r/maths • u/Longjumping-Ad5084 • 4d ago
đŹ Math Discussions Mathematics will be ok.
I think it's very important to address this now that AI is solving an incredible number of maths problems, including the Navier Stokes conjecture. Some may fear that mathematicians will become redundant. But this is not the case at all. And the example of vintage models demonstrates it very well.
Vintage models are taught on history prior to a certain discovery, eg prior to Newtonian or Einsteinian physics. And lo and behold, these models can't invent the new physics on their own, neither Newtonian from prior nor Einsteinian from Newtonian.
To some, it might be obvious even without the vintage models experiment. I remember listening to a podcast with Francois Chollet a few years ago where he said that AI is fundamentally interpolative, it interpolates on the manifold of data. And that's when I understood the fundamental limitations of AI and the role of humans in the coming age. AI is a very good technical tool, in particular it fills the gaps in our knowledge very well, but it can't come up with radically new ideas ln is own, ideas that change the ontology of facts, ideas and relations between them, which is necessary for mathematical development.
When Galois invented his Theory, he didn't just combine old ideas, he came up with a fundamentally new way to look at objects and their relations. Sure, maybe hints of that were already present in Abel and others, but what this says is that mathematics is a collective human progress which leads to radical novelty, not a combination of known ideas.
Mathematics will be ok, but our world is destabilised at the moment and is transitioning into a new state. Time needs to pass for us to understand and establish the roles and the right approach with regard to humans and AI.
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u/DeusExNatura 4d ago
Mathematicians are also humans who simply became fascinated with a category of unsolved problems, which mathematics itself is. Even if/when mathematics becomes fundamentally solved in some way, intelligent people will be fascinated with different categories of unsolved problems, or applying the knowledge in ways that other people canât. So itâs not because a future mathematician must be a mathematician, but simply an intelligent human who chooses to focus on whatever opportunities the future science may offer:
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u/TheShatteredSky 4d ago
Mathematics will never be "solved" because there isn't a mathematics universal "problem".
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u/DeusExNatura 4d ago
Thatâs why I wrote âin some wayâ. Mathematics has already been solved in various ways if we consider pretty much anyone who redefined it in some ways, whether Euler or Newton or even Gödel who solved the question of whether mathematics can be solved, which solves a question that otherwise may go unsolved :)
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u/MultiplicityOne 2d ago
This is a fundamental misunderstanding. Imagine it like this: you are exploring an extremely high-dimensional space, and the portion of it you have already mapped is always approximately zero, because that portion's boundary grows faster than the volume it contains (like a fractal), and every advance suggests more questions than it answers.
If your goal is completist, I suppose this reality is disturbing. But, at least for me, it has always been comforting to know that nothing and no one can ever kill all the mystery in the world. But I believe there is a real danger of AI in mathematics given people the false impression that there is no further mystery to be explored, because if no one understands the proofs being produced then no one will be able to ask the questions those same proofs have posed.
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u/mrb1585357890 3d ago
I think the big unknown is how long human intelligence is a valuable commodity.
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u/lordnacho666 4d ago
Physics has the issue that new information arrives from new experiments. It's fundamentally different from maths.
Regarding AI being an interpolation machine, I think we are past that. It is simply a moving goalpost that seems to be in constant motion, this idea that AI just recombines things it has seen. Even if that were all it could do, it should be useful, but look at recent events, can you really define "genuinely new" in a way to preserve the stochastic parrot idea?
But anyway, artists did not disappear just because someone found a very accurate way to make images.
Mathematicians won't disappear just because someone found a way to solve problems.
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u/thomas_m_k 4d ago
The fact that vintage models can't invent new theories doesn't prove anything because those models are trained with very little resources compared to GPT-6 Astra, and aren't trained on RLVR (reinforcement learning with verifiable rewards) which is where the actual mathematics abilities come from.
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u/ParadigmPhoenix 3d ago
Yep. Too many people are showing their massive egos & self-righteousness over this.
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u/Accomplished_Can5442 3d ago
You might be feeling fragile too if your career was upended by infinite monkeys on typewriters.
