Much of math (or science) research has the strange quality of being mostly curiosity-driven, but having giant benefits that occasionally spin out to the public.
Some questions are more urgent and practical. My feeling is that the more directly practical a question is, the more likely the research community is to support AI usage in that question.
The annoying thing about recent AI advances is that they target questions on the wrong end of the spectrum: Erdos problems are exactly the sort of "useless" questions that people might answer purely for the love of the game. The sort of questions that a young person might cut their teeth on and gain confidence.
Solving questions like these automatically, I think, is not good for the long-term health of research. At least for the foreseeable future you still would like people to become interested and develop skills in these fields. These developments, and especially how they are presented, directly discourage that.
Sounds like yet another example of how AI is kneecapping industries from the bottom by "removing the barrier to entry" but really just removing the training path by doing the work itself with no guidance for juniors.
> However, the declaration argues math is more than a machine for producing correct answers.
There might be more to maths than that, but that is definitely the most important part.
I love science funding. But not because it's a jobs program for nerds.
To further this assertion, there is almost no value to deeply esoteric math that is technically correct, but completely inapplicable to any scientific reality, and completely unintelligible to humans. Consider these findings deep, dark corners in the unfathomably large hyperspace of mathematics. My guess is AI will be incredibly adept at identifying these types of findings, and it will be exceedingly difficult for humans to identify what is meaningful and what is not in the slop.
Once you now something is correct, with a proof. It is MUCH easier to understand why it is correct. Than to start from a slate that you don't even know whether something is correct or not. In that sense AI that can just solve high level math problems is immensely useful. It allows a mathematician to explore ideas at a much more rapid pace.
Probably one of the funniest things to read on a site like this, when you consider that eg. Boolean algebra was entirely abstract and had little practical purpose for almost 100 years until Shannon picked it up for use in circuits
For most engineers a mathemetician is a machine for producing correct algorithms, like a chef is a machine for producing tasty food. In both cases that overlooks the human element, but that's a critical skill for a limited mind with finite resources to grok infinite complexity. You can read that as permission to be an asshole or a neccesary compromise.
> The authors warn the consequences are already becoming visible. AI-generated papers could overwhelm peer-review systems with low-quality work …
It seems like a key problem here is that peer-review is expected but not explicitly funded/rewarded while it is probably one of the aspects where humans still add a lot of value. Academia’s incentives are hugely misaligned (… as usual unfortunately).
Math is one field where you can mechanically prove a paper's findings. The only thing that would need to be judged is the (verified) statement's importance.
That's a bit too simplistic -- if there is a small group that really pushes things forward in a big way, then maybe not, but if this result builds upon decades of prior work, then Cook and Levin might be equally or even slightly more famous than the solver group after the dust settles.
But it is a moot point anyway. Cook and Levin are very well known already in TCS, and credit is not directly enumerable like money, so "more than a lot of credit" doesn't make too much sense.
For this problem in particular, asking the right kind of question was really important for the field and led to a lot of discoveries even before it will be answered.
If the problem resolves to P=NP, that result would probably be more celebratee than being able to formulate the problem, but being able to formulate the problem and get people interested in it is probably worth more than the average primal dual trick to prove a polylog integrality gap for some integer linear program.
The wording in the declaration may be a bit romanticized. But the points are valid:
Is an 80 year old unsolved problem maybe unsolved because it was never prioritized? Some problems stay unsolved because few people consider them worth working on.
Who is going to validate the results? Or do we skip that, with the risk of flooding the literature and collective understanding with unverified proofs?
This reminded me of my 11 yr old who, when I give her math problems to solve, is too focused on “getting the right answer”. I’ve told her plainly, I don’t care if you get the right answer right now, I want to see your reasoning. She has yet to understand this.
Even from the most purely instrumental perspective, what we care about is our ability to make use of correct answers, which is quite distinct from the possession of correct answers.
There are many theorems that aren't directly interesting, but whose proof requires techniques that are of substantial further interest, that lead to new domains, and/or new practical applications. Simply being handed a proof for those theorems isn't enough--we require the ability to apply those techniques in the real world, or discover further areas of mathematical research that build on that proof or its techniques.
It may be that AI can build on its own work for the long-term, but so far, AI does best at exploration in areas that have precisely specified and measurable goals. Actually creating understanding, and making use of mathemtical results outside of pure mathematics is more challenging than simply creating proofs.
