I know a bit about this field. This conjecture reads as somewhat more niche than the cyclic double cover conjecture recently proved by OpenAI, but nevertheless represents a real contribution.
You want to know how long it takes to solve an optimization problem, in this case over convex, lipschitz functions. (The restriction to a spherical domain is not really a restriction, you can just change variables for any bounded domain.) Anyway, showing upper bounds on time complexity is "easy" because it's just the runtime of your algorithm. Showing (nontrivial) lower bounds is usually much harder because it requires constraining all algorithms.
This proof apparently shows that the lower bound time complexity is equal to the time complexity of an existing 30-year old algorithm: it requires Omega(d^2) function evaluations to solve over this class of functions.
My gut says likely implies that d is the minimal number of evaluations if you have a gradient oracle because you can approximate a gradient with d function evaluations, but I'm not sure how hard it is to make that rigorous.
> I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense to work on any low-hanging, or even medium-hanging (you know what I mean) fruit. We'll be needed for problems where actual novel approaches are needed.
I wonder how this compares to what we see happening with "juniors" in software development?
In math research, do you also get the training for the profession from working on the low hanging fruits for a while, to then move to the medium-hanging, and later go on to work on previously unsolved stuff?
My experience may not be entirely representative because to be entirely honest I’m not exactly a great researcher and there are brilliant PhD students. That said it indeed was my experience that in the pre-PhD / early PhD period ( or even longer … ) your advisor proposes (gives) you pretty low hanging stuff that he mostly already knows how to solve, at least at a high level, with the expectation that it will teach you to use the mathematical tools you need.
Certainly. This feels similar, to me, to how building complex software with LLMs works today in practice. You need to know a lot to set up goals and guardrails and verify outputs. For me, making the bits change was always the fun part, not tangling with text in my editor, though that had its moments.
I was thinking this past week I have gotten so lazy w my prompting via CLIs. Back in the before I had put such discipline into my prompting and supporting context.
Now I’m like, “look here and here and here are some tools, and /skill /skill okay go.”
Or “restate this request in your own words and enrich it as appropriate handling any gaps.”
If I recall correctly there was a proposed proof to the abc conjecture by Mochizuki https://en.wikipedia.org/wiki/Abc_conjecture#Claimed_proofs which was rejected due to being rather inpenetrable to humans. Shouldn't this be an ideal target for LLMs?
Crazy how intelligence is cheap, efficient and commonplace now.
We humans better refocusing our energy on our core values/principles, given most of our skills are becoming irrelevant
If it were commonplace, there wouldn't be a post and discussion about it. Cheap? Arguable - while it didn't cost thousands, it wasn't free. Cheap is in the eye of the beholder. Efficient...How do we even measure that? The massive infrastructure and training to take a product to the point where someone could do this is massive. Ignoring everything behind the scenes and acting like one session and result is the whole picture of efficiency doesn't seem right. And no, nothing produced by AI makes skills irrelevant. That is the whole ongoing argument of whether people are losing cognitive ability by moving their thinking to AI.
Overall, this is an impressive proof of capability. But I wouldn't take that proof as anything more than what it is.
Seconded on the "not cheap" argument here. I've spent $25 worth of tokens completing a one-week task in an afternoon, or rather my company spent the money. I would never have personally felt OK with throwing this much money after some prompting back and forth for a few hours, one lazy Saturday afternoon. I ran the risk of not finding the solution before the token usage would be too high for me to want to carry on, if I was my own credit card linked to the account.
Of course money in this situation is a bit of a funny measurement, right, because if I was able to take the rest of the week off as soon as I had solved the one-week problem, then I would have no problem at all throwing even $100 worth of tokens at it, so I could enjoy a nice 4-day "mini-vacation".
How cheap "cheap" is, is indeed "in the eye of the beholder".
Everybody can be an armchair mathematician now. Just fling some thoughts in the direction of your AI setup and let it do breadth first search with AI based pruning heuristics.
