This will be interesting to watch: Where will AI creating and solving problems in a loop lead to.
Considering that this is where the mathematician excels over machine wouldn’t that only offer a new view from such a mathematician that “OpenAI has rapaciously stolen from mathematics that last dignity: of choosing worthy problems”? Perhaps with sufficient effort the community of mathematicians may yet forestall such an effort.
Don't invent things to get mad about, please.
I suspect their internal harness, models, and thinking budget far outstrip anything us peasants have access to (never mind the compute). So saying that they achieve all these headline results with 3 hours of GPT Pro is disingenuous. If that were so, hundreds of math phd students would’ve already recognized it.
I’m coming to the realization that my monthly subscription is only helping subsidize their real internal AGI, and my interactions are a small amount of human feedback and creativity which they can strip mine should they choose to.
Funny when it’s someone else eh?
Just learn a new trade Terry.
(I am kidding if it wasn't obvious)
It turns out it doesn't matter, because outside of a few narrow bands like Claude Code, no one cares what documentation an LLM writes for your project, because no one is ever going to go looking for someone else's project or library to solve their problem anymore.
So either an LLM decides to pull in your project as a library for reasons, in which the LLM can understand the documentation, or else no one besides the creator is using it anyway. So it doesn't matter.
Why would anyone use someone else's AI-coded project if they can get their own version that better fits their own needs in less time?
But we still have no self driving cars. Seems like the automation came by in the opposite direction. Perhaps driving will actually be the final thing automated.
While I agree with your statement overall, as someone who drives everyday in LA alongside Waymos without anyone inside of them I must disagree with this aspect of it.
Because if it became fashionable for pedestrians to wear large green dresses with red balls, and everybody would wear that, we have no idea what the AI would do.
Edit: nevermind. https://www.cbc.ca/news/business/waymo-toronto-winter-self-d...
It was too easy to assume that an AI would never approach human intelligence and hence would only be used for “boring” jobs like driving.
I’ve long disliked the hype around AI but now see that human intelligence is perhaps slightly overrated, at least in terms of the loftier positions seemingly requiring such.
Claude Opus puts to shame any highly caffeinated “10x” software developer. Not saying it’s perfect, but damn good. It can knock out difficult code analysis/reverse engineering more than 20-40x faster than I can. There was even a time long before AI when people thought the same of me…
Hell, at this point, I’d rather deal with Claude than a low-cost offshore team that puts up crappy implementations with endless go-backs and rewrites. I say this from actual experience, not xenophobia. There likely are some high performing offshore teams, I just wasn’t lucky to have the chance of working with one. Have had a couple of local colleagues that were worse… Claude’s probably much cheaper too.
Unfortunately, the “knowledge worker” jobs historically tended to be higher paid.
On one hand, AI is a major asset to experienced professionals with access.
On the other hand, it robs junior engineers hard-fought experience - much like watching a movie instead of reading the book.
And longer term, I think the entire economic structure of society is going to change. Doctors, lawyers, software developers, engineers — none of these are safe from AI reducing the need for headcount.
A truck or a car that has a 99% success rate would be the top threat to society and quickly rise to the leading cause of death under 30 if widely deployed.
99% successful web development where the 1% missing is security that and the company leaks its entire repository of user data every few months is not good.
99% successful car driving where 99% of 5-year periods have zero accidents per car is an order of magnitude safer than the average driver. (And gut feeling, I suspect approaching the tail-end of the safest drivers on the road.)
Wait, aren't human-driven cars already the leading cause of death under 30?
I agree that LLMs have and will continue to increase the number of activities that people can DIY. But I believe many people will still choose to pay for others to do things on their behalf.
Do you live under a rock?
Developers are guilty of hubris and they are getting slapped back to reality.
In 2025 it was occasionally driving weird. Today it's a much better driver than me.
That just makes you less prepared when you do have to take over. That's the danger of almost-perfect self driving.
