It’s more likely that instead of spending a 100K/year direct grant on two PhD students, PIs will hire 1 and have the student spend 50K on AI.
There will be no gap in understanding. Now there is because the models are discovering things at the edge of what they can do and so suck at explaining it. There's nothing particularly special about a newly solved problem in terms of learning it.
If we accept AI can explain all of existing math nicely, why shouldn't it be able to explain new proofs?
So much in AI is dependent on which of these two outcomes occur.
AHM Statement on OpenAI's October 6 Release of Mathematical Documents
https://news.ycombinator.com/item?id=50000421 / https://news.ycombinator.com/item?id=49999159
Of course it's good to have the discussion... So maybe, we listen to the nay-sayers, but defer judgement on the matter... That's wisdom.
Edit, to be clear, I consider Tao to be the wisdom provider, not an early nay-sayer!
The less said about Gary Marcus the better.
If I understand Tao correctly, he's saying that's going to have to be the focus going forward. I just default to thinking the models are going to be much better than us at that, too.
1. Some present a unified line that the whole point of their craft is the human experience, and that automation is the antithesis of that. Marathon runners don't care that a car can get there faster, poets don't care that Poem Bot 2000 can write poems too. I think this is smart if you can credibly take this position. The difficulty is mostly convincing the buy side, which requires being very outspoken about your views.
2. Some appear to be undecided, with one faction taking the pro-human stance and another rushing to accelerate things with AI. A good example of this is mathematics, and I really wonder where they end up in the long haul. They have a very good claim on #1, because mathematics is pretty close to an art form and is robustly insulated from the pressures of the marketplace. But they can also choose option #3, below.
3. Some crafts prioritize results above all else, practitioners either rushing to extract as much money as possible before it all collapses, or believing that they can out-prompt everyone else forever and that their prompting skills are indispensable to their employers in the long haul. That's software engineering. I think this is going to be interesting to watch.
There seems to be more interest in hitting some arbitrary benchmark (we proved X unsolved problems) than in genuinely contributing to mathematics. But what else is to be expected? It's become a maniacal race with too much money. Too much effort is being invested in proving that the exponential curve is still holding.
OAI obviously have a fiscal incentive here, but to presume a year from now we won't see improvements and more succinct work on the results coming from models?
OP didn’t suggest that.
The bar has been raised. Everyone has to meet it now. An inelegant solution squatted onto the internet doesn’t count as discovery per se, even if it’s impressive.
The job of professional mathematician might be the first to be completely eliminated by LLMs, save for those who can make money from a patron. I am hoping they are able to figure something out to save their profession, as other professions could use it as a blueprint as AI comes for them next.
Strong disagree.
Do you work in a math adjacent field? I do and I find having a mathematician around invaluable.
It's like a non-software person writing software. Yes, using a LLM will get you to a solution that works. But just talking with a software engineer will make the quality of that solution enormously better.
I find the same with math - I can get something to work using an LLM, but if I speak to a mathematician they'll say some magic words to try and I put that in the LLM and it is "oh yes this is a much better solution".
This is very different work to generating proofs though. Its things like "I'm trying to get my confidence intervals to properly deal with census like sampling but at small sample sizes" (yes, I know stats not pure math but still..)
This really expresses the heartburn you see across all fields, not exclusive to careerism. I certainly have friends in decomp and fan translation spaces that have been demotivated by the current rash of efforts happening there.
The rush to be "first" has always been over-celebrated, but it would be nice to believe there's a way to get beyond that thinking.
Edit: If you'd like a better medicine based one, look to radiology, where AI is an omnipresent tool but claims that radiologists are no longer needed, based on an ignorant view that a radiologist's job is "classify images according to what diseases they indicate" have only contributed to a crippling worldwide shortage of radiologists.
Up until now the prize in pure (as opposed to applied) mathematics was the _understanding_ and the machine can't do that for you. What does it mean if we get "super powered alien maths" but humans can't do it? It's like inter univeral teichmuller theory all over again but imagine if Mochizuki was right and it came with a lean proof?