It's still clear that LLMs lack spatial reasoning, either in the concrete or abstract, and while that sort of reasoning has been downplayed by academia for at least a century it is fundamental to technology and industry. (And many would say for science and mathematics too).
They will, however, get there as well either directly or as interfaces to models that do, and your core point stands.
I can't stop wondering myself.... I'm writing some software with AI and wondering, why am I doing this? Will anyone need this? Will anyone have money to buy this?
Best I've come up with is we'll need to be adopted by technofeudlaist overlords to be our patrons like in the roman days
That view is incredibly reductionist. It really is an efficient encoding of how nature behaves. It might be a human construct, but given how best it allows to understand nature (through principles of physics), it is uncanny to be any different from the language of nature.
Reminds me of Wigner's Unreasonable effectiveness of mathematics in natural sciences [0].
At a very high level mathematics is basically 100% text/symbolic rewriting. You start from some set of postulate assumed true and you do your thing to get a new different set of equivalent assertions in a form that is more useful.
I don’t know if LLMs will kill the working-mathematicians but at least seem like that it doesn’t seem absurd to imagine LLMs will be good at math…
What I'm feeling is that there's a need to study how to use AI well. I've seen professors using AI, and it was amazing. In that sense, I think AI prompt input will become stratified. In the past, implementation skills were very important, but these days, concepts feel more important this is one of those things.
It's not that AI brings equality, but rather that the output varies depending on how much background knowledge you have. You could call it a stratification of input
I'm starting to feel like there's no place left for programmers like me who focus on quickly churning out MVPs.
I actually think people who are great at understanding problems, coming up with requirements and designing solutions (all things I would expect someone who is good at churning out MVPs would be good at) are exactly the people most empowered by the current batch of LLMs. Its the people who are only good at working on small chunks of problems that I'm concerned about..
Calling it prompt engineer is doing it a disservice. With agents we’re well into process engineering, which is a ton more interesting.
The obvious baby’s first process is “plan -> execute” but as we learn about the strengths and weaknesses of LLMs you have to start unpacking that process into planning, prototyping, testing, validation, reviews, and tons of research. If you treat it like an extension of your brain that can automate some thought processes, it becomes a lot more powerful.
I find it strange that people sometimes think of knowledge as 'public property for everyone.' The essence may be one, but the mental model of knowledge is individual. For an LLM's knowledge to become mine, I need to digest it to some extent.
And programming, as the programmer who created Eliza once said, is the act of becoming a legislator of your own universe. So even if there are black boxes, if you want to build a program that fits your own worldview, studying is essential.
I'm going to keep on repeating this on HN threads until I'm blue in the face, but:
There are two ways to solve a problem. Either solve the problem, or deem it irrelevant.
The implication here is that, you, the human operator, clearly are just confused. The LLM knows best. You're just a stupid human. The LLM knows objective truth, you do not. You have concerns, questions, the LLM didn't understand your question "properly"? Do not worry, the LLM objectively knows the optimal course of action. It thought through the implications of what you said, took into account all possible data, and came to the objectively correct design for your software, your society, your life.
In some sense, this problem would have been a societal problem within the next several decades anyways, but it's been hyper-accelerated by AI.
> I'm starting to feel like there's no place left for programmers like me who focus on quickly churning out MVPs.
Of course there is. The same way this was only possible as a result from the professor who prompted it with his specialized 10 page prompt and most importantly his deep knowledge of the problem space, the muscle memory and intuition you've built over the years is what will allow you to get more out of any AI than some guy who says "make a door dash clone" as the entire prompt
So these days I've been writing down my thoughts on my personal homepage. Things I've learned, my background knowledge, and so on.
I've been realizing that there are more books tied to my background knowledge than I expected, but I'm not sure what will happen as AI advances further.
These days, I'm living for the fun of building my own personal wiki on my homepage
Sharing knowledge is good, but just because an LLM crawls it doesn't mean it fits my mental model. The act of writing is fundamentally about drawing the shape of my own mental model.