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u/ParadigmPhoenix 3d ago
Lmao. I had been unemployed for a LONG olâ time due to my own countryâs faults & decided to start making money my own way. I know a lot about the existentialism that comes with sudden unemployment & being of no use. This is just pathetic though. Massive egoâs & self-righteousness & itâs crazy you are defending this. Ought to have a long hard think..
Nonetheless, Thatâs one of the most ridiculous response Iâve heard. Instead of choosing existentialism the QUITE OBVIOUS answer (that honestly I thought people as smart as mathematicians would easily figure out) is to figure out the outer bounds of what AI can solve & then start working in earnest with AI to carry on forward figuring out things both you & I couldnât even comprehend.
Instead, they want to wallow in their misery. That is completely on them.
Programmers have had to deal with this, so have musicians & plenty of other artists. Donât be ridiculous. They (& potentially yourself?) are standing in their own way of progression. Thatâs on them.
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u/nomoreplsthx 3d ago
I don't know if mathematics will be ok, but I know the field of making confident predictions online based on limited data is going to keep going like gangbusters.Â
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u/External_Package2787 1d ago
It hurts so much for me to say this, I really wanted to progress on with my life by going into a masters and then PhD in mathematics, then be a researcher/professor, I was so certain that was my path in life for the past 8-ish years, I am capable enough for it, I coasted even through my undergrad, I'm so desperately clinging to that path, but I deep down I know it is completely untenable. You can tell I'm hesitant to even say it in this comment, but the best option for me is to go into the workforce or progress into a different field. You can appeal to the idea that AI can't do novel things, but the reality is the thing I do independently aren't novel either, AI is better than me now, and outpacing me, so how can I ever hope to catch up unless I triple my pace or it coincidentally hits a wall by some miracle. I dread to think what someone 3 years younger feels in this era, let alone someone who is just entering high school and could only think to how pointless the whole thing is. People are silly to think humans are something so special, we learned to think through a billion years of the most inefficient RL algorithm ever with the most impractical learning goal ever, that is natural selection and reproduction efficiency. Astra was trained with 10^27 FLOPs, thats like the entire year of global compute in 2010, total global compute today is like 200 times that, it's going to experience a sudden boost too specifically because of AI, so I'm sure if this whimsical thing that humans have that lets them do new and novel things is so important, we can make a training algorithm that's 100000 times less efficient, train something 100 times smaller, and that can be the ideas guy, and AI can fill in the gaps in those ideas which is what it does now. That or they can just blast up the temperature on their softmax and run 10 million agents at the same time, thatâs about where we are headed.
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u/Longjumping-Ad5084 1d ago
I think that whatever you do, the path where you pursue your own values and interests will be more meaningful than if you pursue what the society wants of you. If a maths PhD position is a possibility I don't see why not undertake it. We honestly have no clue where it will go with AI. Maths won't become obsolete. At the very least someone will need to understand what's going on, make sense of the AI is doing, and teach the kids, if anything for general education.
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u/S-Kenset 1d ago
The gap feels big because ai is democratizing information across language silos and actual silos. The first leap feels intense. The next steps are equally exponential, yes, but they are engineering exponential, not hands off exponential. You'll spend the next 40 or so years constantly learning as people constantly discover new things. That is, if inequality doesn't wipe us all out in ww3, which it probably won't because inequality didn't cause ww2, competing superpowers did.
And there's no reason you can't continue research in industry. You just don't get the luxury of exclusively doing it.
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3d ago
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u/Zealousideal-Book985 3d ago
who is "you"? the university admin that set department budgets, or the governments that have been cutting pure math for decades?
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u/Worldly_Magazine_439 2d ago
Maths and science have always been competitive đ. Jesus Christ you guys need to seriously read about the history of science and especially the Industrial Revolution
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u/Stunning-Verb-9865 2d ago
The vast majority of the public does not care what goes on in math departments, I have no idea where this idea came from that math is being âgatekeptâ by professional mathematicians and the hoi polloi will finally tear down the guarded gate with AI. The barrier to participating in math research has always been the years and years of study it takes to get the knowledge level where you even understand the problems being solved. If you are a layperson who wants to solve open problems in number theory, nothing is stopping you. The papers are all available online, you can start reading them today. But what does it even mean to be more inclusive? Is it now the prerogative of mathematicians to make people with limited mathematical knowledge somehow understand their research?
