Sometimes HN is crazy and out of touch.
Most vote-based forums like Reddit end up like that
His end goal was one of the things released in the recent OpenAI publications. It took a model 3.5 hours to do.
Things are wild now on math and theoretical faculties now.
And for theoretical fields labs don’t need human data - synthetic one works well if not better.
The best thing you can do if you’re a scientist, imho - wrapup whatever grant you have now asap with ai, use ai to get more grants if possible, and spend the rest od the year learning what new science you can do with the new tools and participate in creating the new paradigm in your field.
That’s when you’re an established scientist. If you’re new in the field then this is the most exciting time you could wish for - an opportunity to make a name for yourself.
You can't really swear off looking at problems solved by AI, or keep moving away from fields whenever AI starts contributing, and have a viable career.
Today's frontier models, are everybody's local models in the near future.
If this were a change that had expected stalls or reprieves it would be different.
Doing mathematics looks to be the next chess, er, I mean protein folding challenge. The latter's computation demands have dropped significantly.
Yes. The problem isn't that there won't be any problems. The problem will be the rate of general progress and solutions that at least some awareness is required of, to reliably identify a good new unsolved problem will just keep getting more challenging. And then an attempt needs to be make, to solve it in a very short time.
There is always another race to run too, but increasingly slow runners don't find that translates to winning.
This change is not going to slow down, it is going to speed up. Machines will be doing math systematically, checking off the meta-math theorems that ensure axiom combinations are covered, that the search does not stop where theorems are not exhausted, and does stop where it can be proven they are. Humans will never operate at that level.
When things really start going downhill, if we are still in the current mess, it will grease the the wheels, and the brakes.
Why do we ever use PCs, smartphones, Internet, electricity, medicine and so on? Why do we live? For what?
I have the same optimism as Prof Tao. That said, I can understand why so many mathematicians have been so upset or stressed out. It turned out much of the mathematical work is about clever combination of existing methods - this already requires enormous amount human ingenuity and years of dedicated learning. Unfortunately, or maybe fortunately, AI can be very good at knowledge transfer and finding combination of existing ideas to solve seemingly impossible problems. Even though mathematicians are extremely smart and capable, only a small number of them are capable of truly inventing "alien ideas", discovering new ground-breaking mathematical structures, or coming up with new problem-solving techniques. That is, AI can eat many mathematicians' cake. That said, I'm still hopeful. Mathematicians still understand mathematics deeply. If someone can prompt AI to solve an important problem, that person is more likely a good mathematician than an average joe like me. So, I think mathematicians do have a bright future: leverage AI, and make more and bigger math discoveries. It's still the same north star: we must know, and we shall know. It's just that with AI, we will know sooner and more.
This is not written by Tao, but by Álvaro Lozano-Robledo.
That said, in the past couple of month, AI has gained a lot of ground on the 'project management' front in terms of planning capability for a lot of simple to medium-complexity projects. It still needs a lot of help for more complex projects. Just today, it almost fooled me into making a major structural mistake but thankfully I asked the right question and saved myself a lot of future problems; it was essentially dancing around a critical point and giving me the illusion that the critical point had been addressed but only when I phrased my question in a particular way, I understood the core issue was not addressed.
My own suspicion/guess is that AI can break out of the bounds of the convex hull in math, and that’s going to become apparent soon.
> With the latest ChatGPT models, these problems are more equivalent to homework questions: the answer is `in the back of the book.’ I am not discovering new solutions. Instead, I am working on problems whose answer exists and is simply waiting to be retrieved by a user of the model. In fact, I mentioned a problem that I was interested in working on to my advisor and he informed me that he and a collaborator had completely resolved it using ChatGPT – they have no plans to write up the result, so it will sit there until another `researcher’ pulls the proof slot machine.
There is another good point that the most tenured researchers have a sense of what problems are most worth exploring and therefore are more likely to feel excitement than younger researchers:
> I have also heard the contention that math research has `gotten more exciting,’ mainly from established researchers. They have decades of open problems that they care deeply about and want to see resolved. I have no such problems.
As a student, I am actively making decisions which will shape my career for the next forty or so years. At a minimum a discussion like this should acknowledge the possibility that the current rate of AI progress continues apace. I understand the desire to be encouraging, but the best preparation for students involves the consideration of possibilities that current mathematicians negligently paper over.
Of course it will get better at exposition than humans. And it will prompt itself in due time.
But the post does do this: "[...] even if their capacity becomes far superior, there will always be a need for mathematicians at all levels to guide research in paths that make sense for humans to walk (not run)."
