I know why Mathematicians weep(derekthompson.org) |
I know why Mathematicians weep(derekthompson.org) |
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.
> If intelligence becomes less uniquely human, we may come to value more highly what remains uniquely human: our capacity to relate and to care for one another.
Lol. How does the author think relations between people work? (At least those outside the family). Relationships require something that fills them with meaning - a reason why you would want to have that relationship in the first place. Without meaning, no relationship.
I recommended reading this other post that was on HN earlier today: https://thetheorygirlie.substack.com/p/ai-was-great-until-it...
It describes in pretty grim words what happens to collaboration once you have nothing anymore to collaborate on.
> Mathematicians may still teach proofs, argue over what they mean, translate alien logic into human insight, and pass that understanding to students.
This would people to have time to understand and dissect those proofs - it doesn't work if there is a new breakthrough proof every week.
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.
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.
Are there any mathematicians who are genuinely excited about this tremendous leap forward in mathematical knowledge? Where are those articles?
How much do they pay you? Does OpenAI have bulk subscriptions to your Substack?
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.
I hate programming these days - back in the day, the cubicle-hell nature of "popular" frameworks was at least offset by being able to think through and solve interesting problems.
These days most of us are stuck in the "endless-review" loop with LLMs. You can't afford to not use it given the inflated expectations. As with all of modernity, productivity doesn't yield leisure - it just proportionally increases your workload.
Hardly surprising that the other side of the Curry-Howard correspondence is now getting hit with this. Math was one of those depts. where slow/deep-thinking was possible (CS was already insane 10 years back - now it's just absurd) - now even this fortress will be broken. Tragic.
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.
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.
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?
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.
...under capitalism...
Sure we will...
It's not clear from your comment: Are you talking about math professors?
If so, what money? They make a living, but it's not that great. I just checked the salary of two associate professors at my university: $80-85K.
And keep in mind they often start their careers quite late. Often multiple postdocs after PhD. Starting a tenure track position in your mid 30's is not common.
> I'm more shocked that there are so many brilliant people who are so results-oriented and don't even have a concept of value outside of that. I'm kind of disgusted by the tears actually
The whole point of the article is that the person crying is because he loves the process and is worried the human connection will be gone.
Still disgusted?
Ever heard of sour grapes?
This is the lie you tell yourself to handle the situation.
I understand there are many types of math and the mathematicians don't all want to sit around and do KV cache and gradient descent things, but surely a percentage are as interested as I am and can contribute to this new emerging field? I would wager that Xl+1=Bl Xl+Cl ℱl (Al Xl) makes much more sense in their mind than mine.
The dramatic solution can never be: 'we should all just want to do it this way because it felt better to me'. That never seems to work, from what I've seen. So there is a lot of public discourse, arguing, to determine if 'doing things the old way' is perhaps more better. And if not, maybe we just shed a tear and move on (to look for a better fit).
Worth reading: Robert Brandom, “Making It Explicit: Reasoning, Representing, and Discursive Commitment”
I'm interested in the reversal that Sellars proposes - it seems clear to me that "representation" is not prior to the space of reasons, despite how unintuitive it is.
> 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.
I see no reason why this can't be the case in the future, even though I think inferentialist-based theories are generally strong. Can't you force LLM's (or whatever AI architecture will exist in a decade) to stake durable commitments itself, then? They're at least autonomous enough to run computers. I agree that that is a core part to true meaning & autonomy, but nobody just lets them yet. I don't think inferentialism is a consciousness-based argument, either, so that escape hatch isn't available. I also don't think this is a necessary condition to engage in the space of reasons (but maybe then I'm misunderstanding it, or retreating to a more Sellarsian understanding). Could you explain on this more?
Though again, I only have the book sitting on my desk, and I haven't cracked it open...
The participant is not an LLM, the participant is a company. The company learns. It adapts. It has a trillion dollars of skin in the game.
Likewise OpenAI doesn't have "skin" of any shape or value in e.g. the mathematics community or even in mathematics research per se. In my cynical view, they are exploiting the exposure of mathematical research to automation in an effort to create a case study of their product obsoleting a highly visible and well-leveraged and relatively small profession. Regardless, I doubt even they would say they have durable skin in mathematics in any sense, certainly not in either of the senses I mentioned above. But their output inhabits the same space as mathematicians, who have to contend with the consequences
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...
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.
I suppose we would see some interaction with AI in that sense, but it'll take place over the course of learn cycles and when AI starts ingesting its own ideas it typically goes wrong somewhere down the line.
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.
This nails it, however IMHO its almost all bruised egos and feeling of wasted time. I don't know the ratio of A:B but I also don't know anyone that is in the latter category of feeling doom and mourning that their craft is about to regress.