- Hasn't been peer reviewed yet, so take with a grain of salt. This applies to all claimed proofs, not just AI-generated ones. Even humans hallucinate proofs too!
- The prompt is on page 27 here[1]. It is ten pages of advanced mathematics priming the model in the right direction, apparently informed by a year of prior research. That doesn't invalidate the result if it is genuine, but it is worth noting that this wasn't a matter of "ChatGPT, solve this unsolved problem. Make no mistakes." and required substantial domain expertise and human research beforehand.
Saying “solve this problem” doesn’t get good results most of the time with humans either, it’s entirely underspecified so the person assigned that problem may solve it in a variety of unacceptable ways or not at all or perhaps worse solve the wrong problem because you weren’t clear about its definition. This actually happens all the time. What matters is the ability to communicate clearly and with precision as well as the “harness” which for humans is procedure, training, planning and management.
The subtext of this whole post (or at least a subtext that some might read), is "we don't need mathematicians/programmers anymore" or "we will need much fewer mathematicians/programmers". So the fact that this result required a year of prior research and a 10 page prompt of specialized knowledge goes against that subtext. You still needed the human just as much to get to the result, and the LLM ended up being a tool to find the last bit.
> Saying “solve this problem” doesn’t get good results most of the time with humans either
Sure. That is not even remotely the point I was getting at. Already we see the thread filling up with comments about how human skills are irrelevant, using a mathematics PhD applying his expert skills in a way that the people who are saying that could never have done to justify their inane conclusion.
Except solving problem is probably the least (even though it's important) interesting thing in research...
The most interesting thing in research is finding new questions, that we understand and that we know why they are important. And that's something that humans need to do (by definition)
>So I wouldn't really say that this result is using or creating some fundamentally new techniques in convex geometry or optimization theory. What this means from my perspective is that if a result is attainable with existing techniques, modern AI methods will be able to solve those problems. I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense to work on any low-hanging, or even medium-hanging (you know what I mean) fruit. We'll be needed for problems where actual novel approaches are needed.
While they’ll never have the same subjective experience as humans, what stops an LLM from applying similar lines of thought* in a manner that results in a novel conjecture?
They are prediction machines, and so are we in a way. We can give them nearly limitless resources to scale their predictive capabilities. We have billions of years of training baked in. They distill directly from our knowledge and can walk down paths that no human has before.
It’s silly to say they’ll never do anything novel.
At their current capabilities, it sounds like they are already capable of being a specific type is research assistant. What will that look like in 10-20 years?
They also have ability to go deep and wide in a way that humans just can't. We have limits, get tired, distracted and biased where AI does not. I think there a lot of problem where all the information needed to solve them is there, but we just can't put the pieces together. Like no matter how many people you throw at some problems, you hit human limits and more people won't help, but AI will because it is just relentless.
The author explains he's an expert in the domain and that he had worked sporadically on the problem for about a year, also with the help of previous LLMs. So whatever he means by "I wouldn't really say that this result is using or creating some fundamentally new techniques" it doesn't mean that the result was trivial. Also, says it might not make sense to work on low or even medium hanging fruits in the future- and I bet that's by far the largest share of work for most mathematicians.
Sure, it's not a breakthrough that opens new roads in mathematics- is this where the goalpost has moved now?
HEH. Don't know why you're getting downvoted. It's painfully obvious that there is a vicious AI backlash now, where every amazing advancement is met with denial and loathing.
Oh wait, sorry, I do know why you're getting downvoted. Fear.
Lean is the Mizar here. For those who have no clue what this is about, Mizar [1] was an early automated theorem prover. Can't wait for HN to add AI features to explain concepts in the sideline, and autovoting.
Mizar is an early theorem prover. It still exists, see the 2025 issue of Formalized Mathematics journal [1] that publishes math articles formally verified by Mizar (since 1990).
Cool can we use AI to get a cure for cancer yet? Or is math-turbation the only thing these things are good for? Where are the breakthroughs on actually improving our lives?
