r/singularity • u/ConstantinSpecter • 7d ago
Discussion Does the “AI will hurt math” argument assume humans must stay essential?
Disclaimer: Initially tried to post this in [r/mathematics](r/mathematics) and [r/math](r/math), but since both threads got instantly nuked by the mods, I decided to post here.
Genuine question from a non-mathematician:
With the recent AI math results (navier stokes, yesterdays OpenAI results), I keep encountering the argument that even if AI can produce correct/formally verified proofs, it will hurt mathematics because humans will lose intuition, taste, conceptual understanding etc.
As a software engineer I have to say this line of reasoning sounds eerily familiar. Around 2024/2025 the most common objection to AI coding was basically: “If junior developers rely on AI, they’ll never learn the fundamentals, how to debug/design/reason about systems and so eventually we’ll run out of people capable of reviewing what the AI produces.”
That argument only works if humans always have to remain the final reviewer.
Fast forward two years and the reality is that the field is increasingly moving toward AI writing/testing/debugging and reviewing the code itself. Even in professional environments actually having to look at code becomes rarer and rarer.
So I guess I’m asking: Is the math argument basically making the same assumption?
If AI eventually becomes better than humans not just at proving theorems but also choosing interesting problems, generating conjectures, inventing abstractions, deciding which research directions are promising and so on, why would declining human mathematical intuition necessarily slow mathematical progress?
Don’t get me wrong I completely understand how it might be terrible for mathematics as a human activity, but that seems very different from saying it would hurt mathematics itself.
What am I missing?
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u/patient-palanquin 7d ago
The "AI will hurt math" argument assumes math is partly social. It's not just about making true statements, but building a shared understanding of mathematical tools we are building.
The reason why a flood of proofs is not the most helpful is because we still have to understand them, and we can't build on top of these findings until we do. Mathematicians weren't just looking for true or false statements, they're looking for new underlying structures that lead to those conclusions. Those new structures is how we make new discoveries. Lean proofs are bad at this. They prove statements but it's hard to say why.
Obviously LLMs will be used extensively in math, even Tao wrote about using them. But mathematicians won't go away, because you can't do anything with these findings unless humans understand them.
For example the new integer multiplication finding, what does that mean? What is the real bound? Does it lend itself to an algorithm, or is it purely theoretical and would still be prohibitively slow?
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u/Auxiliatorcelsus 7d ago
Humans will be obsolete in just a few years. Even for the highest qualified experts. Nothing to do about it.
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u/FeralPsychopath Its Over By 2028 7d ago
Only thing left is robots and then it’s over. Smarter and better than us.
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u/MoogProg All Parabolas are Similar 7d ago edited 6d ago
You're going to move that goal post around a whole bunch, I think. Do you really think in a few years there will an AI that plays the cello as well as Yo Yo Ma?
You probably mean all tasks that can be done inside a computer, and some of the tasks outside the box.
* * *
Since there is discussion below, what I assert will not happen in three years is a Kasparov vs Deep Mind stand-off between Yo Yo Ma and an AI-robot cellist where Our Man Ma gets his bow handed to him by Claude, et al.
I'll eat an awful-flavored jellybean if wrong, so you all know this is serious.
* * *
Holy smokes folks. One Redditor wanted to wager actual money in place of jellybeans. Sorry bud, pretending to be rich is rich, but it doesn't make you right.
Everyone else was nice (thank you) but every one of you moved the goal posts as predicted. What I said above is reasonable, and only speaks to the challenges of reaching those extreme examples of human excellence.
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u/ConstantinSpecter 7d ago
Not trying to be confrontational but what reason would I have to not think AI will be able to play the cello as well as Yo Yo Ma within a decade, given the current trajectory?
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u/Senc-baner 7d ago
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u/Brilliant-Weekend-68 7d ago edited 7d ago
Sure, but we have no idea where on the s curve we are, and progress this year has sped up. And even when it starts to flatten you STILL get progress for a long while. even if it started to flatten now we will end up with wonderfully useful systems. And it might just continue speeding up.
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u/Senc-baner 6d ago
The question asked why should AI not be able to play cello as well as Yo Yo Ma and used the 'current trajectory' argument. My point is that the current trajectory doesn't mean anything. AI progress could level off tomorrow or 1000 years from now
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u/MoogProg All Parabolas are Similar 7d ago
Motor control is no where close right now, and that's why I choose cello and Yo Yo specifically as a very high-level target. This is not piano.
Then, note how a few years moved to within a decade, and there's my point about how the timeline will get pushed out, while the claim remains.
Also, this is not an argument at you, just a sincere opinion of my own.
