How refreshing to read the thoughts of a human in a blog post instead of the garbage that LLMs produce. As the writer says about some of their proofs, the problem is not one of style or em-dashes, but something deeper about the writing that comes out of LLMs:
The problem is it doesn’t make any goddamned sense.
I'd probably insert a 'sometimes' in there, because many times in small doses it does make sense, it's only when you ask for long form writing/work that it becomes apparent there is no coordinating intelligence there.
Interesting just how much of this advice applies to programming as well as to maths:
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Skills, agent.md and harnesses are probably a dead-end that will die off as the tools become more capable.
LLMs are not good at reducing complexity, however they're very good at adding it, and sometimes it is just unnecessary and he can find ways to cut it by interrogating the LLM.
Some people are responding to the new reality by gleefully using AI to generate lots of semi-OK-ish papers and puking them up on arXiv [this is like people producing mediocre one-shot clones of software].
On the other hand—with creative writing, my advice is not to use AI to write, at all. Ask questions if you want, but write every damned word yourself.
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Definitely worth a read for the programmers here too.
Fairly easy to tell at the moment, LLMs are not very coherent or interesting in long form writing as yet.
But if you want to believe otherwise that's up to you (or perhaps you just hope it could be otherwise?). If you prefer, you can read that sentence as 'How refreshing to read intelligent, coherent thoughts in a blog post instead of the garbage we so often see nowadays.'
The sentiment is the same, it's about quality and intelligent thought, not style or provenance. Maybe one day we'll have to say intelligence rather than human, which is a fun thought. I don't feel we're close to that yet though.
"If you just waited a year, would some other AI produce that same proof independently?"
I had a conversation about this very problem last November, with a visiting mathematician. It's essentially signaling a deflationary spiral in intellectual work: why bother doing the work now, when it will take half as much effort a year from now?
This is perhaps always a possible stance, but it's exacerbated when some proportion of your own agency is handed over to, well, agents.
This might hold up for theoretical intellectual work without any economical value, but if you are researching anything that can be applied to the industry, you will instead have 1 year of market ownership and first-mover advantage.
I think it says more about what the value of math as intellectual work is, than about intellectual work in general.
Like if an Egyptian historian would come and say "let's wait one year until the methods are good enough to decrypt this language", no one would be bothered or surprised.
You imply "worth" being equal to some known economic value.
You even imply, economic value was determined correctly in advance for arbitrarily long future intervals. And the applicability was known in advance to begin with.
Obviously, you're completely wrong.
Applying simplistic models to real life incurs a penalty. The affected scale multiplies with that penalty. When dealing with things affecting humanity as a whole, that makes careless over-generalizations a serious hazard.
“if you are researching anything that can be applied to the industry, you will instead have 1 year of market ownership and first-mover advantage.”
I would like to disagree with you on that point. Given the very popular rise of https://rea.tools/, it appears the time to reverse engineer anything software based (up to maybe 80% or more?) could be down to minutes. With a recent example, some indie video game developers are not going to show off their video game until release as a few have been flipped and made it to market before the original developers have. Point being, a few moths of market ownership could be possible if llms can’t reverse it in any way.
Someone is going to make the case against using LLMs to reverse engineer software solely for commercial gain being as illegal as using guns for extortion.
First movers often lose though in the market. Relevant to today's news about DoorDash acquiring Instacart for a few billion dollars: WebVan came out a decade earlier (i.e. at the wrong time) and went bankrupt after 3 years.
A perhaps more relevant personal anecdote: About a year ago I told a non-technical friend that I'd help him migrate his small business website that was originally set up in WordPress (by a developer who is since long gone) to a format that would be much easier for him to manage with no dev support. I planned to move him over to one of the usual suspects like Wix or Squarespace, but this is one instance where my procrastination was a virtue. In the ~9 months since he originally had an issue with his site, AI capabilities had exploded. Turned out it was a lot easier (and cheaper) to use Claude to fully migrate his site and get it up on Cloudflare workers, and I set up everything so he could manage all the content himself. Plus, it took me less than a day to do the migration off WordPress, and most of that time was just me wanting to learn the ins and outs of Claude Code because I was new to it at the time.
I like this observation very much. Intellectual deflationary spiral is exactly how it feels at the moment and we might end up in a worse place because of it.
The overselling of AI abilities is doing such a disservice to society right now. These companies don’t want to acknowledge how much human collaboration is going into their AI’s achievements because it undermines their value proposition, but I imagine there’s still quite a fair amount going into it and that’s one reason why OpenAI still won’t provide session traces of their models solving open math problems. If they were more transparent about it I think we’d see that human guidance, vision, judgement, taste, and other traits are still highly valuable and complimentary to AI abilities. It should also be a huge red flag how little of any of this output has been formally verified by third parties. I do think AI will eventually do all the things people believe it’s already doing, but I suspect there’s a fair amount of mechanical turking going on behind the scenes as you’d expect any company trying to raise a trillion dollar public offering might do.