It's interesting to see the old "Why would we go to space when there are still uncured diseases" show up in a place like this. Science and discovery are singular, all discovery aids all discovery.
Cancer is also bottleknecked by a lot more than just intelligence. If you have 100 of the smartest PHd students working on a cancer problem you have to wait for funding, lab experiments, and clinical trials etc. Math is deterministic and requires nothing like that.
I know a bit about this field. This conjecture reads as somewhat more niche than the cyclic double cover conjecture recently proved by OpenAI, but nevertheless represents a real contribution.
You want to know how long it takes to solve an optimization problem, in this case over convex, lipschitz functions. (The restriction to a spherical domain is not really a restriction, you can just change variables for any bounded domain.) Anyway, showing upper bounds on time complexity is "easy" because it's just the runtime of your algorithm. Showing (nontrivial) lower bounds is usually much harder because it requires constraining all algorithms.
This proof apparently shows that the lower bound time complexity is equal to the time complexity of an existing 30-year old algorithm: it requires Omega(d^2) function evaluations to solve over this class of functions.
My gut says likely implies that d is the minimal number of evaluations if you have a gradient oracle because you can approximate a gradient with d function evaluations, but I'm not sure how hard it is to make that rigorous.
> I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense to work on any low-hanging, or even medium-hanging (you know what I mean) fruit. We'll be needed for problems where actual novel approaches are needed.
I wonder how this compares to what we see happening with "juniors" in software development? In math research, do you also get the training for the profession from working on the low hanging fruits for a while, to then move to the medium-hanging, and later go on to work on previously unsolved stuff?
My experience may not be entirely representative because to be entirely honest I’m not exactly a great researcher and there are brilliant PhD students. That said it indeed was my experience that in the pre-PhD / early PhD period ( or even longer … ) your advisor proposes (gives) you pretty low hanging stuff that he mostly already knows how to solve, at least at a high level, with the expectation that it will teach you to use the mathematical tools you need.
This apparently required a 10-page prompt. It seems like someone needs to know enough to write it?
Certainly. This feels similar, to me, to how building complex software with LLMs works today in practice. You need to know a lot to set up goals and guardrails and verify outputs. For me, making the bits change was always the fun part, not tangling with text in my editor, though that had its moments.
Yeah, back to the gold-in-gold out use of LLMs.
I was thinking this past week I have gotten so lazy w my prompting via CLIs. Back in the before I had put such discipline into my prompting and supporting context.
Now I’m like, “look here and here and here are some tools, and /skill /skill okay go.”
Or “restate this request in your own words and enrich it as appropriate handling any gaps.”
If I recall correctly there was a proposed proof to the abc conjecture by Mochizuki https://en.wikipedia.org/wiki/Abc_conjecture#Claimed_proofs which was rejected due to being rather inpenetrable to humans. Shouldn't this be an ideal target for LLMs?
Crazy how intelligence is cheap, efficient and commonplace now. We humans better refocusing our energy on our core values/principles, given most of our skills are becoming irrelevant
If it were commonplace, there wouldn't be a post and discussion about it. Cheap? Arguable - while it didn't cost thousands, it wasn't free. Cheap is in the eye of the beholder. Efficient...How do we even measure that? The massive infrastructure and training to take a product to the point where someone could do this is massive. Ignoring everything behind the scenes and acting like one session and result is the whole picture of efficiency doesn't seem right. And no, nothing produced by AI makes skills irrelevant. That is the whole ongoing argument of whether people are losing cognitive ability by moving their thinking to AI.
Overall, this is an impressive proof of capability. But I wouldn't take that proof as anything more than what it is.
Seconded on the "not cheap" argument here. I've spent $25 worth of tokens completing a one-week task in an afternoon, or rather my company spent the money. I would never have personally felt OK with throwing this much money after some prompting back and forth for a few hours, one lazy Saturday afternoon. I ran the risk of not finding the solution before the token usage would be too high for me to want to carry on, if I was my own credit card linked to the account.
