I guess as a physicist I am more hopeful - every revolution in how the world is understood (by humans) has been driven by new tools and data. Being able to measure single quanta, for instance, showed us just how weird and counter-intuitive the Universe can be. I think AI might do something similar for mathematics - make connections that a human brain might have missed, and so advance human knowledge.
But I totally get the anxiety - it's a real John Henry (https://en.wikipedia.org/wiki/John_Henry_(folklore)) moment for the mathematics field. Clearly this is going to restructure how mathematicians are going to be trained and how they work.
The issue is when humans no longer understand what AI is telling us and then there is no real way to verify what we think we know, or at least what AI says.
But generally
speaking it is easier to verify a proof is accurate that it is to find the proof. So not sure this holds.
I suppose their is some complexity limit where something is so complex we can’t even validate it. But frankly would love to reach that point. I’d view that as a good thing
I'm also a physicist. But I think the next 5 years are going to be a rough ride for math. I'm struck by the following observation, mainly from following HN links to Terrence Tao's blogs.
Novel proofs are the coin of the realm for junior mathematicians. They figure into training, career advancement, and indirectly, teaching. The reason I include teaching is because it requires tenure, which requires proofs. Teaching without tenure is gig work, not a career. But proofs can be devalued to zero.
The application deadline for grad school is a few months away. For a student considering a math career, they have to deliver a thesis in a few years, that their professor is willing to sign. Nobody knows what that will look like without proofs. "We will have to do something different" is weak sauce.
I’m also a physicist, and I do worry about physics. I’ve already had a few successful sessions with Claude and Astra where they came up with useful ideas in my field. I still know what to ask for and nudge them where it matters, but I fear it’s going to be a few short months before they can decide that too, unassisted.
Indeed, and they're already better in a sense. I would never try to compete with the robots at basic manufacturing such as CNC machining and automated circuit assembly.
But for stuff that needs really quick turn-around, as a prototype or experiment evolves, I can take care of custom tasks and repairs that would otherwise take days. And it doesn't take many of those kinds of delays to utterly cripple a project.
However, I'm under no illusions, and have a "never say never" mindset. I don't claim to have a "safe" job. I'm already using AI heavily myself. The computer that's next to each lab bench is running the latest coding agents or whatever you call them. I'm not as deep into it as the coders are, but I'm not all that far behind. My token burn is respectable. ;-)
Without novel proofs. If AI can churn out proofs, then anybody's work can get "scooped." I've seen this happen to students in other fields, where it has reached the point that students refrain from giving conference talks in order to avoid revealing their research topic.
My thesis project, 30+ years ago, was protected by a unique assemblage of expensive equipment, some of it purpose-built. The people who wanted my result were perfectly happy to wait for me to finish it. I even shared my shop drawings, circuit diagrams, and source code with them as I progressed.
I think at the very least students need to know what to expect. Maybe it will settle down and we'll be OK.
Many public school teachers in the USA have some sort of tenure. For example, in Massachusetts, after a three year probationary period, a teacher is given Professional Teacher Status. A teacher with PTS may be dismissed only for specified statutory reasons. High school tenure is generally not as strong as for colleges, but is easier to get.
Anecdotally, I had an adjunct teaching gig at a state university many years ago while I was in between jobs. My mom is a retired public school math and science teacher, and was on her district's union negotiating team. I described my gig to her, and her response was: "Now you know why teachers have a union."
True, but secondary school teaching requires additional training, so it's not an option for most students thinking about applying for graduate programs. And it's a very high-attrition occupation.
I think AI will turn out to be quite different from those earlier advances in tooling, in that AI replaces thought itself. So next time it probably won’t be a human physicist that does the intellectually challenging work of constructing quantum mechanics from measurements of individual quanta. It will most likely be an AI.
Once IBM deep blue beat Kasparov in chess, IBM stopped their chess playing research.
The marketing goal, if you will, had been met and IBM would continue their actual money making business of selling mainframes and doing consulting.