Im not sure how that will work, but im convinced the current paradigm of just pushing agents into codebases for not much reason other than you can is going to make building software incredibly boring and push creative people away from the field and stagnate progress.
My prediction is software gets boring and building hardware projects will be the new frontier for creative engineers looking to push computing further. Which is probably a good thing.
Sort of. An elegant proof is useful beyond what it shows. It hints at new mathematics, and can prompt discovery in applied fields. I don’t think I’ve heard of elegant code leading to discovery on its own.
Almost certainly not. It's just going to jump to a higher level of abstraction.
On the other hand, it puts a premium on resources. AI is not cheap for mathematicians. Folks are fancy universities in rich countries with forward thinking ministries of science will have an advantage over the rest.
What is clearly in immediate crisis is the traditional model of doctoral education. Most of the problems that were "given" to ordinary doctoral students are solvable (quickly) even by something like Claude pro. Mathematicians need to adopt training models more like what is done in experimental and laboratory sciences - collaborative and structured.
Where Tao is wrong is in regards to exposition. AI already writes better lecture notes, problems, and exercises for mid level undergrad math classes than do most of my colleagues. It's exposition is generally well structured and clear and it can adjust level on request quite well. It writes research better than most professional mathematicians too.
AI only take us as far as our imagination thinks to ask it. This can be exhilarating when new models drop every month and we can continually reach a new threshold, basically for free. But it is only a one time gain and ultimately short-sighted. Where I find continuous value is using LLMs to help my understanding, full stop.
I use LLMs all day long as a SWE and I have tried many approaches, but the most satisfying and consistent approach is to lean heavily into understanding a problem space and a solution space. Yes, it whips up architecture and code, but I spend most of my time peppering it with questions about the design and how it handles certain situations, what about this edge case and that security concern and this future product need. I have it write a report breaking down the feature and how it integrates with existing code and if the report is too confusing I have it simplify either the report or the code until it makes sense to me, sometimes scaling back the work to a more manageable state. I do all of this before I look at any of the code it writes.
The difference from this approach is that I am not suffering reading through 3000 lines of AI slop but I am reviewing a PR that I fully understand. I can eyeball it quickly for anything that doesn't fit my mental model and dig deeper or quickly revise it. Only after I am happy with the bones do I consider the meat and skin of the code.
What I find most concerning is how frontier AI companies all seem to have this Math 1.0 perspective that they only want to type "solve Riemann" into the chat box and have the magic to happen. It is the same problem Google ran into, where a simple, no thinking solution serves most of the people best and most profitably, so you fully ignore or remove everything else (boolean operators, exact phrase search, verticals, filters, infinite pages of results, "nothing found" if there isn't, etc.) But that choice leads to the situation Google is in now, scrambling to stay relevant. In a different world, Google would have continuously augmented their search capabilities and eventually built a smooth, guidable AI interface.
But no, we must only have an input box and a Go button.
Everything looks like a nail when you build hammers, sell hammers, have infinite hammers to play with however you like and your company mission is to build a hammer starship to explore the hammerverse, whether or not that is even possible.
There is a world where we get to the edge of AI capabilities, and we build on top of that. As humans have always done with every new technology.
There is another more pessimistic view where LLMs just replace every human capability, and our economic overloads dont need us for anything and we just eat the small pieces of bread that are left.
This comes down to the fact of:
is human existence/intelligence just the simbolic representations we make in our brain? Or are they just a tool?
I tend to think of Godels incompleteness theorem as a proof that on the limit LLMs are useless. The real question for me is at what point approaching this limit becomes an issue, and if it has any practical co sequences.