Finding that new knowledge may be exponentially more difficult, but it will be much more valuable.
https://birdsnfrogs.github.io/2026/09/12/Felix_qui_potuit_re...
How do you know this?
Newton was possibly just taking a dig at his small-statured rival, Hooke. Newton was brilliant, but a shit.
Maybe the answer is to look into how Big Science works? There's still plenty of work to be done figuring out what to do with the outputs from these new math-observing instruments.
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.
The vanity, fame, self-improvement, it's very selfish as everyone does.
Now the fame coming from proving things like Riemann Hypothesis is taken away. Self-improvement? relying on AIs make you stupid. It will be lost. Vanity? Who else don't know how to use AIs? It cannot fill your void.
Now also the most important thing is the communication.
There will be less communications amongst mathematicians at least in person. On paper? maybe but mostly via AIs.
It's the same reason you see 'no AI' repo labels: only by forcing some standard on the community can the 'old way of collaborating' continue to exist.
There will for sure be new ways of collaborating, and walled off gardens like you suggest, where communication stops and everyone just shares some final product.
But, in some cases the product must be understood (or demonstrated) before value can be derived, and so collaboration will still exist.
Desire, and the 'shape' of collaboration has changed greatly though. Why collaboration has changed, is a completely separate issue related to economy and how each of us spends our time.
And then once it's solved by AI: do you want to churn through the proof to understand it? What if it takes you 5 years to churn through the proof, and it turns out someone made a mistake with AI (I have no idea what would be realistic amounts of time, but the idea is still worth considering).
The issue is very complex, and you will always be hungry.
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.
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.
What are the relationships between many languages that become apparent, including code as a language that were not obvious before llms? Translation is fairly solved. The study of how and why languages, not at all.
I am also sad, but my sadness is, in a way, priced in.
I just had a chance to flinch first.
It's easy to have that thought, and eventually you'll be correct. One thing about technology is that it only improves. It's always building on top of what already exists. The only uncertainty is the exact timing, not the ultimate outcome.
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.
Honestly, there are much bigger fish to fry, like how will everyone pay their bills, and how will we prevent catastrophic AI.
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?
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.
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 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.
Not "never again", it would be extremely difficult but science and math are also built on random, trial and error, and intuitions that could not arise from AI.
> 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...
I have to wonder if this is the equivalent of teleporting back in time and finding Marco Polo or any of those early explorers who traveled for the love of the game (and fame and money), and opening up Google Maps on your phone and showing them the zoomed out world. And showing them any island or village they could name.
I guess I'm not astonished that people are so bad to each other in general, but more that in the case of genAI it's so prevalent in places that seemed more elevated previously.
Part of me wonders if this is actually a form of self-defense. The misery of others can provoke sympathy or the opposite: Angry pushback to protect oneself from dwelling on their misery.
https://en.wikipedia.org/wiki/Life,_Liberty_and_the_pursuit_...
To me it begs the question: in a theoretical world where we don't have human mathematicians anymore, what is the point of these proofs if there's no human who actually understands it?
If the point of a lot of this math is only to expand the boundaries of human knowledge, it all seems kind of pointless.
None of them have pointed to any of the solutions and said "this is real innovation" - because it's all been mining existing ideas and applying them elsewhere.
Imagine you spend years working on a solution to one of these problems. Only to realize after you publish that more than half your answer already existed in another branch of mathematics and you spent a bunch of time re-inventing it.
Yes the first big solve by OAI was "stolen" and that is tragic, and pretty bad. But it looks like this new batch, the one people are crying about, has none of that stink.
It's not fun to think of a future where knowledge workers become irrelevant in society and we're back to just physical work and managerial elites.
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, too.
And highly visible blog posts written by famous mathematicians with large audiences and closely aligned with the news and hype cycles getting frontpaged on HN doesn't mean that mathematicians are disproportionately whiney, nor that software engineers aren't also writing about their plight or ending up on the front page as well.
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.
Say you have a friend who likes making music (not professionally - just a hobby).
If an invention came out tomorrow that took the joy completely out of making music, would you respond with "It's hard for me to feel sorry about you."
Just because things suck for you doesn't mean it can't suck for others (in different ways).
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/).
In my undergrad math department, only 2-3 faculty members out of a dozen bothered with grants.
This is said by a lot of CEOs trying to make layoffs look good, but I haven’t seen anything that suggests that it’s true.
> Yet I see far more of these blogs about the plight of mathematicians, not enough about the plight of software engineers.
Really?!? We’ve been living through 3 years of blog posts, LinkedIn hot takes, and podcasts talking about the plight of software engineers in the era of AI. There isn’t a week that goes by without an HN post about it.
I can feel empathy for the practitioners in a field that may have been profoundly changed, the same way I can feel empathy toward software engineers who are struggling with the changes in their own field.
In the end, we’re all trying to figure out where this leads. And how this will affect our lives and our work.