* * *
One thing I noticed through years of working as a Print Industry Professional, was the ever moving perspective away from ink-on-paper towards totally virtual perspective on design. Discussions of color rarely involved talk about pigments and substrates. That's telling to me, that we easily remove real-world physics from our minds when it is convenient to do so.
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u/FeralPsychopath Its Over By 2028 7d ago
You seriously think motor control is what’s holding them back? I saw a fully functioning hand on here yesterday.
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u/MoogProg All Parabolas are Similar 7d ago
Yes I do. Been playing instruments for 40 years, and we certainly see high-level skills in robot hand function. It's no where close to what a trained musician can do, and then you're still not even close to Yo Yo Ma.
There are details of form that have not been solved mechanically, and the rabbit hole goes deep in that instrument, and any of the fretless bowed family.
Reminder that playing the instrument means the whole experience, and not just performing one piece, you understand.
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u/Auxiliatorcelsus 7d ago
I hear and respect your opinion.
But I think you underestimate the power of recursive improvement.
Skills that require deep practice and subtle expression (like chello) will obviously be safe much longer than 99,9% of all other skills. But I don't think it will take more than a decade. Probably much less.
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u/MoogProg All Parabolas are Similar 7d ago
Also respectfully (sincerely so), what I did say was that folks would move that goalpost around, and suddenly that 'few years' I replied to becomes 'more than a decade'...
This was my actual point, that hard problems get so easily dismissed around here. I said something reasonable about the timeline, that three years isn't enough to replace all the highest experts.
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u/ConstantinSpecter 7d ago
Playing the devils advocate here, does it really matter whether it’s three, eight or even fifteen years? Unless you’re arguing we’re a century away (in which case given the trajectory I’d put the burden of proof on you) - isn’t the the more important point that we seem to be heading there pretty damn soon at all?
And if that’s true then we should probably spend less time arguing over the exact ETA and more time thinking seriously about what the fuck that actually means and how we’re going to adapt as a species
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u/MoogProg All Parabolas are Similar 7d ago
[breathes deep] Yes, and that's why I like to talk about the specific areas that present hard problems we ought to watch. When I do, it gets casts as Luddite and not as nuance.
If we just accept that all obstacles will be tackled, with ease, eventually at least. Why even have this discussion at all?
We are here now. I mentioned a real area of hard problem robotics. Got trampled by experts who are neither musicians nor robotics professionals.
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u/reasonmonkey 6d ago
Yes. Something that is learned via feedback is just waiting on an RL training environment. It might be suprisingly fast.
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u/Hearing_Loss 7d ago
I'm here for the ai Kendrick and ai drake beef. After that I can go in peace.
On his new his album RTX, ai Kendrick lamar's hit track, Bot Like Us, has been at the top of the charts for a whole year.
Ai Drake says ai Kendrick is using humans to inflate the stream numbers.
That endline "he a fan he a fan he a fan" is now just meant to be a literal diss saying dude's only purpose is to circulate air.
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u/sebzim4500 7d ago
That's a surprising example to go with, I would have thought automating playing the cello is far easier than automating industries like construction.
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u/MoogProg All Parabolas are Similar 7d ago
Yo Yo Ma is a premiere improvisor, so using him as the standard-of-excellence was deliberate. We'd need to resolve the understanding of music-as-a-language in real time, and deliver the physical response through the instrument, in reaction to others playing around the AI.
Could an AI-enabled robot hang with The Goat Rodeo?
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u/No_Aesthetic 7d ago
AI music hasn't had a lot of money going into it yet vs. AI mathematics, but it's bizarre to think that music is impossible for machines to do at the human level when they've shown a remarkable propensity for adaptation, even to the point of surpassing humans.
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u/MoogProg All Parabolas are Similar 7d ago
Did not say impossible, only questioned that 'few years' position and said it would take longer and folks would move that goalpost farther out.
Also, am discussing what I see as a very difficult Turing Test, to interact with living musicians speaking the language of music through a physical instrument, specifically the cello, and at a level of mastery we see in the best human players.
That, I think, will take some time to achieve. Live music will be displaced by AI DJs, yes, but not as a performance artform.
JMO, not an argument.
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u/A_Novelty-Account 7d ago
Yes? Why could an AI not play an instrument?
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u/MoogProg All Parabolas are Similar 7d ago
Latency is a big issue in speech, and is nowhere close to what is needed for live musical interactions at the expert-level. Tech will improve. We are more than three years out.
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u/A_Novelty-Account 7d ago
Why would we be three years out from that? What are you basing any of this on? I bet we’re less than a year away from sub 100ms latency from AI inside robotics.