Take a look at this interview from two days ago: https://m.youtube.com/watch?v=oQypVVv1u1o
The interviewee is worried about the future of math research. He is not strictly worried about being replaced, instead he is worried that he will no longer be able to launder math-as-a-hobby through math-as-something-useful as is the case today. He lays out very clearly that grant proposals claim to have useful outcomes while the proposers know those claims are nonsense.
Business as usual in math, and frankly in all the other sciences, is to do research that furthers the researchers careers or personal interests and pretend that it’s somehow useful. This would be absolutely fine if it were privately funded, but it’s not, this is public money.
In every other endeavour, lying in order to get money is considered fraud.
We have collectively wasted a huge amount of taxpayer money and human time, entire careers, on things not likely to ever matter to anyone.
I look forward to science becoming automated so that we can have real progress instead of the current broken system.
Do you really think a society with zero human mathematicians or scientists will outperform one with both human and AI ones?
So as measured by utility, I absolutely believe we don’t need humans doing science into the future. I’m sure people will continue doing it, but not for utility, for enjoyment - as a hobby. Probably we’ll all end up as dedicated hobbyists.
Sounds like Terence Tao would have said the same about Ramanujan who basically just "solved" problems without much explanation / reasoning / communication other than it just arrived from god.
In the case of Ramanujan, others took on the responsibility of socializing and community building knowing that he wouldn't do it himself. Why can't the same approach happen here?
There will be people who want to just "solve" math problems now that they have a new tool that lets them express themselves this way. Maybe the don't want to participate in the broader math community, etc. Why discourage them, or add friction / a barrier to them participating in their own way? Why not take on the burden of socializing, making sense of, and community building yourself?
There may be valid reasons here I'm missing, but to me this seems a bit like wanting others to approach a field in a particular way even though the field can support many ways.
It’s fine that OpenAI posted their findings. It’s not fair to claim these problems have been solved. Not until someone can understand and verify the proof and then communicate the core, novel methodological element to someone else.
If a random person is given a 60 page proof to digest and not the author, those hidden insights that _aren't_ in the paper might be completely inaccessible. Maybe the AI will "just" be able to provide the insights. Maybe. But pedagogy is tricky work, and despite these AIs being able to do all this fancy math we can't get them to write good cover letters yet, so....
Ultimately we might be left with just a bunch of intellectually unsatisfying proofs. This means way less drive to simplify the proofs or rework them.
End result: we generate a layer of "less efficient" mathematics, that won't get built upon. We will not actually have any shoulders upon which to stand.
And it's not like this is something where we're loaned some top math genius for a limited amount of time and we have to make the most of it. Rather, this is a new high water mark. The accessibility of the results is no longer scarce. The scarcity has shifted, and that's where the focus of the math ecosystem should shift as well. And it doesn't help for a frontier community to saturate and take over messaging pipelines that were typically managed by the math ecosystem. It's not about "stay in your lane" but rather "we need coherence and be careful not to break the system."
Just two cents from someone who could screw up basic cashier math on any given day.
In my view, over the last century, math has turned into an intellectual analogue of extreme bodybuilding competitions. A navel gazing runaway optimization in making useless stuff just to demonstrate cleverness. That's fine, why not. But society has no obligation to fund that, just as it doesn't fund other extreme hobbies. Ideally if we ever get something like UBI, math can be still their hobby.
People thought, back in the 17 century, that imaginary were useless (except as a trick for some calculations). Turns out the research into these numbers back then is amazingly useful today, 300 years later, in electronics and such.
Publicly funded maths research should continue, even if some taxpayers feel it's a waste of money.
However, with AI it actually may become so cheap that the scattergun random approach becomes more viable rather than less. It’s when human time and resources are scarce that you need to optimise. The hobbyist approach may therefore ironically continue, but without the hobbyists.
How much..?
adrianN•58m ago
youoy•40m ago
Everything else is secondary (or the last of our priorities) and would be better automated?
This is a hard pill to swallow
latentsea•9m ago
sankhao•39m ago
adrianN•34m ago
etdznots•19m ago