Of course money in this situation is a bit of a funny measurement, right, because if I was able to take the rest of the week off as soon as I had solved the one-week problem, then I would have no problem at all throwing even $100 worth of tokens at it, so I could enjoy a nice 4-day "mini-vacation".
How cheap "cheap" is, is indeed "in the eye of the beholder".
Everybody can be an armchair mathematician now. Just fling some thoughts in the direction of your AI setup and let it do breadth first search with AI based pruning heuristics.
It's still clear that LLMs lack spatial reasoning, either in the concrete or abstract, and while that sort of reasoning has been downplayed by academia for at least a century it is fundamental to technology and industry. (And many would say for science and mathematics too).
They will, however, get there as well either directly or as interfaces to models that do, and your core point stands.
Is there any proof that they are not good at special reasoning? Arc agi 1 and 2 are saturated.
Intelligence was always relatively cheap. You can pick up a phone and get answers for free in most academic settings.
(within limits)
yeah...right. Go touch some grass
Oh brother
AI hasn’t even taken the class of jobs associated with customer service lmao
Do we employ mathematicians in customer service roles?
Luckily the job situation for pure mathematicians was already bad.
Thats a silly and obtuse comment.
You mean the answer betrays the point: customer service is surprisingly hard, we just have a large number of people that are capable of doing it.
This is what the whole https://people.csail.mit.edu/brooks/papers/elephants.pdf is about.
I stand by my point, you've not read the author's intent, instead you decided to twist words.
What a silly and obtuse comment.
What a child. Fuck off.
And that's why you aren't qualified for a customer service role but might be for something that current AI is competitive with.
Uh.... Have you ever called customer service lately?
Once we figure out the pesky problem of how we're going to pay for housing, food, and healthcare without jobs.
I think the big names behind the AI companies already have that problem solved. A lot of people probably won't like the solution very much though.
When machines are doing all the work - we no longer have to.
> the couple multi-trillioners will have all the wealth of the world, and it will all crumble down
You mistyped it.
Is that what you're going to tell your mortgage lender?
I can't stop wondering myself.... I'm writing some software with AI and wondering, why am I doing this? Will anyone need this? Will anyone have money to buy this?
Best I've come up with is we'll need to be adopted by technofeudlaist overlords to be our patrons like in the roman days
This is some next level cringe stuff that shows why software engineers are easy to exploit - no backbone
Mathematics is a human-designed game that involves rearranging symbols.
That view is incredibly reductionist. It really is an efficient encoding of how nature behaves. It might be a human construct, but given how best it allows to understand nature (through principles of physics), it is uncanny to be any different from the language of nature.
Reminds me of Wigner's Unreasonable effectiveness of mathematics in natural sciences [0].
[0]: https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
At a very high level mathematics is basically 100% text/symbolic rewriting. You start from some set of postulate assumed true and you do your thing to get a new different set of equivalent assertions in a form that is more useful.
I don’t know if LLMs will kill the working-mathematicians but at least seem like that it doesn’t seem absurd to imagine LLMs will be good at math…
What I'm feeling is that there's a need to study how to use AI well. I've seen professors using AI, and it was amazing. In that sense, I think AI prompt input will become stratified. In the past, implementation skills were very important, but these days, concepts feel more important this is one of those things.
It's not that AI brings equality, but rather that the output varies depending on how much background knowledge you have. You could call it a stratification of input
I'm starting to feel like there's no place left for programmers like me who focus on quickly churning out MVPs.
I actually think people who are great at understanding problems, coming up with requirements and designing solutions (all things I would expect someone who is good at churning out MVPs would be good at) are exactly the people most empowered by the current batch of LLMs. Its the people who are only good at working on small chunks of problems that I'm concerned about..
You’re at least 18 months out of date claiming that prompting will be the new hot skill. Turns out LLMs are also good at prompting other LLMs.