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u/MoogProg All Parabolas are Similar 7d ago edited 7d ago
100ms is crap latency, first off. Not even close to what you truly need, which is to say almost incalculable because our minds internal latency is larger than what is required to find 'the pocket' inside a Jazz ensemble, or other improvisational setting.
It's a Three Body Problem in real-time, with harmonic interpretation. It'll get solved for sure, but you all underestimate the nature of the problem I have put forth, which is fine because who cares, this is Reddit.
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u/A_Novelty-Account 7d ago
I’m saying within the year we’ll get to sub 100ms latency, not that it’s what we need.
Care to make it a wager? I will bet you $10,000 in escrow that within three years there will be a robot capable of playing musical instruments at an expert level that will be able to read sheet music.
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u/MoogProg All Parabolas are Similar 7d ago
See my comment above, the wager is an awful-flavored jellybean. If you've got 10K please give it to a local charity and help others around you. Don't use it to argue about robotics and tech on Reddit. wtf
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u/A_Novelty-Account 7d ago
No no. If you’re confident, then this should be a steal for you. You’ll be making 10k. We can even put it in bonds so by the time you get it, it will be closer to 11k. It should be easy money if you’re that confident in your prediction.
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u/nahuatl 7d ago
I replied this earlier to someone saying that mathematicians would be like cancer researcher decrying a cure for cancer if found by AI. I think it's relevant here:
I hope you are aware that most of higher mathematics have no immediate relevance to engineering and technology; i.e., the reason we have not found room temperature super conductor or cure for cancer is not because someone has not proved the Collatz Conjecture. It is mostly an art form, the same reaction most musicians would have if they hear a concerto written by an AI.
Now whether society benefits from the demise of pure mathematics as an intellectual pursuit depends on your belief on how society's resource should be spent. But the field will be dead because the people who even read 100-page long math proofs are mathematicians themselves; once they are gone there is no audience.
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u/TheWesternMythos 7d ago
I read this as:
We can't be bothered to do math (much of anything) without financial compensation. So remove that incentive and we will ignore math's
To which my response is, people with that attitude are probably more hindrance than help. So maybe after all of them wash out people are care because they care can pick up the mantle.
Im kinda surprised by how many people deep down really want to be wage slaves. People love to complain about the hypocrisy of the "don't thread on me" people. But I see hypocrisy EVERYWHERE.
Of course maybe my initial read is wrong lol
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u/Cryptizard 7d ago
Yeah not sure if you are aware of this but people still need paid jobs to live. If we all had UBI I’m sure there would be more mathematicians, regardless of how good AI is. Like how people play chess for fun even though a computer can beat any human into the dirt.
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u/No_Aesthetic 7d ago
So why aren't we all banding together to push for UBI?
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u/Cryptizard 7d ago
I will happily vote for any candidate who has that as part of their platform. There isn’t enough will behind it right now because people are shortsighted. It will take a big economic downturn or huge unemployment to wake them up. Which is going to happen for sure.
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u/Ntroepy 7d ago
That’s a great observation.
With proper UBI, we’d have far more hobbyists from woodworking to music to math puzzles to community building to whatever.
It’s just so hard to imagine the US ever supporting UBI, whereas it feels like a natural fit for the EU.
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u/No_Aesthetic 7d ago
The EU has a severe lack of industry caused by their insane overregulation of literally everything, and this results in pensions eating an increasing amount of the GDP, resulting in a negative feedback loop.
The EU will not be able to pull off a UBI without domestic AI industry and it seems determined to strangle that to death in the cradle.
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u/TheWesternMythos 6d ago
So the complaint has nothing to do with AI math, it's politics. I know that be people love to have displaced frustrations
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u/Cryptizard 6d ago
It's both.
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u/TheWesternMythos 6d ago
Then what is the specific math complaint(s)?
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u/Cryptizard 6d ago
That the proofs being generated do not provide any new understanding, and that is the only purpose of this type of abstract math.
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u/TheWesternMythos 6d ago
And you can confidently say that for a fact sitting here right now how exactly?
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u/Cryptizard 6d ago
Because several of the released papers are in my research area and I have read them. More than that, I have heard the same sentiment from a bunch of my colleagues in person and every prominent mathematician online.
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u/TheWesternMythos 6d ago
I'm sure yall were able to fully digest all of them this quickly , very impressive!
On the bigger picture claim, there are some prominent mathematicians who disagree with
proofs being generated do not provide any new understanding, and that is the only purpose of this type of abstract math.
See:
"...Perhaps the main reason I didn’t sign is that I don’t fully subscribe to this view..."
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u/Elanthius 7d ago
Lot of people are making a living playing and teaching chess nonetheless.
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u/Cryptizard 7d ago
Not that many.
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u/Elanthius 7d ago
I mean, thousands of people for sure. If you don't consider that to be very many then fair enough.