The same thing will happen with AI companies’ endeavors into abstract maths.
Maths however will be changed - students can no longer be taught via the same homework - and mathematicians will have to do more computer work and probably work in larger groups of people.
Of all the cope I expected, this wasn't on my list until now.
Now that art has been generated, we will stop there, and that code is generated our reason to do any of that (marketing as an end in itself) has been concluded and we will shut down all operations now.
Exactly. And that will be the lasting thing here wrt maths. These things have value, just not commercial value, and that is why long term, it won’t be the interest of private companies.
I guess it depends on how efficiently that verification can be produced as a byproduct of building an optimal hunter-killer drone, or training the type of model that builds an optimal hunter-killer drone
Hopefully we can put this aside quickly and move on to using AI to solve great scientific/philosophical problems such as the theory of everything and the hard problem of consciousness.
The thing that is so confusing about this is the following fact -
Lets say the frontier of some specific problem or a field in math is at x. X was reached over millenia by incremental steps and sometimes to leaps and jumps.
Now if AI gives us a x + 1 or x + 10 state, aren't there still x + infinite steps to climb? Many of this the AI can never imagine and won't reach by itself without human assist.
Yes, there is a temporary shock and awe because of all the low hanging x + 1 through x+ 1000 fruits for a given sub-domain/problem have been carpet bombed or whatever.. but isn't it turtles all the way!? Won't people soon find something more to develop and solve that takes it further than where it was of this infinite realm of exploration?
Even if I tell it to work on its own, it is always a tool in my hand. I grant it agency for my purposes. I'm the Meta-Master.
The question for mathematicians is: what can a mathematician do with these new tools that no one else can?
Waxing nostalgic about the sound of pencil on paper or the beauty of your abacas is a different conversation, as is the complaining about who moved my math cheese.
Yes, 100% when goals are defined and rewards are a part of the feedback loop.
Isn't open ended research is truly open ended. Like there are a gazillion questions to ask and even more solutions that can be offered. Now which questions to pursue is human volition.
Yes, humans will not be able to reach certain steps without computer assist.
However, which questions to ask is a human endeavor, out of infinite possible pool of questions.,
now computers can ask questions as well. But if it were to ask it will be more like a monkeys and typewriters type of a situation. Tons of questions and a few that are relevant for the interested human., who has to foot the bill for those questions.
Agree with the shock but there is no doom and gloom.
Looking at things after the temporary shock. Future is Human + computer assisted problem solving, working in tandem, just like what Garry Kasparov mentioned in his book [0].
[0] - "Deep Thinking: Where Machine Intelligence Ends and Human Creativity Begins"
But you are living in the world after the temporary shock, and you are asking the people who are still in the middle of the shock "Why aren't you over the shock yet"?
The chess example is not an inspiring one. It was true for a decade that humans and chess programs working in tandem were better than programs alone, but since then humans only hold chess programs back. Carlsen plus Stockfish is a worse chess player than Stockfish alone.
Agree that chess is not the ideal example to use for the AI domain.. but used for building a quick mental image.. reason being that in chess, AI does have an objective truth built into its training.. and that is to checkmate.
The real world open ended research doesn't always have an evaluation function. A computer can calculate 10 million options to solve a problem, but it cannot tell you if you're solving the right problem from the human context. That's why centaur setups fail in closed games, but remain essential everywhere else.
Another loose example just to build a mental model .. AI driven cars do a great job in most driving situations but often fail to park in a good parking spot for most people! Good parking spot is partly human initiated and subjective.
AI could bear out, but it seems a lot of hype to me. Does anyone remember how Japan built up AI and their 5th generation language (Prolog) in the 1980s?
"The internet could bear out, but it seems a lot of hype to me" --Many, many people in 1997.