I think the field will figure out how to make use of AI, and it will be better off for it. But that is not the same as just saying "answers good, grog want more answers."
Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field.
Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI generates and verifies proofs without humans in the loop. Where the mathematics may be beyond human comprehension.
In that future, does it matter that early career mathematicians are inhibited by these developments? Perhaps not. Programming faces the same issue. As AI crawls up the competence ladder, does it matter that fewer people have opportunities to develop the skillset of a senior engineer? Perhaps not.
Much like for many the point of chess is that it's played by humans, with truly superhuman AI relegated to a training aid, mathematics is in many ways about human comprehension. You can use AI to find and proof new theorems. But if you get to the point where humans can't understand it, is it even still math?
My vague prediction right now is that in five years LLMs will be heavily used by universities in grant-funded math research but nobody else will be able to afford it, much like supercomputer clusters 25 years ago.
Well, if progress in LLMs will steadily continue over next 5 years, then models will be so powerful that there will be no longer place for (most of) human researchers in math (remember that 5 years ago there was no chatgpt!). But I think it's more likely that progress will stall and then open models will catch up to frontier models and almost everyone will be able to afford them.
Seems way too binary a statement. I am guessing you mean "frontier LLMs". Small models keep getting better and better and if you make domain specific ones, it will likely be even smaller. Companies renting smaller LLMs or using enterprise models might very well remain in the future. Consumers getting LLMs whose performance dont improve (think gpt 6 forever on premium or gpt 4.x on a cheap tier) might well become a thing.
> AI-generated papers could overwhelm peer-review systems with low-quality work
That's not a problem unique to math, or even to academia. It's a problem in every context in human life where people communicate via written documents.
Except when someone hands you a magic button that just gives you knowledge?[at least in the framing of this "warning"] Then it's about peoples' livelihoods, about "culture", etc?
"Computer" used to be a job. Did science on the whole lose or gain by making these clerks obsolete?
In a year, none of this will really matter. Intelligence is now a scalable resource independent of biological constraints. Everyone will use it because the system will no longer afford them the luxury of time. In a decade (maybe sooner), references won’t matter either.
Does it matter if the Leiden Declaration is correct? To the humans, maybe but not in the bigger picture.
At scale, correctness and reward are becoming increasingly disconnected. Example: capital continues to compound regardless of whether it reflects underlying human welfare, just as information can spread regardless of whether it is true. Reality still matters, of course. If you want airplanes to stay in the air, somebody eventually has to be correct. The problem is that our economic and social systems are becoming less effective at distinguishing between what is true and what is merely rewarded.
"""
However, the declaration argues math is more than a machine for producing correct answers. The discipline, its authors believe, is a deeply human endeavor built on creativity, understanding, collaboration, and the pursuit of knowledge for its own sake. Those values often clash with the incentives driving AI development. “The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics,” declaration co-author Michael Harris of Columbia University told The New York Times.
"""
I mean, what field doesn't? Everyone works to make money.
Slightly unrelated, but, their website "https://leidendeclaration.ai/" itself gives an eerie feeling of being built by Sonnet. That color scheme and the layout is what Sonnet chooses by default most of the times.
As a mathematician by trade I think they’re overblowing it. You can choose to use it or not. I choose not to because I enjoy the process. But I’m not doing formal research or getting paid to do it these days.
I will note that the average corporate mathematical modelling is usually a fucking circus so adding AI might make it better.
This is becoming less and less true unless you're specifically talking about usage of it outside of a work environment. Many work places are requiring people to use it and/or tracking usage. I don't know about in academic settings, but I'd imagine it's becoming heavily used there too?
The choice only remains if using it isn’t a huge multiplier. If it is a huge multiplier/accelerator, then for a while it will be ambiguous and the choice will remain. But as time goes on, the gains of using it will be so apparent and the advantage of the people who use it so great (in publication numbers, hiring, etc) that it will force others to.
I don’t say that with any particular relish. But I am skeptical of the choice angle past a certain point.
I don't think all universities or research agencies are particularly pressed on this. I mean my daughter is a notable researcher in a scientific field and they have absolutely no pressure to use AI to pump out papers or deliver value quickly.