> Of course it will get better at exposition than humans.
I'm not so sure about this, because I don't know how one would train towards better exposition as it's not easy to check for good or bad exposition at scale.
But nothing is certain. I am trying to avoid overspecialization and remain flexible, just as you advise. If this path fails I might become a paramedic or physiotherapist.
Some of those complaining today are the ones who keep saying "LLMs are just stochastic parrots predicting the next word", "how can AI do math if they can't even count the number of 'r's in strawberry?", etc.
It doesn't take a genius to realize AI will start getting better and possibly become a "threat" even before all this mathocalypse stuff happened.
Go into things expecting you might have to change careers.
Sure you wouldn’t predict what you would work on exactly. And there were better tools, better communication and so on sure, but no disruptive innovations or seismic shifts really.
The sports analogy holds; the future location of the ball may be uncertain, but that is the student's target, and not overcommitting to the present location of the ball. The commenter is expressing disappointment that the commentary seems to be reacting to the present too much.
I think the problem is the reverse. We no longer can make good predictions for four years ahead, certainly not eight.
And yet, people have to make choices - so they need advice and some kind of hope of a guess.
> you might have to change careers.
I hope this is some dust dry humor!
Manual labor and trades is likely to be one of the last things to go, so the whole "dropout of school and go into trades" crowd may have been more correct than ever, though their original reasoning was not.
It's also quite likely that the next big era for humanity will be the space era. And that stands to create the biggest labor boom in human history. It could also happen far faster than many might expect, even moreso as there will be competition between countries, especially as those left with only terrestrial claims will see their influence relatively wane. Space jobs and industry can also, in some ways, act as a more productive Works Progress Administration [1] to compensate for any temporary economic instability that LLMs might bring along.
[1] - https://en.wikipedia.org/wiki/Works_Progress_Administration
Yes, this is likely true. Plumber & Electrician on existing construction will likely take a long time (relatively speaking) to automate. And even if we end up being able to do it, it could be that humans will be the cheapest option when it comes to a lot of manual jobs especially given that there will be a large supply of unemployed humans in many scenarios.
Especially if the timeline is 40 years (as opposed to, say... 4.) I have no doubt AI-assisted robotics development would have solved the plumber and electrician jobs in a decade or two.
But I’m not sure it will take 40 years. I’m quite sure Astra could figure it out, it’s just too slow and robots are too weak. The speed will improve, and robots may lag shortly thereafter but by not much. I give it 1-2 years for AI, and 5-10 years for robots tops (perhaps even quicker).
Why are meta glasses such a big deal? Because they need training data for manual labor.
Meta glasses are a terrible example for the case you're making a point about: 90+% of whatever video they'll capture will be trash data.
It'd be much more efficient to set up dedicated sites just for producing the very same training data you're claiming they harvest.
Realistically the outcome of highly capable advanced AI is an economic dark age more than anything else.
And jobs that require humans’ responsibility.
People can do people stuff, machines can do machine stuff. And market will react accordingly.
Robots automating everything and humans not needing to work was the stuff paradise fantasies were made of.
Sure, it would be the end of capitalism (which, I guess you could describe as "economic dark age"), but people these days have so little imagination what life outside of capitalism looks like that ideal societies sound like a horror story.
The honest answer is via politics not education, but this debate is often had in "apolitical" circles that try their best to ignore this.
The second reason is that we often prefer humans to do it even if a machine can do it faster / cheaper. Sometimes, it's a status thing. For example, some people will buy Ikea furniture, some will have it custom made by a local craftsman. In fact, it's sort of the hallmark of the upper middle class that you can spend more for that human touch. Cupcakes from an artisanal bakery, private banker, etc.
Now, I don't think there's enough people who want to pay extra for human-made software. From the current trends in the industry, my impression is that we don't value our craft, so it would be surprising if others did. For mathematicians, I don't know; it's a bit painful to watch.
This is correct under present day thinking.
But imagine the accounting AI of twenty years hence. If it can reliably do the books, reduce and prevent fraud, significantly better than any human ever could, why would you still need the human in that loop?
In the present day it's a legal requirement, not to mention a practical requirement given present AI capabilities. That doesn't mean it still will be in the future.
To put it another way, if the human is on the hook for the agent, but the agent is proven by a decade+ of statistical evidence to be way less mistake/fraud prone than the human, what's the point of the human there?