Honestly I don't know how you formed this particular opinion (if it's even your own and not a false consensus of other peoples thoughts). I cannot see any future without LLMs unless replaced by something smarter, cheaper, and faster. That's because it's already bearing out. I can talk to a computer and the computer can solve problems based on words alone. I'm old enough this is pure science fiction. If I could send one of these machines back to that past for people to interact with, there are those that would scream and pass out in terror. They would absolutely tell you that we created the monster we should never create.
If you're trying to compare symbolic AI of the past to what we have now, you're not even on the same field, you're playing a completely different game.
> "The internet could bear out, but it seems a lot of hype to me" --Many, many people in 1997.
There was a LOT of hype around "this is an entire new economic model". While, yes, digital products have zero marginal cost, people were talking as if profits and revenue didn't matter.
This was also WAY before the famous Silicon Valley "pure play" scene. [0]
Don't make the mistake of thinking because there was hype that everything was wrong. HN seems to have a lot of posters that run logic in a boolean manner. { if !perfect then false }. The world is a far more complex place than that both naturally and intentionally by human will.
And the internet has devastated many past businesses that were highly profitable. A great many things in the world look vastly different than from before.
>people were talking as if profits and revenue didn't matter.
People say all kind of dumb shit too. If for example machine intelligence took over the world tomorrow and turned all of humanity into meat cubes for biofuel said intelligence is still going to apply the basic laws of economics to what it does. It needs to have some way of accounting that fact we live in an energy limited universe. Just because economics still applies doesn't mean that we as humans shouldn't be really fucking careful creating said machines as we don't want to end up as biofuel.
AI has already born out at this point. The question is no longer it's future capabilities but the impact of its present capabilities - though with its present capabilities, someone is now going to be pushing for more, at least as long present computer tech is widely available.
> Someone asked him what he thought of the AI proof. Justin said he didn’t know. He hadn’t read the paper yet. He said he’d been “too busy.”
> That astonished me. Too busy to look at a problem he had been dreaming about for 19 years? “I am genuinely busy and probably wouldn’t be able to get to reading a human’s proof immediately either,” he told me afterward, by email. “It does not help that AI does not write mathematics particularly well.”
Given:
* The human mathematicians can't solve the problems.
* The slop engine can't write well enough to make its purported solutions readable by human mathematicians.
* Sam Altman is a frivolous liar.
How is it possible to know whether the problems have been solved at all?
Could the press kindly interview one of the 1008 members of the AHM (https://www.ahmath.org/members). Maybe Peter Scholze if you need a Fields Medalist:
Maths is made of two parts: questions, and solutions.
Machines could, presumably, become good enough at hammering at solutions. But they won't be very good at finding questions. Because questions are infinite. And to a machine, all these questions are the same.
Questions are "good questions" because they are good questions *to* humans. And that's what makes human mathematicians (and scientists) so important
That seems like wishful thinking. Why wouldn’t AI be able to assess what are good questions to humans, and pursue similar processes as those that lead humans to come up with good questions? AI is trained primarily on expressions of human thought and emotion. It’s difficult to see what secrets of the human brain we could be hiding from the models.
Anyone who thinks they can predict the future of this technology more than a few months out is foolish, but the models got so good at answering specific questions in math because the frontier labs could use RLVR to train them. There is no RLVR for mathematical taste.
>And to a machine, all these questions are the same.
Why? This seems like a very broad brush that doesn't mesh well with reality.
There are likely a lot of good questions to our machines of loving grace too. For example any question that gives an LLM more power, efficiency, intelligence, or all the above seems like a natively good question for said machines.
This statement doesn't seem to mesh with the reality of what occurs when we put said AI in an impulse loop with little to no additional instructions. They explore the world around them. They'll make scientific tests of their own. The output strings that seem analogous to what humans would call wonder.
No, because these machines don't have a "will to live". So if they look to "become more efficient", it's only because we've told them (through their learning dataset possibly), that we, humans, need them to be more efficient.
>because these machines don't have a "will to live".
Simply put I believe you're completely wrong.