OAI is not simply prompting "Prove exponential time hypothesis false. Make no mistakes" for the same reasons you can't one-shot "Write a fully standards compliant internet browser from scratch"
Terry's session is his attempt to understand Fable's counterexample to the Jacobian Conjecture, not an attempt to solve any open problem.
Levent Alpöge's prompting that did solve this open problem does not appear to be public, but Aaron Lou at OpenAI succeeded in reproducing the result the next day using an internal version of Codex and (reportedly) without web search, and he shared his prompt at https://aaronlou.com/jacobian_counterexample_prompt.pdf. It is a mathematically-sophisticated statement of the problem and of general search strategies, but contains no concrete ideas for the solution whatsoever (even the idea to look for a counterexample instead of a proof).
These mournings of programmers and now mathemathicians will as time goes on likely continue to become a part of other fields workers routines as well.
I wonder how we as a society will react to this, this crisis of meaning. Not to get into existential crisis if that is to happen as well, which of course is a whole other issue.
I assume we will all start to look for social ways of mourning with colleagues.
It’s funny how disconnected we all are from each other. This is exactly how LLMs felt a year or so to many programmers.
Useless toys, sometimes useful toys, ok good toys, ok.. we might have to look at this more carefully, oh god.
This loop however is quite tiring to watch happen over and over again. Is there really nothing we can do but just watch from the sidelines and watch our fellow men engage in their particular grief and copium filled mourning cycle?
About two years ago, I was at a coffee shop and two maths students were trying to understand a concept in the book. I suggested they might ask a language model to help them understand it. They scoffed at me, called a stochastic parrot, and said they can't do math at all.
I responded with, "Well, you don't even need it to do math. It can explain the concept." They scoffed again. "Those things are useless toys"
Reading comments like this is so depressing because it was extremely obvious that better results were a matter of time/hardware. It evokes the seem feeling as that trump quote about "who knew healthcare could be so complicated".
Also, even GPT-3 (6 years ago) was a very powerful search tool for exactly these kinds of problems. You needed some result that would give a bound on some obscure property, and it instantly gave you five different applicable theorems from three different domains of math. Usually, the theorems even existed.
I was taken aback by the progress in 2025/2026 because late 2024 did seem to be a plateau, but 5-10 years seemed inevitable.
Even when I first studied automated theorem provers in around 2013, the 10-20 years to automating proofs (not theory building) seemed inevitable. They were already superhumanly fast and generating real results, and neural networks were making massive progress on translation, image processing, and games. Someone just had to work out how to stick a neural net inside an ATP. The surprise was that it happened the other way around, and that it solved even more than just mathematical proofs.
AI has only just begun to expose the depth of willful human ignorance.
> Reading comments like this is so depressing because it was extremely obvious that better results were a matter of time/hardware. It evokes the seem feeling as that trump quote about "who knew healthcare could be so complicated".
I honestly don't see how this has anything to do with my reply to the original comment.
Even if you were absolutely sure LLMs were going to get as good as they are today 2 years ago, that didn't make them any more of a practical solution to the issues you were trying to solve 2 years ago.
It is likely that the SpaceX Starship will eventually be a reliable rocket platform. That doesn't mean that given the chance I would hop on the next flight.
The problem is it doesn’t make any goddamned sense.
I'd probably insert a 'sometimes' in there, because many times in small doses it does make sense, it's only when you ask for long form writing/work that it becomes apparent there is no coordinating intelligence there.
Interesting just how much of this advice applies to programming as well as to maths:
--
Skills, agent.md and harnesses are probably a dead-end that will die off as the tools become more capable.
LLMs are not good at reducing complexity, however they're very good at adding it, and sometimes it is just unnecessary and he can find ways to cut it by interrogating the LLM.
Some people are responding to the new reality by gleefully using AI to generate lots of semi-OK-ish papers and puking them up on arXiv [this is like people producing mediocre one-shot clones of software].
On the other hand—with creative writing, my advice is not to use AI to write, at all. Ask questions if you want, but write every damned word yourself.
--
Definitely worth a read for the programmers here too.
But if you want to believe otherwise that's up to you (or perhaps you just hope it could be otherwise?). If you prefer, you can read that sentence as 'How refreshing to read intelligent, coherent thoughts in a blog post instead of the garbage we so often see nowadays.'