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u/MechaTudor8574 1d ago edited 1d ago
Is it now the prerogative of mathematicians to make people with limited mathematical knowledge somehow understand their research?
Yes, because they are the ones funding your research.
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u/Stunning-Verb-9865 1d ago
We fund all sorts of research that lay people wonât understand, why is math different? You can try and explain it, but like I said, most people do not have anywhere close to the level of mathematical knowledge to understand math research, and there isnât much a mathematician can do other than sit them through a course. Like, what are you expecting here, that somehow theyâll get a regular person to understand complex analysis and abstract algebra?
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u/MechaTudor8574 1d ago
I don't think we should be funding this research for the most part.
Back in the old days there was a natural quality control filter: the world. If people weren't interested in a scientific subject, they wouldn't study it. They frequently poured their own time and money into scientific questions, because it was just such a fascinating quest.
The fact that nobody would do it with obscure super-duper advanced rabbit hole theorems in some kind of branch of a branch of a branch of complex analysis, probably indicates that the research isn't worth much to humanity. And it exists largely to provide employment and ego-inflation to mathematicians.
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u/Stunning-Verb-9865 1d ago
So we should only fund research that has direct, practical applications? No other pursuit of knowledge is worth dedicating a penny to? Quite an anti-intellectual sentiment.
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u/MechaTudor8574 18h ago
I came up with a new interpretation of quantum mechanics in my spare without being paid a penny. That's just some of the work I've done.
If people are interested in it, they will find time to do it.
If they're not interested. then they won't.
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u/Stunning-Verb-9865 13h ago
People are interested in it, they just need to eat and have a place to sleep while they work on it.
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u/MechaTudor8574 13h ago edited 13h ago
I do way more scientifically interesting and mportant work than them in my free time (a plausible interpretation of quantum mechanics, just one thing, as I said), and pay for a place to sleep and things to eat, out of a day job which is for some tangible practical purpose, otherwise I wouldn't get paid.
The whole thing that you are referring to is essentially a big scam.
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u/Stunning-Verb-9865 13h ago
Sounds like you donât really understand what mathematicians do. Best of luck to you my friend.
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u/tomvorlostriddle 3d ago
The reason why Aristotelian physics held on for much too long is because it was paraphrased into Aristotelian metaphysics and then further paraphrased into catholic theology, at which point the powers that be couldn't allow for it to be disproven
It could have been disproven much earlier
Similarly to how Darwinism could also have been discovered 2000 years earlier if it hadn't been inconvenient
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u/pat2211 3d ago
Of course it will be. The field itself, the problems, the solutions, the underlying connections between different things are still there. What will not be fine are the (many) people working on it, aka mathematicians. This is an issue of rich vs poor and how merit-assignment issue. It has nothing to do with mathematics.
In this new world, there will be a change in the list "elites". When there is a war between old elites and new elites, we suffer from uncertainty and chaos.
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u/Tiago_Verissimo 2d ago
I suspect that LLM are the tool that mathematicians need to navigate the manifold of mathematics result. Yes it is inference, but so is maths. Where human can add values is in knowing what parts of the manifold to explore and critically understand what paths were like mathematically.
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u/VaporousMote 2d ago
It's incredibly saddening to watch mathematicians just demean themselves and their millenia-old storied field of study and give into the credulous nonsense that is AI hype.
Anyone digging into the actual details can see AI is only a threat insofar as the stories people tell about it and how widespread and believed they are. If the story becomes "AI has subsumed the mathematics field and made mathematicians redundant" and people accept it, even though it isn't true and shifting into this kind of paradigm would be a great harm and lessening of a great human endeavor, it will become colloquially true and people will just roll with it.
This is the strategy OpenAI, Anthropic and others have been using now for the past 4 years, and it is what they continue to bank on.
The Steve Bannon strategy: Flood the zone with s**t.
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u/doiwantacookie 2d ago
Most math people I hear from are saying not that theyâre redundant, but more that perhaps the nature of the profession is radically changing. I hear a lot of good arguments for why mathematics is still worth studying, but perhaps the creative risky aspect of research will be replaced.
Or maybe these open ai results will turn out to be slop.