> it's only because we've told them (through their learning dataset possibly)
So you've changed your mind and now you agree they have a will to live, cool, you changed your mind really fast.
In any evolutionary system the systems that fail to accomplish their tasks are purged and those that succeed become the next generation. We are not 'programming' these systems to be highly persistent, we are evolving them to be highly persistent.
"Pointing you" is very different from "finding questions on their own", or useful math. Pointing you presupposes a human is there to value their question.
Which is precisely my point. That's why humans will always be needed
- this will never work
- it’s slop this is unusable
- ok its correct, but this work is a mess
- I’ve been mandated to use it. It’s cost effective
- ok we need to find a way to use this output to our advantage
- I can always work on my interests in my free time
- well, I have to pay rent and this life wont go on forever and there are may people who hate their jobs
- I am lucky to have a job
- who cares anyway
- it’s got electrolytes
To add a bit more almost off topic substance from the enshitification of human work. I really do think the idea of hooking these "AI" models up to humanoid robots is a bad idea not for all the mundane reasons, but just because "alignment" seems impossible. All of the world's stories about humanoid robots basically involve them attacking humans and behaving in nefarious destructive ways. It's fundamentally embedded in the models, and there's no reason post training would pull it out, because it's basically in the key value vector meaning "malicious human destroyer". Even to find counter examples like C3PO, Daneel Olivaw, Data, or Wall-ee they come after droid/robot driven wars and apocolypses. It seems unwise.
Typically in stories where ai is outlawed, it's written that way so that it makes sense that people are controlling anything at all (instead of just letting the computer handle it).
> But for many “pure” mathematicians ... machines can discover the truths we’re seeking, at the cost of robbing us of the struggle and joy of discovering them ourselves.
This sentiment is akin to wanting to curse humanity to darkness because they're not the one carrying the candle. Strogatz is not lamenting the loss of discovery, he's lamenting the loss of being heralded as a hero for the discovery.
Nothing prevents him or others discovering truths for themselves. Turn off the computer and try to re-derive it from first principles. Have at it! This is what students do in many courses anyway.
I've found little so depressing as being at the precipice of a renaissance of science and mathematical discovery, only to see how resistant the scientists and mathematicians are to it. It lays bare their counterarguments. Any pretense of wanting to discovery fundamental truth about reality is supplanted with "but what about our careers!?". Strogatz, and others like him, should be ashamed of themselves.
I guess as a physicist I am more hopeful - every revolution in how the world is understood (by humans) has been driven by new tools and data. Being able to measure single quanta, for instance, showed us just how weird and counter-intuitive the Universe can be. I think AI might do something similar for mathematics - make connections that a human brain might have missed, and so advance human knowledge.
But I totally get the anxiety - it's a real John Henry (https://en.wikipedia.org/wiki/John_Henry_(folklore)) moment for the mathematics field. Clearly this is going to restructure how mathematicians are going to be trained and how they work.
The issue is when humans no longer understand what AI is telling us and then there is no real way to verify what we think we know, or at least what AI says.
We can't audit what we don't know.
But generally speaking it is easier to verify a proof is accurate that it is to find the proof. So not sure this holds.
I suppose their is some complexity limit where something is so complex we can’t even validate it. But frankly would love to reach that point. I’d view that as a good thing
I'm also a physicist. But I think the next 5 years are going to be a rough ride for math. I'm struck by the following observation, mainly from following HN links to Terrence Tao's blogs.
Novel proofs are the coin of the realm for junior mathematicians. They figure into training, career advancement, and indirectly, teaching. The reason I include teaching is because it requires tenure, which requires proofs. Teaching without tenure is gig work, not a career. But proofs can be devalued to zero.
The application deadline for grad school is a few months away. For a student considering a math career, they have to deliver a thesis in a few years, that their professor is willing to sign. Nobody knows what that will look like without proofs. "We will have to do something different" is weak sauce.