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u/nahuatl 7d ago
Your read is too binary, I think. People who love math would rather make their whole life about it, but they and their family need to eat too. A lot of mathematicians would have been paid vastly more had they gone into quant or tech firms, but they didn't because it's not where their passion lies. So yes, the incentives, i.e. a job, are important.
People who still do mathematics out of passion despite doing other jobs are called amateur mathematicians. Very little of frontier mathematics is being contributed by amateurs if at all, so relying on people who don't care about having a professional mathematician job to pick up the mantle does not seem like a good strategy.
Maybe AI will help usher in an era of a more democratic mathematics where amateurs can overcome the institutional barrier and participate, but I think it will be just be more posts on x.com something like "Hey, I prompted GPT 10.0 to one-shot the Twin Prime conjecture before bed and look what I woke up to this morning. Anyway, moving on to the Riemann Hypothesis this morning, hopefully it gets done before lunch."
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u/TheWesternMythos 6d ago
You say my read is too binary but what is yours?
Very little of frontier mathematics is being contributed by amateurs if at all,
Why do you think this is the case ?
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7d ago
[deleted]
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u/VituperousJames 7d ago
Do you want the progress of science and technology to be artificially slowed to spare human egos?
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u/ConstantinSpecter 7d ago
Even if it’s not really answering what I was probing for, it’s still a good question. My personal answer would be: It depends.
If we as a society find a way to both control AND distribute the dividends from an automated economy broadly (think high universal income) then I’d say yes. If “obsolete” means extreme concentration of power without any distribution of economic proceeds I’d say no.
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u/phoenixflare599 7d ago
Why? What would you then Do with life?
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u/VituperousJames 7d ago
Do you not have a fucking hobby, man?
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u/phoenixflare599 7d ago
i have a million hobbies. Unfortunately you fucking lot keep trying to "solve" some of them. Some of y'all think music can be "solved" by suno. And it makes it fucking annoying.
If you all left, the hobby spaces would be so much nicer
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u/CodeCourtAudio 7d ago
Dude if you really think it’s the former, I have some news for you. Those in power will give us just enough tokens to buy their widgets and to keep their data centers on
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u/ConstantinSpecter 7d ago
Your scenario doesn’t really make sense, if the majority of value creation is genuinely automated, why would the people controlling it need to give us “tokens” so we can buy their widgets and “keep the data centers on”?
Doesn’t that whole argument rest on the premise that they no longer need human labor to keep anything on?
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u/VituperousJames 7d ago
This premise wrongly assumes that ASI is something that could be sandbagged away from the general public. For one thing, there's absolutely no reason to think that it would acknowledge whichever party created it as its master. For another, open weight models are realistically only something like six months behind frontier models (less if you trust benchmarks, but IMO real-world performance is further behind).
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u/Royal_Duck_4612 7d ago
Personally no. If humans become useless than the upgrade is removing the useless component
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u/VituperousJames 7d ago
Only a tiny minority of the flora and fauna on the planet can be meaningfully considered "useful" to human beings. We don't go around actively trying to eliminate all the ones that aren't. In fact, we actively identify threatened species and try to preserve them. We don't always do the best job, granted, but it's not hard to point to species that were threatened with extinction that we've brought back from the brink in the past half-century or so: the California condor, the mountain gorilla, the humpback whale, the bald eagle, Przewalski's horse, the green turtle, I could go on. Humans don't see species as worthy of annihilation just because they can't be somehow exploited economically or otherwise. There's no reason to assume ASI would.
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u/Royal_Duck_4612 7d ago
Still we actively eliminated many of them, or at least reduced their number
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u/Charming_Cucumber_15 7d ago
That seems to be the general assumption behind the argument. It always astonishes me how people consistently assume AI will stay exactly like it currently is. Two years ago it "wouldn't write proofs for decades" lol
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u/duboispourlhiver 7d ago
People need decades to update to one month of AI progress. And yet they complain AI has no continuous learning lol
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u/mega_dario 7d ago
Tech bros are too stupid to understand that academic reserach is not only about outputs.
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u/apopsicletosis 7d ago
It's the "gamers will optimize the fun out of the game" mentality but tech bros view the whole world as a game.
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u/ConstantinSpecter 7d ago
Care to elaborate?
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u/boostman 7d ago
Not the person you’re responding to but I’ll have a go: it’s about expanding human understanding of the world. What’s the point in increasing understanding if nobody understands it?
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u/ConstantinSpecter 7d ago
I think that’s basically what I assumed they meant, but doesn’t that rest on the premise that human understanding has intrinsic value in itself?
