Nothing has changed in math. Math is not solved nor has the human been kicked out of the loop. Same with programming.
*I said nothing really changed because LLMs becoming superhuman at deduction was priced in with o3 and neither the peer review, training nor publishing methods will get a revamp beyond what could already be done with SQLite and a website.
But from my perspective proofs have never been the most interesting part of maths. What really interests me is the intuition that leads to new applications, and to new questions. Newton, for example, gets more credit for calculus than Leibniz because he's the one who demonstrated how darned useful it is. Erdos is arguably more famous for asking interesting questions than for answering them.
I still don't see LLMs seriously contributing to that facet of mathematics any time soon. Every so often I ask one to suggest a good binomial confidence interval for a particular application, and it still tends to just suggest one of the subpar options that everyone learns in a first year stats course.
The "moderation by less", as well as the guidelines, are both farcical in nature. They've given way to ruination of an otherwise decent tech discussion forum (or news aggregator, or YC propaganda machine or whatever you want to call it).
If you want actual discussion around things, lobsters, awful or even 4chan are better than HN.
Never been invited, but I've also never felt smart enough for that community. I'm glad I can read it though!
But many people perceive this very differently, see link below. And perception is reality after all.
Is it like Chess and Go? There are still plenty of people playing for fun, but the machines are better at it than we are.
And this is only the beginning.
LLMs haven’t done much in the way of informing me or others I know regarding “who and how many”.
Yes, outsiders (investors, journalists) are given a false impression while insiders (software engineers) are supposed to give up. Double win for the agitprop machine.
Sure, there are people who overstate things. But that isn't an excuse to keep your head in the sand.
Anticipating that something will happen is not the same as evidence that it's happened.
A lot of us knew what was coming. Profs I speak to these days say it's the same old except they need to pick a different kind of problem for grad students
How will it pan out, no one really knows. The leading frontier labs are continuing to hire aggressively. But who knows for how long or for long or near-term goals.
There were mistakes that could easily be seen with a diagram rendering three big results wrong, exposition is terrible, no coherent underlying theory generated from solving so many problems, as Thomas Bloom pointed out even duplicate proofs of the same statement in a single paper.
It clicked for me, "this is slop but slop can be superhuman and useful!". Similar to programming where it can generate as many criticisms of your codebase but you have to weed them out.
I was taking to my friend in OA who was really surprised that the proof of L(F_2) = L(F_3) could be done in the 1980s. We just didn't have a superhuman deducer back then.
> I think I have been underrating the pace of model improvements. In March 2025 I made a bet with Tamay Besiroglu, cofounder of RL environment company Mechanize, that AI tools would not be able to autonomously produce papers I judge to be at a level comparable to that of the best few papers published in 2025, at comparable cost to human experts, by 2030. I gave him 3:1 odds at the time; I now expect to lose this bet.
https://www.daniellitt.com/blog/2026/2/20/mathematics-in-the...
“I’ve slowly updated my timelines over the past year…”
and
“I think I have been underrating the pace of model improvements. … I was not correctly calibrated as to the capabilities of existing models, let alone near-future models.”
Worth reading: Robert Brandom, “Making It Explicit: Reasoning, Representing, and Discursive Commitment”
What an LLM can't do (at least with the current architecture) is sustain a commitment that it can be held accountable for later. It doesn't have durable "perspective". It can't update its priors. Maybe a new architecture will come along that gives LLMs memory plasticity, at which point they will shift into being individuated quasi-persons, but that's not what we've got now.
I've written some about this here, if you're interested: https://elliotmilco.substack.com/p/deontic-scorekeeping-comm...
I think you are also suggesting Mathematics and Language are the same thing.
I'm not suggesting mathematics and language are the same thing, but I am saying (which shouldn't be controversial) that mathematics as a discipline exists within the medium of language, and that mathematical reasoning, discovery, and proof happen via people proposing, justifying, testing, and objecting to formulations in language. This isn't a metaphysical claim about whether math is real or captures inherent structures of the universe etc.
You ended your first post with: "An LLM encodes the normative regularities of our linguistic/conceptual games into its weights, but it cannot be a real participant in our games because it is incapable of staking durable commitments or changing its dispositions over time."