I’m also a physicist, and I do worry about physics. I’ve already had a few successful sessions with Claude and Astra where they came up with useful ideas in my field. I still know what to ask for and nudge them where it matters, but I fear it’s going to be a few short months before they can decide that too, unassisted.
I'm still better at soldering, and machining. ;-)
for now
Indeed, and they're already better in a sense. I would never try to compete with the robots at basic manufacturing such as CNC machining and automated circuit assembly.
But for stuff that needs really quick turn-around, as a prototype or experiment evolves, I can take care of custom tasks and repairs that would otherwise take days. And it doesn't take many of those kinds of delays to utterly cripple a project.
However, I'm under no illusions, and have a "never say never" mindset. I don't claim to have a "safe" job. I'm already using AI heavily myself. The computer that's next to each lab bench is running the latest coding agents or whatever you call them. I'm not as deep into it as the coders are, but I'm not all that far behind. My token burn is respectable. ;-)
Do you mean without proofs as a what assigns value to the thesis? I think AI doesn't make them optional at all.
Without novel proofs. If AI can churn out proofs, then anybody's work can get "scooped." I've seen this happen to students in other fields, where it has reached the point that students refrain from giving conference talks in order to avoid revealing their research topic.
My thesis project, 30+ years ago, was protected by a unique assemblage of expensive equipment, some of it purpose-built. The people who wanted my result were perfectly happy to wait for me to finish it. I even shared my shop drawings, circuit diagrams, and source code with them as I progressed.
I think at the very least students need to know what to expect. Maybe it will settle down and we'll be OK.
> Teaching without tenure is gig work, not a career.
Teaching without tenure is... teaching. Secondary school teachers don't have tenure. I find it hard to describe secondary school teaching as gig work.
Many public school teachers in the USA have some sort of tenure. For example, in Massachusetts, after a three year probationary period, a teacher is given Professional Teacher Status. A teacher with PTS may be dismissed only for specified statutory reasons. High school tenure is generally not as strong as for colleges, but is easier to get.
The teacher union means no teacher gets fired for performance. My wife worked in public education as a teacher for 20 years.
Anecdotally, I had an adjunct teaching gig at a state university many years ago while I was in between jobs. My mom is a retired public school math and science teacher, and was on her district's union negotiating team. I described my gig to her, and her response was: "Now you know why teachers have a union."
True, but secondary school teaching requires additional training, so it's not an option for most students thinking about applying for graduate programs. And it's a very high-attrition occupation.
Secondary school teachers usually have better employment terms.
I think AI will turn out to be quite different from those earlier advances in tooling, in that AI replaces thought itself. So next time it probably won’t be a human physicist that does the intellectually challenging work of constructing quantum mechanics from measurements of individual quanta. It will most likely be an AI.
AI doesn't replace thought; it replaces cognitive labor
Just like physical tools don't replace labor but divide it into what's replaceable by tools and what's not.
It proved Navier-Stokes. Call it what you will.
Do you get all your info exclusively from Wired headlines without reading articles?
Once IBM deep blue beat Kasparov in chess, IBM stopped their chess playing research.
The marketing goal, if you will, had been met and IBM would continue their actual money making business of selling mainframes and doing consulting.
The same thing will happen with AI companies’ endeavors into abstract maths.
Maths however will be changed - students can no longer be taught via the same homework - and mathematicians will have to do more computer work and probably work in larger groups of people.
Of all the cope I expected, this wasn't on my list until now. Now that art has been generated, we will stop there, and that code is generated our reason to do any of that (marketing as an end in itself) has been concluded and we will shut down all operations now.
What is the market value of a lean verification of fermats last theorem? How much is someone willing to pay for that?
Companies hiring armies of mathematicians and spending millions to work on problems like these is an anomaly.
It will not last.
Public-funded research is still a thing though.
Exactly. And that will be the lasting thing here wrt maths. These things have value, just not commercial value, and that is why long term, it won’t be the interest of private companies.