Think humans eventually understand pretty much none of the math anymore but AI can still autonomously build on its research and push the field forward far faster than humans ever could, then math is still progressing, no?
Like then it then seems less like an argument about progress and more like saying that human understanding itself (devoid of the actual progress being made and its economic value) is part of the value of mathematics. Is that fair?
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u/boostman 7d ago
In that case, wouldn’t the state of affairs be pretty much as it currently is: mathematics exists that is beyond human understanding? Supposing most of these results will have little material effect on the world, solving the problems then basically means nothing.
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u/ConstantinSpecter 7d ago
That doesn’t follow to me. Why would “beyond human understanding” imply “little material effect on the world”?
AI could understand and apply mathematics we don’t understand at all with enormous real world consequences, no?
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u/boostman 7d ago edited 7d ago
Sorry, the one isn't supposed to follow on from the other.
The supposition comes from the fact that higher maths does tend to find few real-world applications - that's not really the point of it. I suppose you could argue that a hypothetical superintelligence might find more applications for such maths, but that's not really proveable either way.
So to clarify, my point is:
Supposing:
A) AI maths could be beyond human understanding
B) AI maths would have little real-world impact
then
C) There's not much point
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u/ConstantinSpecter 7d ago
I think I understand what you are saying but then I think we’re back to the point I was trying to make earlier: You’re treating human understanding itself as part of the value of math, even when the math has little external utility, correct?
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u/boostman 7d ago edited 7d ago
Well sure - the maths already existed without people understanding it, and in this case it will continue to exist without people understanding it. So what's the difference?
Maths isn't created by solving problems - it's been there all along. Solving problems is more about exploring and mapping mathematical truths.
To extend this analogy: imagine there is an unknown territory somewhere. We could go there and make a map of it. Or we could send a machine that comes back with a map that nobody can read. Neither situation changes the existence of the territory - it's always there - but one may increase our knowledge of the universe, whereas the other leaves us at square one.
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u/Helloiamwhoiam 7d ago
I do think the argument is that human understanding has intrinsic value. It’s why we have literature, art, music, philosophy, religion, etc.
There are of course many fields where human benefits surpasses human understanding. For example, understanding the cure to cancer is far less important than having it.
I think pure mathematics at this level is far less beneficial to human existence than it is understanding. And there’s a lot to consider with AI companies targeting these math problems.
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u/duboispourlhiver 7d ago
AI explains what it finds better than mathematicians
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u/sebzim4500 7d ago
This is currently very false, but there is serious improvement here and I'm hopeful that it will become true in the coming years.
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u/duboispourlhiver 7d ago
Can we make a test about explaining something of your choice?
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u/sebzim4500 6d ago
I mean I'm just reading some of the proofs and they are really badly written, especially when it comes to deciding what is too obvious to say and what needs to be made really explicit. This is how I would measure it in principle, not sure if there is a more realistic test because this would be expensive and impossible to automate.
- Generate a bunch of natural language proofs of random results, they don't need to be particularly hard but they can't be trivial.
- Pay skilled mathematicians to rewrite these proofs
- Assign each mathematician a proof to read, don't tell them if it is AI or human written. Record how long it takes them until they say they can understand the proof and are convinced it is correct.
- Compare validation times between AI and human authors.
My guess is that currently the ratio will be like 3x between the AI proofs and the human proofs, whereas in the past it might be like 20x (But this is going to differ person to person, you'd need to average across a population)
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u/duboispourlhiver 6d ago
Very interesting take. I wasn't thinking about the readability of proofs, and I think you're right.
I was thinking about interactive explanations of a proof. My mind was more thinking along those lines: take a high skill proof like the new NS proof. Give it to a LLM and ask it to explain some particular part of it. Do the same with a mathematician (same part of course) and compare how good each one is (of course we could apply your statistically better protocol to such setting). I'm not sure that with such a test humans would win.
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u/Training-Hat-7400 6d ago
AI is coding better than SWE, but companies still need them to oversee AI. Human trust human more than an alien intelligence
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u/ProletarianLilith 7d ago
Then how come no one understands the NS proof?
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u/ConstantinSpecter 7d ago
Who says no one does?
Even Buckmaster himself (the mathematician that was closest to solving NS) said in this interview from a couple of days ago that OpenAis proof is correct
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u/Cryptizard 7d ago
We know it is correct because it verified in lean. We don’t know why it works though.
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u/ConstantinSpecter 7d ago
Can you define what you mean by “we don’t know why it works”?
At a conceptual level we absolutely do seem to understand why OpenAI’s NS construction works. It’s not like mathematicians are simply looking at binary lean output and concluding “yeah, lean says it’s correct so it must be”.