The sentiment is the same, it's about quality and intelligent thought, not style or provenance. Maybe one day we'll have to say intelligence rather than human, which is a fun thought. I don't feel we're close to that yet though.
I had a conversation about this very problem last November, with a visiting mathematician. It's essentially signaling a deflationary spiral in intellectual work: why bother doing the work now, when it will take half as much effort a year from now?
This is perhaps always a possible stance, but it's exacerbated when some proportion of your own agency is handed over to, well, agents.
In 1-2 years the AI will give an instant answer to most conjectures anyway.
I think it says more about what the value of math as intellectual work is, than about intellectual work in general.
Like if an Egyptian historian would come and say "let's wait one year until the methods are good enough to decrypt this language", no one would be bothered or surprised.
You even imply, economic value was determined correctly in advance for arbitrarily long future intervals. And the applicability was known in advance to begin with.
Obviously, you're completely wrong.
Applying simplistic models to real life incurs a penalty. The affected scale multiplies with that penalty. When dealing with things affecting humanity as a whole, that makes careless over-generalizations a serious hazard.
I would like to disagree with you on that point. Given the very popular rise of https://rea.tools/, it appears the time to reverse engineer anything software based (up to maybe 80% or more?) could be down to minutes. With a recent example, some indie video game developers are not going to show off their video game until release as a few have been flipped and made it to market before the original developers have. Point being, a few moths of market ownership could be possible if llms can’t reverse it in any way.
A perhaps more relevant personal anecdote: About a year ago I told a non-technical friend that I'd help him migrate his small business website that was originally set up in WordPress (by a developer who is since long gone) to a format that would be much easier for him to manage with no dev support. I planned to move him over to one of the usual suspects like Wix or Squarespace, but this is one instance where my procrastination was a virtue. In the ~9 months since he originally had an issue with his site, AI capabilities had exploded. Turned out it was a lot easier (and cheaper) to use Claude to fully migrate his site and get it up on Cloudflare workers, and I set up everything so he could manage all the content himself. Plus, it took me less than a day to do the migration off WordPress, and most of that time was just me wanting to learn the ins and outs of Claude Code because I was new to it at the time.
I think they would have employ just about every mathematician on earth for that to make sense.
OAI is not simply prompting "Prove exponential time hypothesis false. Make no mistakes" for the same reasons you can't one-shot "Write a fully standards compliant internet browser from scratch"
Levent Alpöge's prompting that did solve this open problem does not appear to be public, but Aaron Lou at OpenAI succeeded in reproducing the result the next day using an internal version of Codex and (reportedly) without web search, and he shared his prompt at https://aaronlou.com/jacobian_counterexample_prompt.pdf. It is a mathematically-sophisticated statement of the problem and of general search strategies, but contains no concrete ideas for the solution whatsoever (even the idea to look for a counterexample instead of a proof).
Aaron reported that this 2-page prompt found a counterexample in one shot. (https://x.com/aaron_lou/status/2079222629794189515)
Lex Fridman recent podcast on the AI crisis in math, https://youtu.be/ZAzWPE9CItg
I wonder how we as a society will react to this, this crisis of meaning. Not to get into existential crisis if that is to happen as well, which of course is a whole other issue.
I assume we will all start to look for social ways of mourning with colleagues.
Useless toys, sometimes useful toys, ok good toys, ok.. we might have to look at this more carefully, oh god.
This loop however is quite tiring to watch happen over and over again. Is there really nothing we can do but just watch from the sidelines and watch our fellow men engage in their particular grief and copium filled mourning cycle?
I responded with, "Well, you don't even need it to do math. It can explain the concept." They scoffed again. "Those things are useless toys"
2 years ago LLMs were a great tech demo but were mostly awful for actual practical purposes and hallucinated almost as much as they got right.
They'd be wrong today, but that's a different thing.
I was taken aback by the progress in 2025/2026 because late 2024 did seem to be a plateau, but 5-10 years seemed inevitable.
Even when I first studied automated theorem provers in around 2013, the 10-20 years to automating proofs (not theory building) seemed inevitable. They were already superhumanly fast and generating real results, and neural networks were making massive progress on translation, image processing, and games. Someone just had to work out how to stick a neural net inside an ATP. The surprise was that it happened the other way around, and that it solved even more than just mathematical proofs.
AI has only just begun to expose the depth of willful human ignorance.
Why? o1 was released in late 2024
I honestly don't see how this has anything to do with my reply to the original comment.
Even if you were absolutely sure LLMs were going to get as good as they are today 2 years ago, that didn't make them any more of a practical solution to the issues you were trying to solve 2 years ago.
It is likely that the SpaceX Starship will eventually be a reliable rocket platform. That doesn't mean that given the chance I would hop on the next flight.