I highly doubt there is any overt pressure in academia right now to use AI. It’s a relatively conservative institution. But there’s certainly pressure to publish (publish or perish being a common phrase for decades), and competition for jobs in academia is fierce. That’s what I meant in referring to long term pressure.
Well I rather like to be paid more than a mathematician so left academia rather quickly. In my case corporate modelling mostly involves making prediction models based on shitty data and metrics to make poorly contrived business decisions that lose millions of dollars.
I've said it before, but there's a massive risk that we simply stop educating researchers. So much of a Ph.D revolves around the person learning how to do research.
They learn how to read papers and literature rigorously. They get low-hanging fruits to practice on, which can take months. Their funding doesn't come from thin air either.
So what happens when the group leaders would rather spend money on compute, and get models to solve the low-hanging fruit? Which the models could very well do in mere hours, compared to months.
Nor does it help that publishing is the number 1 measure in academia. Furthermore, the access to compute and capital could end up be the defining factor between researchers and research groups.
It is basically the "junior problem", but even more severe.
> Furthermore, the access to compute and capital could end up be the defining factor between researchers and research groups.
That's not new - especially in the experimental sciences ( ie perhaps more than maths ) - where the ability to have access to the latest kit is often what determines success - a huge amount of science progress is driven by new experimental technology rather than smart people thinking beautiful thoughts.
Absolutely, but at least in the pure / less applied fields, access to computation hasn't really been that critical. The more towards the pure and theoretical, less so.
But now you have people like Gowers and Tao, pure mathematicians, hyping up what the SOTA models can do - and I figure they both are getting access and tokens us mortals can't afford.
So I guess the question is - will everything be as expensive as applied fields?
I still don't understand how "AI" is ready for serious use beyond entertainment purposes
Every time I ask ChatGPT to make a table for a subject I know well, I will find an error in one of the results and it is very confident about it until I question it in detail
Every time I ask ChatGPT for nutritional breakdown of some dense food source and give it a quantity like 8 ounces and ask for the weight of each ingredient, the weights will be wrong and add up to more than the original weight of 8 ounces
These are variations of the old "how many Rs in strawberry" problem, it's still not solved, "AI" cannot reassemble a complex problem properly
A lot of what it tells me in detail about some subjects sounds suspiciously like Reddit posts reassembled out of order
Are maths AI models now using "tools", aka formal solvers?
I understand that the "language interface" of a "maths AI" could be some specialized trained LLM (Large Language Model) that to convey, with human language, "high level" mathematical mental contructs and intuition.
But then, you would need some models which does the reasoning using formal mathematical solvers (and probably a ton of "scratch" memory, it would be interesting to see how those models end up storing "mathematical" lema data). I guess you can have ML (Machine Learning) for those models on 'general maths', but also we can think about more mathematically focused ML for a specific problem, area, etc.
And in the end, ML for maths, would it be mostly permutations of truth statements fed to a neural net?
When we were talking about "AI", one decade ago, that was what most had in mind (it may help a bit in physics, but it seems less likely, because reality/experiments are hard to teach to "AI"s).
If that becomes a reality (aka easy hardware access, and some "working" models), mathematicians will have to be as good in maths than in maths ML. And this is were there is an issue: training honestely good mathematical human brains may become very hard with some broad availability of good general maths reasoning "AIs".
I will argue that AI and flood of low quality slop makes genuine human work more valuable, not less.
The ability to clearly outmatch trillion dollar machines is a very unique satisfaction. I even write ordinary internet comments with an intention to make them clearly better and more fun to read than boring Claude output.
Much of math (or science) research has the strange quality of being mostly curiosity-driven, but having giant benefits that occasionally spin out to the public.
Some questions are more urgent and practical. My feeling is that the more directly practical a question is, the more likely the research community is to support AI usage in that question.
The annoying thing about recent AI advances is that they target questions on the wrong end of the spectrum: Erdos problems are exactly the sort of "useless" questions that people might answer purely for the love of the game. The sort of questions that a young person might cut their teeth on and gain confidence.
Solving questions like these automatically, I think, is not good for the long-term health of research. At least for the foreseeable future you still would like people to become interested and develop skills in these fields. These developments, and especially how they are presented, directly discourage that.
Sounds like yet another example of how AI is kneecapping industries from the bottom by "removing the barrier to entry" but really just removing the training path by doing the work itself with no guidance for juniors.