In the case of Tesla, daring to call such a system "Autopilot" is a breathtaking level of irresponsibility. You are responsible for the vehicle you are driving, practically, morally and legally, even if a companies' marketing and the system itself does its very best to divest you from that simple and obvious truth.
Something I'm noticing a lot is that automation finds easy footholds in unregulated industries because there's no basis to push back on it. And there's a lot more tolerance for poor quality work in unregulated industries too.
All past inventions have put some of the most miserable humans out of a job. Farming by hand is hard, so is copying books and don't even get me started on the dullness of making clothes by hand.
Driving all day isn't all that far off, though still much better than the above and definitely better than riding horses all day.
Telegraph operators? Hell no. Dude sitting in an elevator all day? No thanks.
It's always been from the other end. This time around, there's gonna be some 10-20 years of robot manufacturing, then a universal lifetime of robots fighting misaligned robots until enough paperclips have been manufactured.
Or you know, we block out the sun and live in caves or whatever you fancy.
Is the cost prohibitive , or a proprietary model?
Given the trajectory of LLMs to date I see them helping construct proofs for conjectures but not devising new conjectures of any material substance any time soon. The challenge is, as Tao has said elsewhere, part of being able to formulate a conjecture is by exploring the landscape around it by doing proof research. Seeking answers finds useful questions. The fear is the tools will take away the exploration of the landscape. But that’s silly IMO. It takes a special type of lazy to let a tool take away your understanding that’s important for what you’re goal is, and a special type of passion to learn with a powerful tool. The passionate will adapt and progress will accelerate, not slow down.
For instance Tao has posted some of his interrogations of proofs with AI assisted reasoning and it didn’t seem to diminish his ability to establish insight rapidly, but to shut down avenues rapidly and to pivot and expand his understanding rapidly. The insight was all his own, as was the path of inquiry. The understanding of the output was his as well. He carries it into tomorrow and uses it to formulate new more interesting conjectures the next day. The AI ceased to “exist” as soon as the inference turn was over.
The hand wringing is pointless and lame. John Henry moves aren’t necessary or useful, and when I see a tunnel boring project now I see tons of people well employed there, just the holes are bigger and better, and they’re engineers instead of strong backed hammer slingers.
Case in point: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
The information in the article suggests that he regrets his prior hyping of AI.
Terrence Tao was very supportive of AI and formalizing math with lean when it looked like it was giving ‘generalists’ like him an edge over mathematicians too deep into one particular niche field.
But now that it’s letting everyone, including mathematicians who are perhaps too specialized, explore ideas and patterns from related math fields, he’s suddenly ‘on a war footing’.
Consider any man at his job, fighting the good fight. Your boss says "I've hired this man to assist you" and you are happy to finally have some help with your difficult task. Then one morning you come into work and see that the coming day’s work was done overnight by this other fellow. And the realization sinks in, he isn't there to help you, he is there to replace you.
In this view his reaction seems totally expected. I expect many professionals, e.g. doctors, lawyers, accountants, etc. will make this realization sooner or later. The companies are saying these tools will assist professionals, but in reality they are aiming to replace them.
If anyone doubts this, consider that Anthropic considers its TAM to exceed $30 trillion which is nearly the entire GDP of the US and 25% of the world GDP.
Only makes sense if they believe they will massively replace labor. Which, to their credit, they used to admit openly and publicly and only stopped because some crisis PR people told them "hey maybe you shouldn't say the quiet part out loud while the hoi polloi still have the power to stop this from happening".
They have practically infinite investor money to throw at salaries (lost in the noise of how much they are spending on compute) so why not use it for now to reach their goal as fast as possible?
My thesis isn't that they have already achieved the ability to replace massive amounts of the labor pool, just that that has to be their goal given their stated TAM.
> If they want to flex the power of their models to automate human jobs, why not lead by example?
They don't want to flex this. They realized (after a false start) that it is better for them to avoid talking about this in public.
That doesn't mean their goals changed, they just realized that flexing before the goal is achieved could endanger the goal being achieved through political backlash.
lol. lmao even.
