were worth it. Now you generate a prototype and can make much better judgement calls what is possible and what is worth pursuing.by stabbles
- I think it's possible that it will play out that way, and that it's just too soon to see it. Tao was very optimistic about AI up until a few months ago, and I think what's changed is that an AI generated proof isn't that informative unless it is understandable by humans. So far experts are finding the solution to Navier-Stokes incomprehensible, so we only learn one thing (it's false), instead of the hundreds of things we learn from reading a proof we can understand.
Maybe this is a one-off, or maybe in a few weeks we'll figure out how to get AI to explain the proof in terms we can understand. Then math research will accelerate. But maybe it's not a one-off, and by this time next year we will have an oracle that just answers all of our questions, but in such a way that we don't even know what questions to ask anymore. Then AI will just mop up the existing and the subject will end.
by QuesnayJr - Maybe, but what remains of the human professional mathematics will be unrecognizable (at least for those without tenure I guess). All of our credit assignment systems are breaking and access to computational/financial resources is becoming way more important. Math has been one of the most open academic fields but everyone is becoming afraid of sharing their ideas. Personally, my job has slowly been moving from open-ended brainstorming to prompting/digesting LLM output (or LLM output transmitted by grad students). And the students are so demoralized! Also, the academic funding structures which have supported math departments are looking less and less stable - I imagine many of them will shrink.by qbit42
- It might feel that way, but I'll ask again: where's the payoff? Where's all the amazing software that everyone is now supposedly shipping 10x faster than before?
If I look at the software I'm actually using day-to-day, or that my friends are using, all this stuff looks exactly the same as it did in 2021. Not a single product release from Google, Microsoft, or more scrappy companies in the past 6 months made me go "wow, they couldn't have pulled that off before". All the vibecoded "Show HN" projects seem to be half-broken and then abandoned before being finished.
It feels like we've gotten less ambitious, not more. Because yes, you can prototype more easily, but this means less commitment to what we create.
Mathematics is probably the same way. There's a short-term rush when you pull the lever, but there's less desire to get invested in what comes out.
by matherial - This kind of argument is always dangerous, because it essentially resorts to moving goalposts. "Oh, AI can now do X? Sure it is amazing, but it can't do Y yet, so we're totally safe!"
Just because humans can't process the proof or see the advancements, it doesn't mean that it will remain that way in the future or that it will not change the field. If you only define yourself by things AI can't do yet, you're about to have a rude awakening. We've gone from high school, to university math, to Euler problems all the way to Millennium problems in a time frame most people couldn't even do a PhD. If you start any math research now with a horizon beyond the next two years, I'd be terrified of the current rate of progress.
by sigmoid10 - Technology advances, but extrapolating the value of human labour to 0 is equally invalid.by alansaber
- > This kind of argument is always dangerous, because it essentially resorts to moving goalposts. "Oh, AI can now do X? Sure it is amazing, but it can't do Y yet, so we're totally safe!"
It's not about moving goalposts. What you're not understanding is that, even if for you is crystal clear that AI will be 100x smarter tomorrow, those in charge cannot simply bet all on that. Right now AI cannot really replace the core sauce of mathematicians (all the "understanting" and "asking the real questions" stuff), so it'd be unwise for, say, countries to start making decisions as if AI is capable of that.
by robotpepi - > This kind of argument is always dangerous, because it essentially resorts to moving goalposts.
Nope, introspecting motivation is useful. There have been similar posts made about people using bots in PvP competitive online gaming: some people play to enjoy the game, and hopefully get better until they reach their skill ceiling. Others play (just)to win, and are open to buying aimbot hardware and software
by overfeed - Strongly reminiscent of God of the Gaps [1]by stabbles
- If you ask an AI if "P=NP", it will certainly give an answer. It has to, because the answer is either "yes" or "no".
If you ask it to then prove its assertion, it will then certainly output the tokens that look like a plausible proof. It has to, as it is programmed too.
This "proof" might even be thousands of pages of very technical looking and professional sounding jargon.
It's not a real proof though, and as an artifact it is 100% useless to both the field of mathematics and humanity.
- The authors are absolutely not saying "we are totally safe". They are not denying that AI will affect math deeply in the short and the long run.by kaffekaka
- Fundamentally, the question is this: what is a large language model, what is it capable of, how does it differ from human cognition, and what can humans do that it cannot do?
A lot of people seem to believe that with more time and training, LLMs will surpass human intelligence. But they are fundamentally not like human intelligence. They do not reason, learn, conceptualize, think creatively or abstractly, even though we have some hacks to mimic these behaviors.
I posit that treating LLMs like GPU-powered brains that will eventually surpass us in most fields is pure science fiction if you know anything about how they work. I think they will remain astronomically powerful in some areas (pertaining to fuzzy deep search and recombining existing knowledge) and hilariously bad in others.
by archagon - The elephant in the room no one talks about yet, imo, is "should public funding of math studies be adjusted due to AI breakthroughs?"
The sports comparison is wrong here because general public never paid for the specific match results. The value was always in the show, the advertising and betting around it, the health and educational value of doing sports, etc. And the sport mostly lives on what it earns, not on public funding.
Math, on the other hand, was paid for because people and states believed progress in math might lead to meaningful improvements in other branches of science, and, in turn, in our lives. If this is better served by AI, should we keep paying for the same number of tenure positions? Should we increase their number to handle the speedup brought by AI? Or decrease because they're being replaced? Should we pay more to those using AI to do their research, or to those explaining and exploring the AI-generated results?
by reisse - > The elephant in the room
...is the fact that the people pontificating on AI and math the most are also the people who understand AI and math the least.
- > Math, on the other hand, was paid for because people and states believed progress in math might lead to meaningful improvements in other branches of science, and, in turn, in our lives. If this is better served by AI, should we keep paying for the same number of tenure positions?
That is a pretty huge "if". The ultimate purpose of mathematics and really all scientific inquiry is human understanding of the natural world. It's not at all clear whether large language models can replace that any more than calculators can replace human mastery of arithmetic. Is society ready for engineers to design bridges and airplanes without understanding the underlying mathematics by simply handing off the entire process to a black box "AI architect"? Are people ready to ingest drugs "vibe-designed" by human drones pushing buttons on an "AI drug discovery" machine and just going "meh, seems about right!"
It might also be useful to take a step back from the hype that the frontier labs are obviously incentivised to incite. Before speculating about how "AI math" capabilities might supplant cutting-edge research in mathematics and other sciences, take a look at OpenAI's own job postings (https://openai.com/careers/search/?). Why doesn't OpenAI demonstrate its world-beating AI capabilities by automating more routine roles like "Account Associate", "Systems Architect" or "Android Engineer"?
by curt15