Calling it prompt engineer is doing it a disservice. With agents we’re well into process engineering, which is a ton more interesting.
The obvious baby’s first process is “plan -> execute” but as we learn about the strengths and weaknesses of LLMs you have to start unpacking that process into planning, prototyping, testing, validation, reviews, and tons of research. If you treat it like an extension of your brain that can automate some thought processes, it becomes a lot more powerful.
Ah, but who prompts the prompters?
I find it strange that people sometimes think of knowledge as 'public property for everyone.' The essence may be one, but the mental model of knowledge is individual. For an LLM's knowledge to become mine, I need to digest it to some extent.
And programming, as the programmer who created Eliza once said, is the act of becoming a legislator of your own universe. So even if there are black boxes, if you want to build a program that fits your own worldview, studying is essential.
Rather than prompt engineering, I think it should be called overall harness engineering. Anyway, that's how I feel these days
That doesn't make any sense; you can't have one LLM to read your mind to prompt another LLM.
Waiting for the next Neuralink announcement...
I'm going to keep on repeating this on HN threads until I'm blue in the face, but:
There are two ways to solve a problem. Either solve the problem, or deem it irrelevant.
The implication here is that, you, the human operator, clearly are just confused. The LLM knows best. You're just a stupid human. The LLM knows objective truth, you do not. You have concerns, questions, the LLM didn't understand your question "properly"? Do not worry, the LLM objectively knows the optimal course of action. It thought through the implications of what you said, took into account all possible data, and came to the objectively correct design for your software, your society, your life.
In some sense, this problem would have been a societal problem within the next several decades anyways, but it's been hyper-accelerated by AI.
And yet in this case a human prompted the LLM for this result, not another LLM
I think there's a lot of interesting things to the side of development that don't get the resources they deserve
Debuggers, testing techniques, testing layers
Essentially things that could be used to ground your ai back to reality and work good for humans too
> I'm starting to feel like there's no place left for programmers like me who focus on quickly churning out MVPs.
Of course there is. The same way this was only possible as a result from the professor who prompted it with his specialized 10 page prompt and most importantly his deep knowledge of the problem space, the muscle memory and intuition you've built over the years is what will allow you to get more out of any AI than some guy who says "make a door dash clone" as the entire prompt
So these days I've been writing down my thoughts on my personal homepage. Things I've learned, my background knowledge, and so on.
I've been realizing that there are more books tied to my background knowledge than I expected, but I'm not sure what will happen as AI advances further.
These days, I'm living for the fun of building my own personal wiki on my homepage
Why write it down? LLM crawlers will ingest it in a second.
Sharing knowledge is good, but just because an LLM crawls it doesn't mean it fits my mental model. The act of writing is fundamentally about drawing the shape of my own mental model.
Two points:
- Hasn't been peer reviewed yet, so take with a grain of salt. This applies to all claimed proofs, not just AI-generated ones. Even humans hallucinate proofs too!
- The prompt is on page 27 here[1]. It is ten pages of advanced mathematics priming the model in the right direction, apparently informed by a year of prior research. That doesn't invalidate the result if it is genuine, but it is worth noting that this wasn't a matter of "ChatGPT, solve this unsolved problem. Make no mistakes." and required substantial domain expertise and human research beforehand.
[1]https://arxiv.org/pdf/2607.13335
It is lean-verified, so it can be trusted unless the Lean statement of the hypothesis is not an accurate description of the hypothesis.
Saying “solve this problem” doesn’t get good results most of the time with humans either, it’s entirely underspecified so the person assigned that problem may solve it in a variety of unacceptable ways or not at all or perhaps worse solve the wrong problem because you weren’t clear about its definition. This actually happens all the time. What matters is the ability to communicate clearly and with precision as well as the “harness” which for humans is procedure, training, planning and management.
The subtext of this whole post (or at least a subtext that some might read), is "we don't need mathematicians/programmers anymore" or "we will need much fewer mathematicians/programmers". So the fact that this result required a year of prior research and a 10 page prompt of specialized knowledge goes against that subtext. You still needed the human just as much to get to the result, and the LLM ended up being a tool to find the last bit.