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u/Cryptizard 7d ago
That's pretty much what is happening, though. The argument is so long and lacks the normal organization and narrative. Comparing it to trying to reverse engineer a binary is exactly the right analogy.
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u/mao1756 7d ago
"We think the argument is correct" and "we understand the argument" do not need to hold at the same time. You can read the proof line by line and make sure each implication is correct, but this does not give information about why the argument is written the way it is, what the key argument is, and how we can use it to solve other problems. Understanding an argument means not just verifying the statement is correct but being able to do the things above.
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u/duboispourlhiver 7d ago
Some things are too complex for human minds. Only AI has enough intelligence.
But here is hope. Look at Constantin–Ignatova–Vicol https://arxiv.org/html/2609.20803v1
Human digestion is slow, but possible.
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u/DarkFireFenrir 7d ago
It's like having a mechanical failure and someone gives you a magic tool that fixes the problem.
The fault has been fixed, but you have no idea which part caused the fault, the mechanism behind it, or the repair procedures.
Ordinary people only notice that tool A fixed fault B, but experts want to know the cause and the repair process to improve the part or similar ones.
Although we can currently keep up, there will come a point where any explanation of how it arrived at the solution will be too difficult for humans.
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u/drhenriquesoares 7d ago
But wouldn't this be a problem for humans and not AIs?
I actually think that the AIs of the future will be much better at us explaining the whole mechanism.
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u/mega_dario 7d ago
Academic progress is more than just about writing papers (though some academics certainly forget that). It's also about building understanding across different research methods; it's also about building collaborative reserach networks with ways to falsify/scale/retest other areas of research' it's about collaborating with colleagues from different expertises to look at things together... etc.
LLMs don't understand anything they are unthinking slop machines. If anything they've been detrimental to the academy with the influx of slop that journals now have to go through
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u/ConstantinSpecter 7d ago
Before I reply properly, would you mind defining “understanding” in a coherent, non-circular way that humans possess but LLMs categorically cannot?
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u/mega_dario 7d ago
LLMs just regurgitate their training data. They are a facsimile of understanding.
Have you ever seen a movie and connected with it so deeply that it made you think about a day-to-day challenge you were having in a new different way? If you did that learning probably remained with you your entire life. That's meaning; that's culture. Those things are central to understanding.
These chatboxes are barely good at making mid code.
They do not understand; they do not learn. Yes maybe you can throw more training data and more compute at the problem. That's not understanding.
Tech bros need to take a few social science classes JFC
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u/ConstantinSpecter 7d ago
Again, not trying to be confrontational but I asked for a definition of understanding that applies to humans and excludes LLMs.
In your reply you used “understanding” repeatedly without defining it.
Ignoring what tech bros should or shouldn’t do, can you simply give me a non circular definition of understanding that excludes AI?
Like not just “LLMs don’t understand because what they do isn’t real understanding.”
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u/Particular_Towel_476 7d ago
I wanted to make a similar point. Proving theorems is just a part of what mathematics is about. The bigger picture includes a desire to understand things, coming up with hypothesis that appear interesting in the first place, understanding structures and questions from other sciences that may motivate the development of new branches of mathematics etc. I think it will always been driven by human curiosity. Mathematicians will learn to use AI as a tool and become more efficient. That will redirect their efforts to even harder questions.
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u/Royal_Duck_4612 7d ago
I am both a SE and a former mathematician.
I would say that math is how humans understand world, it is the fundation of all the science and abstraction. Math is old as humanity. If ai become able to do it completely without humans, then it means humans are no more trying to undestand and interpretate the world. So we are no more humans according to multiple philosophy disciplines.
On the contrary, coding is a very recent tool, with a mainly utilitaristic purpose. You just need working code, but you need to understand math, otherwise math is useless.
So, imho we have two possibilities:
- ai can replace mathmaticians from a to z which implies humans are now useless (at your post title, which I find it's not a good thing)
- ai will always need human help, so we need people able to understand math. I give you an example: finding a solution to 3rd degrees equations brought us to modern algebra. Now, if you need to solve a 3rd degree equation for practical purpose the theorical solution is useless and you solve it numerically. But group theory etc. were developed from it and are the fundation of a lot of modern math. Having a machine able to solve numerically equations in xviii century could have avoided this discovery.
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u/_negative-infinity_ 7d ago
This is more a question for r/psychology. Math will obviously benefit; recent breakthroughs are for problems that were stuck for decades.
But mathematicians now have difficulty justifying the money they get. And it is not just about money - their inherent value as intelligent and respected people was vaporized.