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 recent barf-out done by LLM companies is useful if what are you are interested in is an unreadable mess and someone giving you the final answer. You might be able to extract some new "aha!" moments out of it, but we will have to wait and see what happens once people go through it. I would hypothesize the LLM output will be good at hinting at some non-obvious relationships and patterns, but I doubt it will yield anything of substance in its own right.
Historically, proving difficult theorems required mathematicians to sometimes invent new fields, new ways of looking at problems, the discovery of which itself yielded incalculable contributions to both mathematics and other fields. It is this that is the greater contribution of and to mathematics.
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”.
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.
Jokes aside, its like working for a company, individually you can lift mountains and someone else will take credit. When you use LLMs for a single bit, all credit goes to LLMs lol
Now the thread has been cleaned up and a pro-defeatism comment is the top comment and the submission is on the front page again (I'm not alleging moderator intervention, user mechanisms are sufficient).
https://en.wikipedia.org/wiki/IBM_and_World_War_II
the above, a "sorting" machine is the primary usage of hyperscalers currently, they're just trying to find new uses to boot for extra money/legitimation.
the browser industry the phone industry the CAs JavaScript
it's all paid for by those wanting to sort humanity into whatever bucket the can fear monger the peasantry into for aweek or however long it takes the classification system to sort out.
gentrification works, but we chose forcible displacement now we have to live with the forever consequences.
would you give guns and bombs to the displaced native americans who taste blood over their beads and trinkets?
we've been inside the event horizon of the singularity for years, the tax bill will only get worse unless we recognize it for the tick that it is.
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.
Sometimes you think you’ve been accused of everything you could be accused of. Wonders never cease!
> 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
The guidelines have been constant (with minor updates) for most of the two decades HN has existed. Dan’s a moderator for 14 years and I’ve been one for several. Both of us have been active participants almost since the beginning. When did the ruination begin?
Your comment seems a generic vent, largely unrelated to the parent comment but if you have any actionable suggestions you’re welcome to email us.
Never been invited, but I've also never felt smart enough for that community. I'm glad I can read it though!
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.
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.
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.
> 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.
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.
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
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.”
Proofs are somewhat like legos. A bigger toolbox of them can only help in solving other, possibly practical, problems.
As far as the utility of a human being involved -- In a non-theoretical world where we don't have feline mathematicians, what is the point of these proofs if there is no cat which actually understands it? The cats can benefit from, for example, advances to optimziation algorithms that reduce costs for cat food delivery, of course.
If I were a mathematician working on the Riemann Hypothesis, I'd probably be rather pissed off right now but continuing my work, i.e. the same as I am as a software developer.
Social creatures that share a common space, with finite time that nobody wants to waste.
You are probably right that some companies are factoring AI into headcount but I'd imagine that the interest rate and energy crisis are bigger concerns
It was long predicted that the sign that AI is here in macroeconomics is rising interest rates, because investors can get MUCH higher rates of return doing AI investments than borrowing governments, why would I lend money to Greece when I can lend it to Anthropic?
There it is, the "off topic" play. Well done, Tom.
If you'd put anywhere near the amount of attention in moderating the site for over all quality that you put into my "largely unrelated" comment, this entire comment thread would not exist. Think it over.
I’ve worked in tech for 20+ years and I’ve never seen it like this. Sure there are job openings, but sooo many applicants it seems.
(This is Sweden, YMMV.)
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.
But it can continue to inconceivable levels before it gets to that point.
Humans have cognitive limits. Humans hold a specific slice of all knowledge at a time and necessarily limits what correlations can be leveraged. This is similar to "context windows" in modern AI. Human minds are wildly variable in efficiency. AI is has constant inefficiency, largely controlled by the speed of light, physical RAM, and processing power, with superior (no cost) "thought" context switching. The AI also has superior accuracy without the need for "concentration" because the AI is processing on a Turing machine with the limited operations that it's superior at in terms of time and energy - eg find an element in a list of 1 million elements.
- 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.
It sounds increasingly dumb to bring this up given how advanced models have become, but it remains true - they are still fundamentally token prediction algorithms. And that imposes hard constraints on their potential. These constraints are relatively academic in our current world because there's just so absurdly much information and no human can hold more than a negligible amount in his mind at once. So they'll certainly be able to connect many 'obvious' dots that we don't see simply for a lack of carrying capacity, but they're not going to discover concepts that do not clearly follow from the comprehensive knowledge of an era.
Certain of predictions? I think that's an unreasonable ask.
And I'm comfortable with my prediction. Rather than argue about it - let's wait a year and see what happens, and then we can discuss it.
Oh, good point! I misread your comment. Sorry for that!
> Rather than argue about it - let's wait a year and see what happens, and then we can discuss it.
Deal!