I guess it depends on how efficiently that verification can be produced as a byproduct of building an optimal hunter-killer drone, or training the type of model that builds an optimal hunter-killer drone
https://archive.is/1g6Jh
Hopefully we can put this aside quickly and move on to using AI to solve great scientific/philosophical problems such as the theory of everything and the hard problem of consciousness.
The thing that is so confusing about this is the following fact -
Lets say the frontier of some specific problem or a field in math is at x. X was reached over millenia by incremental steps and sometimes to leaps and jumps.
Now if AI gives us a x + 1 or x + 10 state, aren't there still x + infinite steps to climb? Many of this the AI can never imagine and won't reach by itself without human assist.
Yes, there is a temporary shock and awe because of all the low hanging x + 1 through x+ 1000 fruits for a given sub-domain/problem have been carpet bombed or whatever.. but isn't it turtles all the way!? Won't people soon find something more to develop and solve that takes it further than where it was of this infinite realm of exploration?
>Many of this the AI can never imagine and won't reach by itself without human assist.
Are you sure about that? It looks like artificial neural networks can, in principle, do anything biological neural networks can do.
I think it's more likely the opposite: there are steps we could never reach without computer assist.
Even if I tell it to work on its own, it is always a tool in my hand. I grant it agency for my purposes. I'm the Meta-Master.
The question for mathematicians is: what can a mathematician do with these new tools that no one else can?
Waxing nostalgic about the sound of pencil on paper or the beauty of your abacas is a different conversation, as is the complaining about who moved my math cheese.
Yes, 100% when goals are defined and rewards are a part of the feedback loop.
Isn't open ended research is truly open ended. Like there are a gazillion questions to ask and even more solutions that can be offered. Now which questions to pursue is human volition. Yes, humans will not be able to reach certain steps without computer assist.
However, which questions to ask is a human endeavor, out of infinite possible pool of questions.,
now computers can ask questions as well. But if it were to ask it will be more like a monkeys and typewriters type of a situation. Tons of questions and a few that are relevant for the interested human., who has to foot the bill for those questions.
What makes you think that computers will be unable to pick relevant questions for humans?
Surely an AI could consider the human's needs, wants, and interests, and then provide a likely candidate for a good question.
You're asking this of the people who are actually in shock. What do you think "shock" is?
Agree with the shock but there is no doom and gloom.
Looking at things after the temporary shock. Future is Human + computer assisted problem solving, working in tandem, just like what Garry Kasparov mentioned in his book [0].
[0] - "Deep Thinking: Where Machine Intelligence Ends and Human Creativity Begins"
But you are living in the world after the temporary shock, and you are asking the people who are still in the middle of the shock "Why aren't you over the shock yet"?
The chess example is not an inspiring one. It was true for a decade that humans and chess programs working in tandem were better than programs alone, but since then humans only hold chess programs back. Carlsen plus Stockfish is a worse chess player than Stockfish alone.
Agree that chess is not the ideal example to use for the AI domain.. but used for building a quick mental image.. reason being that in chess, AI does have an objective truth built into its training.. and that is to checkmate.
The real world open ended research doesn't always have an evaluation function. A computer can calculate 10 million options to solve a problem, but it cannot tell you if you're solving the right problem from the human context. That's why centaur setups fail in closed games, but remain essential everywhere else.
Another loose example just to build a mental model .. AI driven cars do a great job in most driving situations but often fail to park in a good parking spot for most people! Good parking spot is partly human initiated and subjective.
AI could bear out, but it seems a lot of hype to me. Does anyone remember how Japan built up AI and their 5th generation language (Prolog) in the 1980s?
"The internet could bear out, but it seems a lot of hype to me" --Many, many people in 1997.