> Saying “solve this problem” doesn’t get good results most of the time with humans either
Sure. That is not even remotely the point I was getting at. Already we see the thread filling up with comments about how human skills are irrelevant, using a mathematics PhD applying his expert skills in a way that the people who are saying that could never have done to justify their inane conclusion.
Except solving problem is probably the least (even though it's important) interesting thing in research...
The most interesting thing in research is finding new questions, that we understand and that we know why they are important. And that's something that humans need to do (by definition)
Waiting for comments saying that LLMs can't produce anything new and general goalpost moving.
From the post lol
>So I wouldn't really say that this result is using or creating some fundamentally new techniques in convex geometry or optimization theory. What this means from my perspective is that if a result is attainable with existing techniques, modern AI methods will be able to solve those problems. I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense to work on any low-hanging, or even medium-hanging (you know what I mean) fruit. We'll be needed for problems where actual novel approaches are needed.
If knowledge is a Swiss cheese, LLMs can help fill the holes, but not make the cheese bigger.
Today maybe. I disagree in the long term.
While they’ll never have the same subjective experience as humans, what stops an LLM from applying similar lines of thought* in a manner that results in a novel conjecture?
They are prediction machines, and so are we in a way. We can give them nearly limitless resources to scale their predictive capabilities. We have billions of years of training baked in. They distill directly from our knowledge and can walk down paths that no human has before.
It’s silly to say they’ll never do anything novel.
At their current capabilities, it sounds like they are already capable of being a specific type is research assistant. What will that look like in 10-20 years?
They also have ability to go deep and wide in a way that humans just can't. We have limits, get tired, distracted and biased where AI does not. I think there a lot of problem where all the information needed to solve them is there, but we just can't put the pieces together. Like no matter how many people you throw at some problems, you hit human limits and more people won't help, but AI will because it is just relentless.
> While they’ll never have the same subjective experience as humans
You state this as a fact - are you aware the question is unresolved?
so it seems like The New Big Question In Math is
How's It Hanging, Brother?
The author explains he's an expert in the domain and that he had worked sporadically on the problem for about a year, also with the help of previous LLMs. So whatever he means by "I wouldn't really say that this result is using or creating some fundamentally new techniques" it doesn't mean that the result was trivial. Also, says it might not make sense to work on low or even medium hanging fruits in the future- and I bet that's by far the largest share of work for most mathematicians.
Sure, it's not a breakthrough that opens new roads in mathematics- is this where the goalpost has moved now?
HEH. Don't know why you're getting downvoted. It's painfully obvious that there is a vicious AI backlash now, where every amazing advancement is met with denial and loathing.
Oh wait, sorry, I do know why you're getting downvoted. Fear.
Oh brother I can tell you didn't read the entire article.
No mizar no proof
Lean is the Mizar here. For those who have no clue what this is about, Mizar [1] was an early automated theorem prover. Can't wait for HN to add AI features to explain concepts in the sideline, and autovoting.
[1] https://en.wikipedia.org/wiki/Mizar_system
Mizar is an early theorem prover. It still exists, see the 2025 issue of Formalized Mathematics journal [1] that publishes math articles formally verified by Mizar (since 1990).
[1] https://reference-global.com/issue/FORMA/33/1
Cool can we use AI to get a cure for cancer yet? Or is math-turbation the only thing these things are good for? Where are the breakthroughs on actually improving our lives?
It's interesting to see the old "Why would we go to space when there are still uncured diseases" show up in a place like this. Science and discovery are singular, all discovery aids all discovery.
Cancer is also bottleknecked by a lot more than just intelligence. If you have 100 of the smartest PHd students working on a cancer problem you have to wait for funding, lab experiments, and clinical trials etc. Math is deterministic and requires nothing like that.
Have you not heard of things like AlphaFold?