Comment by rakel_rakel
13 hours ago
> I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense to work on any low-hanging, or even medium-hanging (you know what I mean) fruit. We'll be needed for problems where actual novel approaches are needed.
I wonder how this compares to what we see happening with "juniors" in software development? In math research, do you also get the training for the profession from working on the low hanging fruits for a while, to then move to the medium-hanging, and later go on to work on previously unsolved stuff?
Around here AI isn't really more of a threat to juniors than it is to seniors. It's a threat to the people who have been taught "recipies" rather than applied computer science. You can have excellent seniors who can do TDD, DRY, SOLID and so on, who also happen to have no idea what a L1 cache miss is. The current AI models know all of those things, but they struggle applying them correctly without someone piloting them. Even in the energy industry where I work, where you'd think it would be obvious from the context that you should prioritize runtime safety over debug safety, the current AI models struggle to do so. As far as seniority goes, though. If we can find a young developer with little experience who actually knows computer science, we're much more likely to hire them... Since they are cheaper.
This isn't something which is unique to software development though. We're currently building enterprise AI apps that we can deploy into the AI agents working for anyone of our employees. The key thing we're currently seeing is that the people in a team who are the ones that everyone turn to for advice, are the only people who aren't in "danger". Even people who are great at their jobs are being outperformed by AI in many cases.
I think it'll be a massive challenge for our society in the coming years. Maybe we're even going to get to the point where the AI will also be capable of replacing a lot of the "domain experts". Right now that seems far out, but then, if you had asked me about AI four months ago I would've told you it was all hype.
AI is a threat to everyone. People who claim that AI will never be able to do X have consistently been proven wrong.
The only people who are safe are those whose jobs depend in some way on their humanity. e.g. yoga teachers, bouncers, etc
Nobody knows.
It's not a zero sum game. You can have AI "senior engineers" working under humans building bigger things than we've been able to.
We also don't know where the capabilities of current AIs will plateau. The benchmarks aren't really telling the entire story. From my perspective of using the models there are certain axis where they're not making a lot of progress, like being able to have large accurate context on the scale that humans can. There are other dimensions where there is still a large gap between human capabilities and LLMs. It's true that relative to other areas (lessay chess) LLMs are more generalized but they are still not fully generalized (back to the chess example, LLMs are not good at chess).
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This was sort of what I wanted to say, but I guess I should have worded it differently. I certainly didn't mean to say that I thought AI would stop improving. If anything I'm surprised at how much we have to fight the AI models to do what NASA has been doing for 60(?) years.
Your first two sentences were correct. The last one is already being proven false.
It's a threat to everyone. UBI is the only way.
i'd take a yoga class from a bot
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Interesting, thanks. I don't know where "around here" is, but the signals I've seen in a lot of articles is that the demand for junior software people has taken a dive since a year or two back, with student programs etc getting cancelled. One googler said they were getting a junior to their team and that was kind of a big deal because it hadn't happened in that whole department for a long time.
In relation to that, I guess my question becomes: if the same thing will happen in math research, who will write the ten page math proof prompts in the future?
There is definitely the effect of less or de-growth in the industry, which started before the current AI hype. And now there's the additional effect of companies hoping AI will replace their need for (junior) devs. Nobody knows if or to what degree this will work out (yes, we all have opinions, but no crystal balls), but they are holding back the hiring until they know how all this pans out.
I'm from Denmark and I've been an external examiner for various CS educations for the previous 13 years now. Some of them teach you a lot about how the hardware works, others mainly teach you design patterns. Five years ago the latter was in high demand, because a lot of software development frankly doesn't need computer science (until it does). Now there is almost no demand for them.
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It's funny how you applied on your own argument several logical fallacies about why ai is only a threat to people who have been taught "recipies" versus who know what L1 cache miss is.
Actually it's sad there are people out there dumb enough to believe knowing L1 cache is any different than knowing recipies when it comes to the story which jobs AI will take. I'm convinced by now it will be the jobs of those people believing such crap.
So... The AIs with no model of the world are replacing software developers that have no model of the world?
Unless you’re claiming that AIs will suddenly (and very soon) stop improving, they are obviously a threat to everyone’s job.
Calling notable conjectures that have been open for decades “low-hanging fruit” is an act of desperation. Most professional mathematicians couldn’t have proved those conjectures if their lives depended on it.
I wouldn’t call it “low hanging fruit” but it’s easy to think of problems that seem harder. Apparently solving notable math conjectures is easier than building a practical robot to deliver a package to someone’s porch?
So, yes, AI is a big deal and we don’t know what it’s going to affect, but the goal of replacing everyone’s job is extremely ambitious and there’s a long way to go.
This has to be assessed separately for each kind of job.
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The thought that anything could improve without bounds would be absurd. We are living in the physical world after all. The (open, interesting) question is how close we are to the limit.
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> COUNTEREXAMPLE TO EULER'S CONJECTURE ON SUMS OF LIKE POWERS
> BY L. J. LANDER AND T. R. PARKIN
> A direct search on the CDC 6600 yielded:
> as the smallest instance in which four fifth powers sum to a fifth power. This is a counterexample to a conjecture by Euler that at least n nth powers are required to sum to an nth power, n>2.
https://www.ams.org/journals/bull/1966-72-06/S0002-9904-1966...
It is a conjecture whether grinding it out on Lean is a difference in kind, rather than degree. I say degree. But it remains to be seen.
>Unless you’re claiming that AIs will suddenly (and very soon) stop improving
Most technologies level off sharply after bouts of boundless improvements.