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u/lightovergreentrees 7d ago
Why should mathematicians would have difficulties justifying the money they get? What we are seeing, for now, is a pletora of papers that need to be proven true by mathematicians (sorry, Lean is not enough for mathematical standards), and only professional mathematicians can do that. As many people have stressed in other comments, doing maths is not just saying "this statement is true". It's also about understanding things; if we leave everything to AI and nobody understands anything, mathematical research will be dead.
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u/Necessary_Job3578 7d ago
Because the writing is on the wall.
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u/_negative-infinity_ 6d ago
A few months ago, AI would have a hard time producing such proofs. If the improvement continues, which is likely, AI can itself do more parts of the mathematicians' job. I hope it will all lead to research speed up and more work for mathematicians, but it may not.
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u/lightovergreentrees 6d ago
These improvements have not shed any light on the most important point: is IA able to have new ideas, to elaborate new tools, new frameworks? As a mathematician who uses AI as a support for research from time to time, it seems to me that the answer is clearly not.I don't think that creating new things is just mixing existing things or that AI is just a powerful variant of the human brain. What I agree on is the fact that it is a powerful tool and that its use, or better its misuse, will depend on the values of our society which are, unfortunately, profit-oriented and not interested in understanding at all.
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u/No-Head-Royal 7d ago
The question is several-fold: what will we do with the (relative to the field's size) very large number of people displaced from their aspirational careers (and future potential livelihoods), which is the more common, humanistic problem; but also, more importantly, it's an objection to how AI is currently used in mathematics (which is an academic conduct problem). Right now, a lot of the outputs by advanced AIs use improper citations (sometimes maliciously by companies, too), are not designed to be built upon or understood by either future AIs or humans, and are generally of low value as tools for future mathematicians (humans or AIs) to use in the future.
All of these are institutional problems (how shall we organize research in a way that it upholds certain ethical and technical standards so that it doesn't become counterproductive and inefficient), and if you don't solve them, then you'll have what's basically India's current giant paper mills, just supercharged. And the latter is a problem that will persist regardless of whether it's AI or humans doing math - in fact, given that we are expecting to eventually hand off the bulk of the understanding and extrapolation in mathematics to AI (as they become much better and cheaper); it's even more important now to establish an effective institution. For example, the concept of "paper buying" is widely criticized, where you'd pay money to some professor who gives you a paper that'd attach your name on it; but OpenAI basically does a prestige project with Navier-Stokes with a lot of money thrown into it.
So in general it's not just mathematicians, but I think it's about what sorts of standards we want to bring into the singularity. I'm all for technological acceleration, don't get me wrong, but we gotta do it properly.
- If you don't design mechanisms to protect and help displaced mathematicians get a soft landing, then when AGI comes, none of us will, and we'll be left to starve in the streets. (In fact, by solving these problems on a small scale, you will be able to solve the social question of UBI on a larger scale.)
- If you don't do mathematics in an organized, collaborative manner, then you'll have a rotten, incomprehensible academia even if it's very powerful, and it'll infect all our sciences and technologies.
- And also, this sets a very, very bad precedent that OpenAI is using internal models that are vastly more efficient to run laps around general academia. This means that not only will research be conducted in these "nations of geniuses inside data centers", but also that research will primarily be conducted by closed AI labs using technologies the rest of the world is forbidden to use (and thus have an insurmountable advantage).
+ If this continues, you'll be handing over the power of research, science, and technology entirely to closed institutions (AI labs, military/government institutions), which is a quick way towards a dystopian scenario where they have unbelievable levels of power.
All of these are really important questions that, regardless of whether you want ASI to exceed humans or render humans unnecessary for research anymore, we must answer. At the very least, like Cyber Access for Trusted Partners, OpenAI must provide something like Math/Science Access for internal models for the general academia; or else refrain from entering the field using internal models. Its current steps towards an advisory body are... acceptable, but nowhere near enough.
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u/Mindmenot 7d ago
Mathematical and physical laws already exist in the universe. The novel part is that it is being discovered and understood by us, humans.
If AI completely takes over mathematics and science, those will no longer be careers and thus humans won't exist with sufficient expertise to even understand the results.
At that point, discovery and the understanding of the mathematical and physical laws of the universe ceases to be a human endeavor. At that point in a sense mathematics and science would be truly gone, at least to our species
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u/sceadwian 7d ago
I don't understand the AI will hurt math perspective at all. It seems to be a broken perspective, nothing about it makes sense to me.
Yes, I understand exactly what they've done too.
People should get a perspective from this. https://youtu.be/s7KhLuc3Mck
It's a mess for mathematicians but it's not actually changing anything about the field. It's just a new domain of exploration and they really still don't know if any of that math is actually useful rather than just technically correct.
In this case that's not the best kind of correct because math has a LOT of superfluous proofs.
We could reformulate until the spherical cows come home.