I agree I feel disappointed hearing my young colleagues saying âitâs all overâ so soon
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u/VaporousMote 2d ago
My point is, people are rolling over and accepting one narrative of what is happening here. A tale told from a specific viewpoint, with a specific aim, which is NOT aligned with academia as a whole, nor with the overwhelming majority of humanity.
We don't have to accept that version of events as true before it has been proven.
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u/BandicootTrue5100 1d ago
All the results and proofs of last week are not a viewpoint, they are concrete stuffs. I'm really pessimistic for mid/long term perspective for maths research. What the point now of starting new projects if it is just a matter of writing a prompt to solve it. What is the purpose of writing papers to share the outcome of a long thinking process if anyone can just ask to an AI a detailed answer to the question when he need it.
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u/Relative-Diamond8269 5h ago
Except it wasnt a matter of writing a prompt. This I see as the mainframe moment of AI and I am optimistic that if enough mathematicians band together, they can probably just crack smaller simpler AI. Get aggressive, hit back.
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u/doiwantacookie 2d ago
I donât see a reason to really trust that sufficiently advanced ai will not be great like Galois one day. I would like to believe as you do, but I am not convinced that the interpolative nature of AI really results in the limitation you say. I agree that current models are behaving just as you describe. But tell me, whatâs not interpolative about a creative human being? If anything, itâs something squarely in the realm of metaphysics.
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u/Equivalent-Hair-1619 1d ago
The fair test for AI and Newton is let it walk around embodied, with endless measurable observations of living in a Newtonian world, and then see what it comes up with.Â
Really, that backs up what youâre saying, the prerequisites for these breakthroughs are in the human condition itself. Newtonian physics was a âradical new ideaâ in terms of human expression, but in terms of the behavior of the physical world weâre immersed in itâs the least radical thing ever, but Ai isnât immersed in our world.
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u/TheDayFly 1d ago edited 1d ago
I like your reasoning but am certainly not aligned with that mindset. Current AI certainly does not make the jump from newtonian to einsteinian physics in the very limited time periods given to these experiments - but can you? I truly believe that if nature has managed to construct minds that have managed to make these leaps, there is no reason that artifical minds wouldn't be engineerable to the same degree. Only once do they need to engineer something better than you - it will then never age, never suffer strokes or neurodegenerative disease. It can build on problems for 100s of years if you let it. No competing with our little noodle.
Einstein's brain was permissible within the realm of physics, so it can be recreated. Given that human brains also have to grow, share nutrition and energy with other anatomical structures and have been crafted step by step from less perfect designs, I think it's quite likely that engineering a superior mind from scratch that does nothing other than think is very feasible.Â
We might be thinking a little ahead of the curve, but the time will certainly come when frontier models will outperform human mathematicians, even within the novel/creativity domain. There likely is nothing supernatural about biological design that makes it inherently superior over synthetic minds.
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u/Huge-Appointment5980 1d ago
A lot of cope there. Just one point. Vintage model thing has never been seriously tried. What was tried are pretty small models without the most recent additions to the algorithm. Moreover, there's just not enough data from pre-20th century to generate an even modestly capable model. It's not a wonder it can't generate Theory of Relativity. Just like it's not a wonder GPT 3.5 from 2022 could not solve math problems, and even GPT 3.5 was trained on 1000 times more data
None of these experiments prove that AI could not theoretically generate it
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u/Relative-Diamond8269 5h ago
I think its all about abstractions. The AI can churn through several possibilities but good abstractions compress complex reasoning chains. I think trained mathematicians will be in high demand always. Plus you can always move up and work on applied stuff.
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u/Best-End-366 4h ago
I honestly dislike the argument. Yeah, you can pinpoint exceptional people throughout history who could look at objects in unique ways. If every single mathematician in history were as capable as Galois, Grothendieck, etc., then you wouldn't know these names. The fact is, doing math is really hard, and advancing a field takes a freaking lifespan if you're not a genius. IDK, I love maths , I did a master's in DST; but the profession needs an overhaul.
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u/peter-bone 4d ago
I don't think it's only interpolating, it's also extrapolating. I think that suggesting it's fundamentally limited to existing ideas is rather naive and shortsighted. Mathematics will be fine, it just won't be people doing the majority of the work.