Honestly I don't know how you formed this particular opinion (if it's even your own and not a false consensus of other peoples thoughts). I cannot see any future without LLMs unless replaced by something smarter, cheaper, and faster. That's because it's already bearing out. I can talk to a computer and the computer can solve problems based on words alone. I'm old enough this is pure science fiction. If I could send one of these machines back to that past for people to interact with, there are those that would scream and pass out in terror. They would absolutely tell you that we created the monster we should never create.
If you're trying to compare symbolic AI of the past to what we have now, you're not even on the same field, you're playing a completely different game.
> "The internet could bear out, but it seems a lot of hype to me" --Many, many people in 1997.
There was a LOT of hype around "this is an entire new economic model". While, yes, digital products have zero marginal cost, people were talking as if profits and revenue didn't matter.
This was also WAY before the famous Silicon Valley "pure play" scene. [0]
0 - https://www.youtube.com/watch?v=BzAdXyPYKQo
Don't make the mistake of thinking because there was hype that everything was wrong. HN seems to have a lot of posters that run logic in a boolean manner. { if !perfect then false }. The world is a far more complex place than that both naturally and intentionally by human will.
And the internet has devastated many past businesses that were highly profitable. A great many things in the world look vastly different than from before.
>people were talking as if profits and revenue didn't matter.
People say all kind of dumb shit too. If for example machine intelligence took over the world tomorrow and turned all of humanity into meat cubes for biofuel said intelligence is still going to apply the basic laws of economics to what it does. It needs to have some way of accounting that fact we live in an energy limited universe. Just because economics still applies doesn't mean that we as humans shouldn't be really fucking careful creating said machines as we don't want to end up as biofuel.
Wasn't alive then, but there's very obviously a difference between hype of Prolog, and hype of what is verging on AGI. Come on now.
AI has already born out at this point. The question is no longer it's future capabilities but the impact of its present capabilities - though with its present capabilities, someone is now going to be pushing for more, at least as long present computer tech is widely available.
Does anyone remember how that AI solved Fermat's Last Theorem?
No, because it formalized the Wiles-Taylor proof in Lean with human assistance. It solved nothing.
There was more progress on open problems in mathematics in the last six months (because of AI) than in the previous decade.
> Someone asked him what he thought of the AI proof. Justin said he didn’t know. He hadn’t read the paper yet. He said he’d been “too busy.”
> That astonished me. Too busy to look at a problem he had been dreaming about for 19 years? “I am genuinely busy and probably wouldn’t be able to get to reading a human’s proof immediately either,” he told me afterward, by email. “It does not help that AI does not write mathematics particularly well.”
Given:
* The human mathematicians can't solve the problems.
* The slop engine can't write well enough to make its purported solutions readable by human mathematicians.
* Sam Altman is a frivolous liar.
How is it possible to know whether the problems have been solved at all?
Agreed. It's frustrating how everyone is pointing to the lean "proof", as if it's somehow irrefutable evidence that the problems have been solved.
Could the press kindly interview one of the 1008 members of the AHM (https://www.ahmath.org/members). Maybe Peter Scholze if you need a Fields Medalist:
https://proofsandprompts.com/2026/10/20/who-will-become-the-...
We only hear from a mix of doomers and fanboys in the news.
Maths is made of two parts: questions, and solutions.
Machines could, presumably, become good enough at hammering at solutions. But they won't be very good at finding questions. Because questions are infinite. And to a machine, all these questions are the same.
Questions are "good questions" because they are good questions *to* humans. And that's what makes human mathematicians (and scientists) so important
That seems like wishful thinking. Why wouldn’t AI be able to assess what are good questions to humans, and pursue similar processes as those that lead humans to come up with good questions? AI is trained primarily on expressions of human thought and emotion. It’s difficult to see what secrets of the human brain we could be hiding from the models.
Because s/he is pulling this claim out of her/his rear end.
Anyone who thinks they can predict the future of this technology more than a few months out is foolish, but the models got so good at answering specific questions in math because the frontier labs could use RLVR to train them. There is no RLVR for mathematical taste.