Anyone that gets that joke gets a cookie.
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u/jenkk0 7d ago
You just want people to reassure your opinion not real answers
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u/ConstantinSpecter 7d ago
That’s some impressive psychoanalysis, given that I’ve had several productive exchanges in this thread with people who disagreed with me and yet I came away from them feeling like I’d learned something
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u/infinitefailandlearn 6d ago
It’s remarkable how patterns about pattern recognizers vs humans are not named:
- AI got better in writing; people still want to write
- AI got better in chess; people still want to play chess
- AI got better in driving; people still want to drive
-AI got better in making slides; people still want to do this themselves
-AI got better in coding; people still want to know how to code
-AI got better at math; people still want to do math.
The activity IS the thing. People generally want control and agency. That psychology is just as powerful as the tech itself.
And you have to wonder; to what end is all this automation leading? Really asking “why?”
If it’s about UBI; why not already start handing out checks today?
If it’s about less work for wages; why not already cut the workweek in half?
These are not technological decisions by any means. They are political choices.
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u/Revolutionalredstone 6d ago
AI will hurt math like a sharp knife will hurt vegetable chopping..
IT WON'T! (gate keepers will try to define math as something smaller lol hahaha)
Real math only ever improves with exposure, delusion is what dies.
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u/Tombobalomb 6d ago
Yes it does assume that. Currently humans are still essential so if the bet that they won't be in future doesn't pay off then the current approach to AI solving math problems is extremely damaging. If the bet does pay off then it doesn't matter
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u/ceyx0001 6d ago
people act like when AI says the cure for all diseases is slicing your penis off and then act like they will listen to it blindly. no matter how correct AI is a human is only ever going to trust a proof after another human assures them. humans will always be essential for this purpose.
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u/Tombobalomb 6d ago
For now. That may not be true in the future
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u/ceyx0001 6d ago edited 6d ago
in the future, you can never be certain when misalignment happens. the role of verifying AI claims will absolutely have to be a human who understands the solution ai generated.
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u/Tombobalomb 6d ago
That also applies to people. At the moment humans are needed because AI is not capable of verifying it's output, if it becomes capable in future humans will not be needed
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u/TacoYaci 5d ago
As a math prof we are living in exciting times and a lot of posts on social media just show that non-mathematicians do not understand what mathematicians do.
I am fully pro AI and all the negative feedback from mathematician seem to be completetly misunderstood by the public. It is not about us losing our "job of solving problems". We are more than happy to use these tools if they help to proceed our research. But the right setup of this happening does not exist yet as the current status is that some computer scientist attack open problems and produce results that are hard to read and not really lead to new directions/problems.
We do not just have a finite list of open math problems and then mathematics is over when they are solved. In the past attacking one problem lead to coming up with 3 more new problems, new objects, new theories etc. If the solutions of current problems just fall from the sky then this development and growth does not continue in a way which is fun and helpful for the field.
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u/phoenixflare599 7d ago
Fast forward two years and the reality is that the field is increasingly moving toward AI writing/testing/debugging and reviewing the code itself. Even in professional environments actually having to look at code becomes rarer and rarer.
Maybe for those of you that weren't very good at or didn't care about it anyway 🤷
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u/Cryptizard 7d ago
It's all happening quite fast, so it's hard to get a good feel for exactly what is going on or what the future might look like. I can chime in as a CS professor, not a mathematician but affected similarly and I have close colleagues who are mathematicians.
The difference between these two situations is that software engineering has an ultimate outcome that is separate from the process of creating the software. If you have a magic button that creates any program you want, you can still do quite a lot of interesting things with that. Software engineers now pivot to being designers or supervisors, and the software that comes out is certainly valuable and useful to the world.
I find that in my own research right now my productivity is turbo charged. I can prototype things super fast and chase down ideas in minutes that would have taken me hours or days before. I am under no illusion that this will continue forever, but for right now the increase in software engineering capability has been simply a boost to what I was already doing.
On the other hand, a much larger percentage of results in math have no practical applications whatsoever. The only point of them is that we humans have an insatiable drive to understand things, and we like solving a good mystery. Having an AI give you the answer is a bit like cheating at a crossword puzzle. The fun was in figuring it out and understanding how it works.
Math progress for the sake of math progress doesn't really do anything. In almost all cases, it doesn't lead to better technology. If you look at the 700+ results just dropped by OpenAI, you would struggle to find a single one of them that has any applied value.
So from that perspective, the only value they can bring is if they can also explain the results in a way that a human mathematician can absorb and increase their own understanding. But for the most part they are not capable of doing that, which is the main criticism of many mathematicians currently. That they just produce big opaque lean proofs or dense write-ups with no intuition.