> However, the declaration argues math is more than a machine for producing correct answers.
There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.
The most important part of math is advancing human understanding. A correct answer by itself is not as important as understanding why it is correct.
"What is the answer to the Ultimate Question of Life, the Universe, and Everything"
42
To further this assertion, there is almost no value to deeply esoteric math that is technically correct, but completely inapplicable to any scientific reality, and completely unintelligible to humans. Consider these findings deep, dark corners in the unfathomably large hyperspace of mathematics. My guess is AI will be incredibly adept at identifying these types of findings, and it will be exceedingly difficult for humans to identify what is meaningful and what is not in the slop.
Once you now something is correct, with a proof. It is MUCH easier to understand why it is correct. Than to start from a slate that you don't even know whether something is correct or not. In that sense AI that can just solve high level math problems is immensely useful. It allows a mathematician to explore ideas at a much more rapid pace.
Probably one of the funniest things to read on a site like this, when you consider that eg. Boolean algebra was entirely abstract and had little practical purpose for almost 100 years until Shannon picked it up for use in circuits
For most engineers a mathemetician is a machine for producing correct algorithms, like a chef is a machine for producing tasty food. In both cases that overlooks the human element, but that's a critical skill for a limited mind with finite resources to grok infinite complexity. You can read that as permission to be an asshole or a neccesary compromise.
> The authors warn the consequences are already becoming visible. AI-generated papers could overwhelm peer-review systems with low-quality work …
It seems like a key problem here is that peer-review is expected but not explicitly funded/rewarded while it is probably one of the aspects where humans still add a lot of value. Academia’s incentives are hugely misaligned (… as usual unfortunately).
Math is one field where you can mechanically prove a paper's findings. The only thing that would need to be judged is the (verified) statement's importance.
Yes in theory, but not yet in practice because not everything is fully formalised.
No, it's not the most important part. It can be argued that most important part is asking the right questions
Assume someone solves P=NP
Do you think Stephen Cook and Leonid Levin deserve more credit than whoever solved it?
That's a bit too simplistic -- if there is a small group that really pushes things forward in a big way, then maybe not, but if this result builds upon decades of prior work, then Cook and Levin might be equally or even slightly more famous than the solver group after the dust settles.
But it is a moot point anyway. Cook and Levin are very well known already in TCS, and credit is not directly enumerable like money, so "more than a lot of credit" doesn't make too much sense.
For this problem in particular, asking the right kind of question was really important for the field and led to a lot of discoveries even before it will be answered.
If the problem resolves to P=NP, that result would probably be more celebratee than being able to formulate the problem, but being able to formulate the problem and get people interested in it is probably worth more than the average primal dual trick to prove a polylog integrality gap for some integer linear program.
I agree with both OP and you
I disagree with everyone, self included, but especially with Cretans.
Cretani eunt domo!
Monty Python fan detected :D love your profile desc btw
The wording in the declaration may be a bit romanticized. But the points are valid:
Is an 80 year old unsolved problem maybe unsolved because it was never prioritized? Some problems stay unsolved because few people consider them worth working on.
Who is going to validate the results? Or do we skip that, with the risk of flooding the literature and collective understanding with unverified proofs?
This reminded me of my 11 yr old who, when I give her math problems to solve, is too focused on “getting the right answer”. I’ve told her plainly, I don’t care if you get the right answer right now, I want to see your reasoning. She has yet to understand this.
Even from the most purely instrumental perspective, what we care about is our ability to make use of correct answers, which is quite distinct from the possession of correct answers.
There are many theorems that aren't directly interesting, but whose proof requires techniques that are of substantial further interest, that lead to new domains, and/or new practical applications. Simply being handed a proof for those theorems isn't enough--we require the ability to apply those techniques in the real world, or discover further areas of mathematical research that build on that proof or its techniques.
It may be that AI can build on its own work for the long-term, but so far, AI does best at exploration in areas that have precisely specified and measurable goals. Actually creating understanding, and making use of mathemtical results outside of pure mathematics is more challenging than simply creating proofs.
I think the field will figure out how to make use of AI, and it will be better off for it. But that is not the same as just saying "answers good, grog want more answers."
People need jobs. What's wrong with nerds having jobs via a program?
well put.
Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field.
Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI generates and verifies proofs without humans in the loop. Where the mathematics may be beyond human comprehension.