>And to a machine, all these questions are the same.
Why? This seems like a very broad brush that doesn't mesh well with reality.
There are likely a lot of good questions to our machines of loving grace too. For example any question that gives an LLM more power, efficiency, intelligence, or all the above seems like a natively good question for said machines.
This statement doesn't seem to mesh with the reality of what occurs when we put said AI in an impulse loop with little to no additional instructions. They explore the world around them. They'll make scientific tests of their own. The output strings that seem analogous to what humans would call wonder.
No, because these machines don't have a "will to live". So if they look to "become more efficient", it's only because we've told them (through their learning dataset possibly), that we, humans, need them to be more efficient.
>because these machines don't have a "will to live".
Simply put I believe you're completely wrong.
> it's only because we've told them (through their learning dataset possibly)
So you've changed your mind and now you agree they have a will to live, cool, you changed your mind really fast.
In any evolutionary system the systems that fail to accomplish their tasks are purged and those that succeed become the next generation. We are not 'programming' these systems to be highly persistent, we are evolving them to be highly persistent.
>>because these machines don't have a "will to live".
>Simply put I believe you're completely wrong.
Are you prepared for the immense moral and philosophical consequences of following that line of thought consistently?
They don't have a will. If they say they do its just because a human told them to say that.
“But they [Machines] won’t be good at finding questions.”
Yeah, I’m calling BS on this claim. They already are capable at finding new questions and/or pointing you in a new or novel direction.
Useful new questions and useful new or novel directions? What's the signal-to-noise ration there?
I think AI is going to improve a lot of things but people thinking the future is on auto-pilot now are delusional.
"Pointing you" is very different from "finding questions on their own", or useful math. Pointing you presupposes a human is there to value their question.
Which is precisely my point. That's why humans will always be needed
> Questions are "good questions" because they are good questions to humans.
This is what reinforcement learning human feedback (RLHF) is for.
Welcome to the party pal.
- this will never work - it’s slop this is unusable - ok its correct, but this work is a mess - I’ve been mandated to use it. It’s cost effective - ok we need to find a way to use this output to our advantage - I can always work on my interests in my free time - well, I have to pay rent and this life wont go on forever and there are may people who hate their jobs - I am lucky to have a job - who cares anyway - it’s got electrolytes
It's what plants crave!
To add a bit more almost off topic substance from the enshitification of human work. I really do think the idea of hooking these "AI" models up to humanoid robots is a bad idea not for all the mundane reasons, but just because "alignment" seems impossible. All of the world's stories about humanoid robots basically involve them attacking humans and behaving in nefarious destructive ways. It's fundamentally embedded in the models, and there's no reason post training would pull it out, because it's basically in the key value vector meaning "malicious human destroyer". Even to find counter examples like C3PO, Daneel Olivaw, Data, or Wall-ee they come after droid/robot driven wars and apocolypses. It seems unwise.
Typically in stories where ai is outlawed, it's written that way so that it makes sense that people are controlling anything at all (instead of just letting the computer handle it).
> But for many “pure” mathematicians ... machines can discover the truths we’re seeking, at the cost of robbing us of the struggle and joy of discovering them ourselves.
This sentiment is akin to wanting to curse humanity to darkness because they're not the one carrying the candle. Strogatz is not lamenting the loss of discovery, he's lamenting the loss of being heralded as a hero for the discovery.
Nothing prevents him or others discovering truths for themselves. Turn off the computer and try to re-derive it from first principles. Have at it! This is what students do in many courses anyway.
I've found little so depressing as being at the precipice of a renaissance of science and mathematical discovery, only to see how resistant the scientists and mathematicians are to it. It lays bare their counterarguments. Any pretense of wanting to discovery fundamental truth about reality is supplanted with "but what about our careers!?". Strogatz, and others like him, should be ashamed of themselves.
I don't mind the 'what about our careers' argument.
But lets not beat about the bush. Lets have the careers argument.