What we're seeing so far is consistent with the training data being the upper bound for capabilities. They get better at recall / synthesis / reasoning over the corpus, but they don't, for example, acquire trans-human ethics; they're at best as ethical as we are, except not grounded by the fear of consequences. A perfectly-behaved, perfectly-moral LLM is not a given in 20 years, not unless your position is that there's room for unbounded, exponential self-improvement without any loss of fidelity. In that case, we'll probably have problems more pressing than the outlook for accounting jobs.
Not needing to work is a neat future that might be ahead of us. But it could unlock some new negatives as well as positives.
A lot of people put a lot of their self-worth into their work and that’s a good thing that won’t change.
But the ball is flying out of the court and into the abyss.
Don't go classically into that qubit night.
Do you know where “the ball” is going? Do these math students? Do the professors? It’s easy to say a vague nothing platitude like “target where the ball is going to” but such empty vague platitudes do not help anyone and just waste time.
Human-crafted religious items and artwork may be more appealing than machine-crafted replicas.
I assumed the student ultimately wants a career that is financially viable.
> Then what?
Literally anything else?
Ironically, this very attitude could lead to AI creating one of the biggest slowdowns in progress in history.
It's this one, but different careers will diminish at different rates. Mathematics was already not financially well rewarded, and current AI is basically better than everyone in the field.
> this very attitude could lead to AI creating one of the biggest slowdowns in progress in history
I think there are enough young people with pre-AI experience that we'll probably develop superintelligence before they retire, so I don't really think a near-term lack of fresh talent will result in any significant slowdown.
> What specific direct advice would you give then if you could talk to someone who is currently studying math?
Do it for personal satisfaction, but find another way to pay the bills.
FWIW, I did like that the article at least acknowledged that the fundamental question is whether LLM-based approaches will eventually "max out", i.e. will they be limited to the "convex hull of ideas outlined in literature" as the article out it.
If LLMs do eventually hit a wall, then great, humans will still have a role to play. If not, though, we're all completely fucked - none of this nonsense about "humans managing agents" or providing "unique human insight" and what not, as agents will be more than capable of managing themselves and providing superior insight.
Mathematics was historically "just a hobby". Much theoretical work is still "just a hobby". But, for the past few hundred years, humans that better understood the theory could find very profitable applications.
That is no longer true. Computers have solved mathematics, like they did chess two decades ago. A human will never find a better application than a computer, just like they will never find a better chess move. Yet people still play chess, and people still make money tutoring chess.
That is the future of humans in mathematics. Mathematics will become mathematics competitions. It will be just another intellectual sport. Sure, a sport that teaches valuable life lessons, but still "just a game". If you are going into mathematics today, your future career is as a competition mathematics coach.
For all the arrogance the hard sciences have, in the end they are just as human as their humanities counterparts. They just thought they were above becoming worthless because science was elevated above the softer sciences.
I expect it will remain true into the future (10+ years). I have moderately high confidence (75% or higher) in this prediction.
I use frontier AI models in my work all the time. I think they accelerate my work by helping me understand faster and prompt better.
The models are most useful and most productivity-enhancing in the hands of experts and in the area of their expertise.
I don’t expect a jobs apocalypse, not even in math.
It's definitely (again, to the article's credit as it points out) up in the air whether LLMs have inherent limitations. But I can't fathom how someone can say "I don’t expect a jobs apocalypse, not even in math." Because if AI does end up surpassing humans, what exactly will there be left for humans to do? And even if they don't surpass humans, there will still be a jobs apocalypse. Probably the majority of people today work in jobs where AI can surpass their performance.
Simple case in point: years ago I used TurboTax to do my taxes, but I eventually needed to hire a CPA because I had some complicated situations that TurboTax couldn't handle, and I also needed some tailored advice. I ended up finding a great CPA. Now though, AI agents can literally do 100% of the job I hired my CPA to do, including asking me the right questions and offering advice. I'm sure there may still be tasks for a CPA in the corporate world, but for personal taxes, I literally can't imagine a CPA providing value over what an AI agent can provide. And to emphasize, I would have probably considered that a ludicrous statement a year ago with all the mistakes LLMs made. But so many of those mistakes have been fixed, and you can get better-than-human performance by having agents check each other's work. And AI will only get better when tax season rolls around next year.
It's not like "should I get a PhD" is a new question. It's not unheard of for unpredictable events to drastically affect the career prospects of PhDs in my field. During my lifetime:
1. Mandatory retirement of professors was ruled illegal. While good for civil rights, it created a 10+ year gap in faculty retirements.