In that future, does it matter that early career mathematicians are inhibited by these developments? Perhaps not. Programming faces the same issue. As AI crawls up the competence ladder, does it matter that fewer people have opportunities to develop the skillset of a senior engineer? Perhaps not.
Much like for many the point of chess is that it's played by humans, with truly superhuman AI relegated to a training aid, mathematics is in many ways about human comprehension. You can use AI to find and proof new theorems. But if you get to the point where humans can't understand it, is it even still math?
Perhaps P=NP. The new algorithms are handed down to us. We can apply them without fundamentally understanding why P=NP.
My vague prediction right now is that in five years LLMs will be heavily used by universities in grant-funded math research but nobody else will be able to afford it, much like supercomputer clusters 25 years ago.
Well, if progress in LLMs will steadily continue over next 5 years, then models will be so powerful that there will be no longer place for (most of) human researchers in math (remember that 5 years ago there was no chatgpt!). But I think it's more likely that progress will stall and then open models will catch up to frontier models and almost everyone will be able to afford them.
Seems way too binary a statement. I am guessing you mean "frontier LLMs". Small models keep getting better and better and if you make domain specific ones, it will likely be even smaller. Companies renting smaller LLMs or using enterprise models might very well remain in the future. Consumers getting LLMs whose performance dont improve (think gpt 6 forever on premium or gpt 4.x on a cheap tier) might well become a thing.
Sounds very good for regular joe software dev, almost too good to be true
> AI-generated papers could overwhelm peer-review systems with low-quality work
That's not a problem unique to math, or even to academia. It's a problem in every context in human life where people communicate via written documents.
>and the pursuit of knowledge for its own sake
Except when someone hands you a magic button that just gives you knowledge?[at least in the framing of this "warning"] Then it's about peoples' livelihoods, about "culture", etc?
"Computer" used to be a job. Did science on the whole lose or gain by making these clerks obsolete?
In a year, none of this will really matter. Intelligence is now a scalable resource independent of biological constraints. Everyone will use it because the system will no longer afford them the luxury of time. In a decade (maybe sooner), references won’t matter either.
Does it matter whether any of this is correct?
(Mathematics at least has the potential for automated non-AI proof checking, although I don't think that's as widely used as you'd expect)
Does it matter if the Leiden Declaration is correct? To the humans, maybe but not in the bigger picture.
At scale, correctness and reward are becoming increasingly disconnected. Example: capital continues to compound regardless of whether it reflects underlying human welfare, just as information can spread regardless of whether it is true. Reality still matters, of course. If you want airplanes to stay in the air, somebody eventually has to be correct. The problem is that our economic and social systems are becoming less effective at distinguishing between what is true and what is merely rewarded.
""" However, the declaration argues math is more than a machine for producing correct answers. The discipline, its authors believe, is a deeply human endeavor built on creativity, understanding, collaboration, and the pursuit of knowledge for its own sake. Those values often clash with the incentives driving AI development. “The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics,” declaration co-author Michael Harris of Columbia University told The New York Times. """
I mean, what field doesn't? Everyone works to make money.
Slightly unrelated, but, their website "https://leidendeclaration.ai/" itself gives an eerie feeling of being built by Sonnet. That color scheme and the layout is what Sonnet chooses by default most of the times.
Actual "warning":
https://leidendeclaration.ai/
Far more interesting as it's outlaying a set of principles for using AI to augment human involvement and science, rather than replacement.
As a mathematician by trade I think they’re overblowing it. You can choose to use it or not. I choose not to because I enjoy the process. But I’m not doing formal research or getting paid to do it these days.
I will note that the average corporate mathematical modelling is usually a fucking circus so adding AI might make it better.
> You can choose to use it or not
This is becoming less and less true unless you're specifically talking about usage of it outside of a work environment. Many work places are requiring people to use it and/or tracking usage. I don't know about in academic settings, but I'd imagine it's becoming heavily used there too?
My academic connections that I keep in touch with never really left the 1990s. And no one is pushing them on AI.
The choice only remains if using it isn’t a huge multiplier. If it is a huge multiplier/accelerator, then for a while it will be ambiguous and the choice will remain. But as time goes on, the gains of using it will be so apparent and the advantage of the people who use it so great (in publication numbers, hiring, etc) that it will force others to.