And so if there is an agent, a thinking loop, that can recursively adjust over time...how does your statement hold up? I'm particularly talking about 'staking durable commitments or changing its dispositions over time'. Recursive self improvement is all about these 2 things.
But you're right, Mathematics exists as a medium within Language. But then Language is just a transfer of ideas from one mind to another.
This principle is the heart of what the article is talking about: a transfer of logical mathematical ideas passed from a human to another. And the sense of 'shared understanding' that comes with it. It has nothing to do with keeping score.
It's about getting a 'sense' for why someone thought or rationalized an idea in order to connect some other idea. You get an 'ah-ha' moment, and those moments are now gone. That is what the 'weeping' is about.
Both depend on Logic, which is where "deontic scorekeeping" comes in. You can only establish something (score) is true and believable by 'keeping score' and having some level of understanding about the language or math you are reading.
The article is mostly referring to the connection that comes from shared understanding between humans, particularly mathematicians, as they build new shared understanding, and realize there are limits to what they can know and 'leave behind' logic for others to pick up and carry on.
That connection has been severed, or strained a bit, but I'm sure new ones will be created. It just might be of the same flavor that mathematicians prefer, therefore they weep.
And if I understand "deontic scorekeeping" correctly, these forums are a better representation of the concept. You will lend some amount of belief to what is said/read based on what you know.
Neither sits right with me. Can't we just all collectively acknowledge that we have to grapple with this new piece of technology that either is already or at least seems to be going to be hurtful to a lot of individuals?
Instead of looking at the in comparison limited group of people currently pushing this technology and asking ourselves whether we should be on board with their doing, we look to one another and are happy that someone else is now suffering just the same as we are. What a sad state of affairs.
I don't personally grieve for the likes of Strogatz or Tao, it seems likely both of them will be fine however this pans out. But many more mathematicians have been toiling away in precarity and obscurity and without tenure for years and years. And of course many mathematicians went into private sector roles as software engineers, actuaries, analysts, ML engineers and similar, and have been displaced there.
Visible blog posts written by famous mathematicians closely aligned with the news and hype cycles getting frontpaged on HN doesn't mean that mathematicians are disproportionately whiney, or that software engineers aren't writing about it or ending up on the front page
The bean counters laying off software engineers ought to take notes from the frontier labs' own hiring practices. They're still hiring lots of humans for business and engineering roles even when they would be better positioned than anyone to automate away those jobs with their world-class models (https://openai.com/careers/search/).
Finding that new knowledge may be exponentially more difficult, but it will be much more valuable.
How do you know this?
- random,
- from the environment,
- from other AIs.
That increases the space considerably.
In particular, note that your argument also applies to humans: A human, being finite, can only produce finitely many things. But you add other humans, the environment, and pure chance to the mix, and it'll be pretty infinite for all practical purposes.
Maybe that is the limits of my imagination, but it seems unwise to take humans completely out of the loop. Having mathematicians around that can understand what it is doing so that we can utilize that knowledge in a way that we can have some confidence in seems important.
I think mathematicians aren't bemoaning their lost sunk costs. They're now aware that they may never again have the joy of being the first to pull up the edge of the tarp of ignorance and see the raw truth beneath _for the first time_. Their voyages of discovery, which give life meaning, may never leave dry dock again.
> You are a helpless onlooker. Before you a channel through which humans have accessed the ineffable and sacred for thousands of years is being sealed for eternity.
https://kirwinhampshire.substack.com/p/the-dark-night-of-mat...
Does relating to someone pay my bills? People will use the informational tools to improve their social status and resource accumulation, there is no doubt about this.
> Today, the mathematicians are weeping, because the machine smashed their tower first. But tomorrow, it may be the physicists, the economists, the illustrators, or the writers who weep over their fallen blocks.
Isn't it extraordinary that these models still can't write well? I mean, they write passably well, but they all have a highly characteristic style that you can spot from a mile away. These language models can crack the toughest open problems in math, but they haven't yet cracked human-like writing, especially long-form writing, without exposing themselves. This is very very odd, IMO.
Their math is as just as good as their rambling writing and their Ghiblified poster art. Most people don't seem to realize that.
I read this passage and thought, "has Derek even talked to software developers"?