I guess there is a first time for everything.
Regulated fields - another clueless poster lol.
I know many of you really hate whats happening but don't try and project it on other professions where the environment is different.
Society largely never cared about maths.
You are, of course, right that doctors, lawyers and accountants have more control over the environment they work in compared to mathematicians. But it doesn't change the underlying argument Tao is making. Your observation that those professions will react differently is likely to be true and only time will tell how effective their response will be.
But AI "assistants" is a marketing approach being made to all professionals at this time. Tao is implying this is a Trojan-horse strategy. If you let the assistants in without reasonable protections, you may lose control over the environment you are trying to protect.
basically both sides now dislike that he flip flopped
its either you are anti-AI all the way or flexible and adaptive without making strong opinions that can be put on record.
most people are in the latter and its growing. math is solved.
No, the dumb thing is the idea that there are "sides".
> basically both sides now dislike that he flip flopped
Literally the only people with this opinion of Tao are internet forum warriors who have no expertise in the field and who's opinion of Tao don't matter in the slightest.
Similarly, Tao being ‘on the warpath’ does not matter in the slightest when it comes to formalizing math and finding proofs to important unsolved problems with AI.
Do you think that this is a quote from the article you just read?
I swear half the comments here are just from people reading dunks on r/singularity and x and getting real mad at strawmen.
Terrence Tao is famous because of solving problems better that most mathematicians because he has an uncanny ability to look across different math fields. AI gets everyone this ability for 20 to 200$ per month, eventually free.
Most mathematicians are happy to see interesting problems in their field being solved, and are looking to build on these to find more interesting problems.
The point is to make the field progress by discovering new things!
Who gets credit for what and how credibility is assigned is going to be muddy for a while but that’s the case whenever a bunch of new science happens in close sequence. History is full of math/science discoveries having debated and dubious provenance.
It provides deep insights into logic, computation, provides tools for us to understand the universe, establishes mind blowing relationships between seemingly unrelated things.
For example “how much information can a black hole contain?”
To whom? If there are no humans in the field, there is no one to get the insight. Maybe you are right, and there is just a new type of a mathematician being born, but as an outsider I just can't see what they could look like, what will be left for humans to contribute
Most math is already being done by meagrely funded mathematicians. The entire US federal budget for mathematics is like $100M. One college football coach can already make 10 percent of that. No mathematician is making bank.
Is the implication of all this that mathematics research should get a cash injection to pay for high-powered computational tools?
Math will, sure. Mathematicians, doubtful. After all, most high end physics research with billions in funding is now done by postdocs making a lower middle class salary.
AI solves math problems to
> If there are no humans in the field
Realistically, math will be done by well funded teams of people instead of cult of personality mathematicians.
Also, insights from scientific discoveries are for everyone. You do not have to understand the complex multi dimensional algebraic geometry of general relativity to appreciate that gravity bends time as well as space. You don't need to understand fifty years of linear programming research to use a modern solver.
Eh... That “everyone” is a multi billion (trillion?) $ company paying top mathematicians specifically hired for generating math proofs.
I think this sort of progress, compounded over the next N years will serve to cleanly split useful math from the ego driven math you speak of.
Certainly there are enormously impactful pure math results yet to be found, but we have no idea really which directions to pursue.
I wonder if this is going to look like the chemistry-alchemy split in the rear view mirror.
There are plenty people in every discipline that prioritize their ego over measurable progress towards a stated goal - even less so a community focused goal.
Humans have been guilty of burying things we don't understand for millenia. Will we continue to do so "because AI"?
OAI first paper on the prize was a pretty shitty thing to do. But the rest of this looks like they are just mining the corpus and taking a brute force approach to do it.
Im going to say this again, the "pure math" academic types need to get a grip. Plenty of your peers got PHD's and happily made a fortune in finance, while screwing the world (See 2008 housing bubble) and none of you said a peep about that.
They call it the most populist post of all time.