I don’t say that with any particular relish. But I am skeptical of the choice angle past a certain point.
I don't think all universities or research agencies are particularly pressed on this. I mean my daughter is a notable researcher in a scientific field and they have absolutely no pressure to use AI to pump out papers or deliver value quickly.
I highly doubt there is any overt pressure in academia right now to use AI. It’s a relatively conservative institution. But there’s certainly pressure to publish (publish or perish being a common phrase for decades), and competition for jobs in academia is fierce. That’s what I meant in referring to long term pressure.
OOI, and my own total ignorance, what does a mathematician by trade do if they are not doing formal research? What does corporate modelling entail?
Well I rather like to be paid more than a mathematician so left academia rather quickly. In my case corporate modelling mostly involves making prediction models based on shitty data and metrics to make poorly contrived business decisions that lose millions of dollars.
Read the declaration. The article misrepresents it imo. It is not strongly opinionated.
I've said it before, but there's a massive risk that we simply stop educating researchers. So much of a Ph.D revolves around the person learning how to do research.
They learn how to read papers and literature rigorously. They get low-hanging fruits to practice on, which can take months. Their funding doesn't come from thin air either.
So what happens when the group leaders would rather spend money on compute, and get models to solve the low-hanging fruit? Which the models could very well do in mere hours, compared to months.
Nor does it help that publishing is the number 1 measure in academia. Furthermore, the access to compute and capital could end up be the defining factor between researchers and research groups.
It is basically the "junior problem", but even more severe.
> Furthermore, the access to compute and capital could end up be the defining factor between researchers and research groups.
That's not new - especially in the experimental sciences ( ie perhaps more than maths ) - where the ability to have access to the latest kit is often what determines success - a huge amount of science progress is driven by new experimental technology rather than smart people thinking beautiful thoughts.
Absolutely, but at least in the pure / less applied fields, access to computation hasn't really been that critical. The more towards the pure and theoretical, less so.
But now you have people like Gowers and Tao, pure mathematicians, hyping up what the SOTA models can do - and I figure they both are getting access and tokens us mortals can't afford.
So I guess the question is - will everything be as expensive as applied fields?
I'm curious about whether we will start discovering new maths in the next few years that provide insight into unsolved CS or Physics problems!
For all you know, some of this has already happened but kept secret for national security reasons
I still don't understand how "AI" is ready for serious use beyond entertainment purposes
Every time I ask ChatGPT to make a table for a subject I know well, I will find an error in one of the results and it is very confident about it until I question it in detail
Every time I ask ChatGPT for nutritional breakdown of some dense food source and give it a quantity like 8 ounces and ask for the weight of each ingredient, the weights will be wrong and add up to more than the original weight of 8 ounces
These are variations of the old "how many Rs in strawberry" problem, it's still not solved, "AI" cannot reassemble a complex problem properly
A lot of what it tells me in detail about some subjects sounds suspiciously like Reddit posts reassembled out of order
Are maths AI models now using "tools", aka formal solvers?
I understand that the "language interface" of a "maths AI" could be some specialized trained LLM (Large Language Model) that to convey, with human language, "high level" mathematical mental contructs and intuition.
But then, you would need some models which does the reasoning using formal mathematical solvers (and probably a ton of "scratch" memory, it would be interesting to see how those models end up storing "mathematical" lema data). I guess you can have ML (Machine Learning) for those models on 'general maths', but also we can think about more mathematically focused ML for a specific problem, area, etc. And in the end, ML for maths, would it be mostly permutations of truth statements fed to a neural net?
When we were talking about "AI", one decade ago, that was what most had in mind (it may help a bit in physics, but it seems less likely, because reality/experiments are hard to teach to "AI"s).
If that becomes a reality (aka easy hardware access, and some "working" models), mathematicians will have to be as good in maths than in maths ML. And this is were there is an issue: training honestely good mathematical human brains may become very hard with some broad availability of good general maths reasoning "AIs".
Another mathematician already predicted this, but you didn't listen. His name was Theodore Kaczynski. It's time to reap what you've sown.
I will argue that AI and flood of low quality slop makes genuine human work more valuable, not less.
The ability to clearly outmatch trillion dollar machines is a very unique satisfaction. I even write ordinary internet comments with an intention to make them clearly better and more fun to read than boring Claude output.