That feels to me like the first discipline to go through this, where their daily activities are massively changed by GenAI.
What is true, is that chat models (and by extension agents) have a very characteristic style after their LLM went through post-training. But the pre-trained language model doesn't have that style.
So if you want to write well with an LLM, you could and it is a well understood problem. It is more a matter of that not being of much interest, as it competes with having the model be good for chat interfaces.
How to have a well-aligned, RL'ed, safe or thinking model, which also writes well in long-form, is a bit an open problem. Though presumably agents could do it when they have access to a pretrained model.
That is why it's so disturbing. After several paragraphs, you realize there's nothing human there even when the actual information is present. People that do create AI piece are OK with it because they already have the context, but for the reader, it's always the uncanny valley.
So how can they possibly solve problems that humans have worked for decades or centuries on without being able to solve? How did they find something new? Is it that they were able to deduce the solution by examining all current data sets? Or simply brute force it until the produced solution passed all necessary tests?
Lots of mathematics entails recognizing that a tool/techniques that works in one area can be adapted to a completely different problem. For a human to do this requires having a robust mental model of the technique and the problem itself, and probably having just the "right" mental model to see how they fit together. And we are talking about extremely hard/sophisticated techniques and extremely hard/sophisticated problems, so the ability to deeply appreciate either can require years of study. And on top of that, even if the mathematician has sufficient understanding to develop the intuition that the technique might work, they will need profound fortitude, skill, and patience to see the solution through.
Unlike human mathematicians, who will develop a deep understanding of only a relative handful of techniques and problems in their lifetime, LLMs have ALL written techniques, problems, solutions, etc stored in their internal representations. So when they ably match a problem to a technique, we can imagine the operation as a supercharged autocomplete, or even an extremely proficient search engine. Their stroke of genius is really a consequence of capacity, moreso than cleverness.
Yes, both of these + an infinite token/compute budget and SOTA+ models. It's not like some hobbyist out in the woods with a GPU running Qwen 27B can do this.
Questions: (1) Do you still weep for what has transpired? (2) Do you continue to do what you used to do (with optional AI assistance)?
For me: (1) no, (2) yes and I think the same would be true for most people. So I can't help but believe that most of the anguish about AI is far more about a direct economic hit to people's livelihoods than it is about the impact to their respective fields. Which is more than reasonable. But then why not frame the conversation that way instead of beating around the bush?
heck, we have the resources to that now but we don't do it.
Considering I currently live in Ithaca and have a friend doing a Math PhD, so I've heard from him some of the discussions in the department. I think the biggest shock for people is that individuals spent significant portions of their time on some of the problems that OpenAI supposedly solved (I say supposedly because all of the proofs have yet to be independently vetted). I understand that it's a shock, but I'm confident that in time it will be no more of a blip than it was for NLP.
[1]: https://xxcancel.com/mayhewsw/status/1636476184098643968
[2]: https://xxcancel.com/andriy_mulyar/status/163613925780582809...
Seeing AI being lauded for solving problems like this makes me feel... uncomfortable.
We are feeding all works of the giants that we have all stood on into a huge vat, in the hope to generate something meaningful.
If we can't understand the output, internalize it, or build from the time and experience that a human would have gained from solving the same problem, it feels like a dead end.
When all the problems have been "solved" by AI, what's next? If humans no longer struggle to solve the problems that the previous generation have left behind, how do we progress?
I am also sad, but my sadness is, in a way, priced in.
I just had a chance to flinch first.
The people struggling right now - they were told. 30 years ago. They really should have come to terms with it by now.
But these are also the people who refused to believe it, for whatever reason. Their heads were in the sand. So I do feel bad for them... but... this is somewhat self inflicted.
Also, it's impossible to really know how you're going to react to something until it happens to you. When ChatGPT came out, I already thought "in the long run they're going to automate almost everything humans love to do". Despite having 4 years to brood about it, I did not really know what it would feel like until it happened to me directly.
That's how the singularity works. It's going to keep getting quicker, incomprehensibly so.
Even before LLMs it was feeling like the design of society wasn't really for people any longer, instead it's more and more designed for corporations and their convenience. In the US at least. Same with how the internet has stopped most people with socializing the same way they did in the past.