2. End of the cold war.
3. Transition of college teaching from tenured professors to gig workers, aka "adjuncts."
The one constant during this time was the perpetual optimism of the faculty for the employment prospects of PhDs. "There will always be a need for physicists." My dad, also a PhD, confirmed that this goes back as early as the 1950s.
I would add one question to the student's letter: What are the ethics of AI and its owners?
This is a huge, and likely permanent, change.
https://philip.greenspun.com/careers/women-in-science
Basically, it's arguing that science (really academia) is generally an awful career path for most Americans.
We studied maths because it is interesting, because it teaches you how to think, you often pair it up with something that's more employable like economics or software development, or you go for a teaching career. Unless you're one of the few people who are heavily invested in cutting edge research I don't even see how new research tools change the profession.
An undergraduate maths education isn't going to change because you have people with computers churn out 400 page proofs. It's like being worried about 30 move Stockfish opening theory if you're a club level chess player.
But it's a construction based on very basic properties of the real world, at least on those properties we accept and perceive as very general and we use them as building blocks.
At least for now someone still has to decide what to prove and why. Like why are you trying to prove that thing to begin with? Presumably it's a step along some journey, right? Maybe the journey is where you need to start deriving your satisfaction from, then.
You haven't tried the latest gen of frontier models, I take it? These things aren't just hype.
> At least for now someone still has to decide what to prove and why. Like why are you trying to prove that thing to begin with? Presumably it's a step along some journey, right? Maybe the journey is where you need to start deriving your satisfaction from, then.
Beautifully said. I had been thinking about the same thing and the analogy b/w CS and mathematics and these were some that I had found:
1.) to prove/disprove from the proofs that OAI created, you needed an mathematician to do so and OAI had to withdraw three mathematical proofs.[0]
But it was only because an expert within the field could verify if it was true or not, I feel as if software engineering is the same as well. We are/can be paid to prove/disprove if a software is working as intended or not.
2.) for someone to be that said mathematician who disproved it, he had to learn the basics of mathematics and multiple branches of it to then perhaps specialize in one thing that he most strongly resonated with and within all this learning, there was some struggle definitely involved. They had to learn algebra etc.,
this analogy can also extend to how we teach children algebra/calculations and other things even though we have had calculators for a long time, yet, we teach children how to do calculations because it is still valuable enough and either teaching maths can help them perhaps in future make a mathematician or it can help them be less reliant on simply calculators and more confident on on the spot calculations and help them within this skill.
As knowing calculation has become the norm rather than exception, even though we have calculators. In fact knowing how to do calculation by hand can perhaps better help you write a problem to calculator. Knowing the technical aspects of CS can help you express a problem to AI with much more depth and effectiveness as well.
I’m frankly a bit disappointed that Tao published the blog post I linked to above.
Telling OpenAI they shouldn’t test frontier math on their internal models is just plain nuts and illogical. It’s surprising that the advanced math community can lack so much logic.
God, the absolute decimation that is going to come for middle income countries.
Hell, right now the people quitting frontier labs are rediscovering trust and safety isues, like language parity problems, except all the work being done is in the first world and exported back to the rest.
[...]
> After I finished writing this blog post, and had already sent it to Terry, OpenAI released a huge treasure trove of results in mathematics [including] the resolution of the so-called quasi Riemann Hypothesis
We ought to all be careful about underestimating the speed and magnitude of the change that is coming.
> if you are a student who is passionate to learn what is new and what is left to do, then a PhD is definitely the right path for you
This is an awful lot of confidence to put behind career advice in a wildly changing world. Markets are real and tradeoffs bite. We're not in gay communist space utopia yet.
What actual industries where you could get a phd in, died?
If I was to ever suggest one, it would be Philosphers.
Yet they have found ways to get tenure and/or other jobs for as long as the field exists.
You should also tell them “better luck next time” as they have to create and find their own luck unfortunately.
This game was meant to be unfair because the ones who have “won” want to keep it unfair for others, and cannot stand losing due to complete greed.
The truth is they (students) have to find a way to outsmart the incumbents. The best advice is to find your own strategy and listen to no-one.
“42.”
But no one could understand what the answer even meant. So they designed a computer to build the question itself again, and that was Earth. Then the story begins with Earth being destroyed because of a cosmic highway problem (I won’t write more since that would be a spoiler). In the opening background of this work, I found it interesting that after calculating for 7.5 million years, they didn’t even know what they had originally been asking. The story now feels similar to that story from back then.