Certainly, it’s like being made aware of cheat codes to video games: One doesn’t enjoy the game as much after but surely knowing something is true means you can find many other things that come from the pathway to it now that you know it’s true. Lots of science and tech is like this where someone shows something is doable and then people find better ways to do it but until that person showed it was doable there was no progress.
> I am horrified by the many person-years” of research, particularly by young mathematicians, “being casually disrupted or destroyed,” he wrote.
That’s what technology does. And he might be upset but we’re the ones paying for it and frankly, I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Most notable is the fact that the released facts are like “treated waste”. But if the question was worth answering and the value is only in a good answer and not simply a correct answer, then the value has simply not been realized.
But that feels strange then that the value is in the good answer, not just a right answer and yet one finds oneself unable to go get the good answer because a correct answer exists.
The fact that any answers are made public at all is useful to us all. That’s free knowledge. Would it have been better if OpenAI had discovered this very achievable fact and not said anything? Surely the papers, post discovery would have spoken of the “hoarding” of such “essential human knowledge”.
Overall, I find the thing unconvincing wholly.
When mathematicians discover new results, they automatically become experts during the process, and then go around giving talks to explain their results, methods, and intuitions to other mathematicians. After years or sometimes decades of refinement and a healthy dose of serendipity, some of the mental frameworks percolate to other fields.
No one from OpenAI is willing to give a talk on any of their 300+ results because their machines have decoupled formal proofs from actual knowledge.
edit: lest this be misconstrued, it can become their problem if it is wildly unpopular and undesireable behavior is regulated away.
I advocate for this path.
But the value in seeking mathematical answers was never in the answers themselves. It was in the things one discovers along the way, the questions asked, the tools developed. The artisanal fashion is the part that benefits non-mathematicians.
These AI proofs only serve as an I-told-you-so. They're not creating surrounding theory which can later turn out to have useful applications elsewhere.
Would you prefer if graph theory didn't exist but we could answer if you can pass all bridges in Königsberg, without going through same bridge twice?
Or if we could answer any question without knowing why? What about answering Hilbert without theory of Godel's Incompletness theorem? Or knowing Nth digit of Pi without calculus.
Because that's essentially what you're asking for. If you gave humans a Djinn that could answer perfectly any question, it would kill most of our endeavors. Because it's not a problem that was unsolved for years "It's just the thing Djinn already answered so why bother?" Even if one is extremely curious, and devote a chunk of their life answering it, others would not see value in that curiosity. Because a Djinn can answer it in a few minutes.
Now math isn't my wheelhouse, but every LLM I've seen provides far more than just the final answer and is quite willing to answer questions.
Imagine you are Euler and magical Djinn's exist (that possess all mathematical knowledge written up to that point exist and function identical to LLMs). You ask it to tell you answer to the bridge riddle and it says that's not possible and even gives some plausibly sounding examples even. Then it throws a 11 pages of gibberish proofs at you, which are all true but very convoluted.
And what if you start digging into it? Won't other people say - "Hey Euler go back to ploughing the fields? We can have Djinn's answer all the math questions but this field isn't going to plough itself."
Today's, the Djinni-Euler's equivalent of someone looking at LLM's Navier Stokes equation proof.
Perhaps they would discover new Liquid Set theory that would turn Liquid dynamics from a field fraught with problems into a beautiful mathematically simple meadow.
Seems like an overly pessimistic take to me.
If you have a magical Djinn happy to answer questions, why wouldn't you badger it a bit for the details? I can't imagine Euler of all people just wanted the answer.
Given that this is pure mathematics we're talking about, for the most part: Why?
Perhaps you are a mathematician and so these questions are relevant to you, but for most of us, these questions and their answers will not make any tangible difference in our lives or society.
It used to be that Pure Maths got to affect the real world via Physics (and that odd thing where last decade's interesting mathematical exploration turned out to be the solution to this decade's Physics discovery). But t'internet consumes Pure Maths pretty much raw.