Now we have a new layer that will be optimized for these digital entities. We see it in writing all over the internet. There will be tons of other places they show up and doing things that don't make sense to us.
Either these mathematicians thought it would never come for their jobs, because all of these other jobs were simpler or they've been living under a rock.
Either way, I don't feel for them any more than I do for all of humanity.
These guys know because they looked at it. Denying it is useless. But maybe some of these guys can figure something new using it and asking it to look for it.
How much do they pay you? Does OpenAI have bulk subscriptions to your Substack?
So I wonder if mathematics will go through that too? A period of chaos and doubt, but finding new and more effective ways of working.
I never appreciated hard math much because my brain just can't get there. I thought so much of math was much ado about nothing, but now I see the art in math...not in the inscrutable formulas, but in the creation of AI.
Well done, mathematicians. You can now rest from your labors.
If it was about understanding interesting proofs that some AI came up with, and extracting their essence, I don't think the situation would be so bad.
I see the much larger problem in the now existing career prospects of non-tenured researchers in mathematics. Everybody know how precarious the career prospects in academia and how precarious often the non-tenured positions in academia already are. With the new AI breakthroughs in math, these have in my opinion even worsened a lot.
UPDATE: For a related point, see also pixl97's post: https://news.ycombinator.com/item?id=50104145
I think they might find comfort in knowing it's not just mathematicians - this is coming for all of us. Computers putting us out of work has been coming for a long long time.... and now it's here.
The same goes for math.
Let's find some things that bring value other than just the price of a stock.
At worst its time is past, but even that is unlikely.
I note that that these conjectures being solved by AI are named after people, minds knowledgeable and and brilliant enough to come up with the question in the first place and recognize its value. What we have in these AI math solving systems is the equivalent of the chess and go software that can beat humans: something that can adhere to a set of rigid rules to reach a win state once given a starting point. But, as Pablo Picasso said, “What good are computers? They can only give you answers.” These AIs are a magnificent achievement and will change mathematics and coding but can they ask earthshaking questions? Could an AI identify conjectures that mathematicians recognize as a worthy question that will lead to new insights? Where is HAL9000's theorem or the M5 Multitronic's conjecture? Maybe they can someday but I don't see any immediate prospects for it.
Please spare us the "AI will surely keep getting better forever" (unlikely and don't call me Shirley), "moving the goalposts" (I myself haven't set any), etc. non-arguments.
This is what it seems like so far for software. The speed limit has changed. It’s interesting to explore what that means. Extending the analogy, long ago you could be a race car driver part time; that would be pretty laughable for an F1 driver. It’s a very specialized skill and the optimal athlete is quite different for driving a car than for running, for example. That feels like what I’m seeing in software.
The most effective folks are much faster and better with these tools than average. It’s a different skill set.
I think that formal verification makes Math much closer to code than many other fields. But I’m eager to see the first mathematicians that are dramatically more proficient with the new tools than average.
Isn’t that in itself the new frontier for human understanding?
I would have thought that mathematicians would have found alien forms of maths to be astonishingly compelling, must learn, must know, must understand.
Instead there seems to be a sort of shoulder shrugging lament “we don’t understand it”.
I would barely be able to sleep with excitement at the potential for where this could lead. Like finding an ancient tomb full of answers to our deepest questions along with the promise of more.
How deep does maths go? Is it “solved” or have we just been given tools to delve ever deeper?
Where is their curiosity - don’t the want to find the bottom?
This seems like a good summary of the article, and I think the answer here is obvious.
So what?
News flash folks: we do not have the knowledge to survive on our own. If a solar flare deletes the electric grid, the first thing that happens is 8 billion people die in the next year.
We survive on abstractions others have built, and we have a global dependency web.
AI abstracting knowledge is neither new or dangerous; if it is dangerous, this certainly isnt the argument to prove it.
Where or what do solving these math problems lead to?
Is there some suggestion that they lead to deeper understanding about something else? Do they solve physics problems?
What’s the benefit? What’s the point?
It is mostly impossible to figure out what we find when we solve these problems. But occasionally they'll lead to real world efficiency in algorithms we use and it changes the world.
Still disgusted?