In 1968 they thought we'd be flying to the moon by now but instead we're flying across the ocean in planes not that different from the 747 that existed back then.
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I was trained as a mathematician and worked as a math researcher for a little while (now working as a private tutor), and based on my experience I'd say this description is basically right, with one extra wrinkle.
In order to get a Ph.D., you have to do some sort of original research, so in that sense you're working on "previously unsolved stuff" basically right from the start. But that doesn't entail doing anything all that ground-breaking; most Ph.D. dissertations (very much including mine!) contain work that a more senior researcher in the same subfield could probably have produced without too much difficulty. The software development analogy is a pretty good one: a lot of the point of getting junior researchers to do research is to help train them to one day become senior researchers, and often the work itself is nothing all that special.
Given the trajectory of these LLM proofs, this seems like it's going to have to change pretty soon, and to be honest I'm pretty grateful that I'm not in charge of deciding what that's going to look like, because I don't have any good ideas! I'm actually pretty worried about the future of the field.
Indeed. Perhaps my article here will be of interest to some: https://blog.oberbrunner.com/blog/ai-math-as-humanities/
My experience may not be entirely representative because to be entirely honest I’m not exactly a great researcher and there are brilliant PhD students. That said it indeed was my experience that in the pre-PhD / early PhD period ( or even longer … ) your advisor proposes (gives) you pretty low hanging stuff that he mostly already knows how to solve, at least at a high level, with the expectation that it will teach you to use the mathematical tools you need.
This apparently required a 10-page prompt. It seems like someone needs to know enough to write it?
The author also used GPT-5.6 to write the prompt. This did involve giving GPT-5.6 access to his previous work and a back and forth process (so definitely still used the author's expertise to some degree), but the prompt itself is also largely AI generated.
What's the difference between using GPT to write the prompt to GPT, and "thinking"? The LLM uses the first tokens to predict more tokens, and then uses those tokens to predict even more tokens.
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Certainly. This feels similar, to me, to how building complex software with LLMs works today in practice. You need to know a lot to set up goals and guardrails and verify outputs. For me, making the bits change was always the fun part, not tangling with text in my editor, though that had its moments.
Yeah, back to the gold-in-gold out use of LLMs.
I was thinking this past week I have gotten so lazy w my prompting via CLIs.
Back in the before I had put such discipline into my prompting and supporting context.
Now I’m like, “look here and here and here are some tools, and /skill /skill okay go.”
Or “restate this request in your own words and enrich it as appropriate handling any gaps. Okay go”
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Math is way more automatable than programming.
In math, a proof is a proof. We don't know if we can get there and so getting there is the hard part.
In software, we always know that we can solve the problem. So HOW to solve the problem is the hard part. Because the type of solution involves maintainability, which involves planning, LLMs suck at it. This leads to "LLM slop code" whereby the LLM creates ad-hoc convoluted logic with redundancies and no reuse of existing standard library batteries.
Unless you're a Grothendieck who gets mad at Deligne for not solving the Weil's conjecture "THE RIGHT WAY", software is fundamentally different than math in this respect.
So I'll say it again, AI will win a fields medal for before managing a McDonald's simply because there are enough big problems within arms reach than their current capacity to plan over time
I've spent some time working both as a math researcher and as a software engineer, and I think this comment actually underrates the similarity between the two fields as they're actually practiced.
Some math research does involve grabbing a single, fully specified conjecture off the shelf and hunting for a proof of it, and it's true that if you manage to solve a long-standing open problem, other mathematicians will be interested no matter how you did it.
But this isn't all of what they do, probably not even most of what they do. Like in software engineering, it's not always obvious which question would be the most useful one to ask. A lot of mathematical work also goes into what we call "theory-building", where you could say that primary work goes into coming up with definitions rather than theorems. Mathematicians also care a great deal about how something is proved; a lot of them are some of the most aesthetically picky people I've ever met. Words like "ugly", "beautiful", "creative", and "boring" are used to describe both definitions and proofs all the time.
From the outside, it can look like all they're doing is pumping out proofs at any cost. But I promise you that when I talk to mathematicians who don't have any experience building software, they have a similarly narrow view of that field as well! Both fields, from the inside, look a lot more human than you might expect.
I think that your take is quite optimistic. Having published in top tier journals my only experience is that mathematicians care about what other mathematicians worked on and failed to solve. Theory building papers are dime a dozen and don't get published in high tier journals unless they solve a problem.
Math is such that most theories are built after solving a problem and actually don't solve a larger class of problems. Etale Cohomology is an example of a rare exception. Grothendieck was mad that Deligne used adhoc complex analysis techniques to prove Weil. But everyone else was thrilled.
Whereas in CS, a good theory (library) solves a large class of problems. The reason being is that CS tackles general problems while math specific ones. Math on average solves problems that don't lead to solutions to other problems.
To me at least, math is more of a game like chess and coding is more of an art. There are aspects which are a game, like performance engineering but I'm pretty sure that LLMs will become superhuman at that soon
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It seems to me you hooked onto the wrong part of proofs vs software compared to what OP meant. The difference OP cares about isn’t how much one cares about style. Instead the important difference lies in validation. A proof can be validated as either correct or wrong. That type of hard feedback really helps combat the optimism and desire for shortcuts of modern models.
Now, that still doesn’t help an LLM distinguish between good and bad correct proofs. But it still really helps a lot. On top of that, taste in proofs is a lot more uniform than taste in coding. That helps LLMs be better at judging the quality of a proof, because there’s less disagreement in the wider world.
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The types who do ugly proofs, when they write code, produce spaghetti code. It's the same thought process going into how to approach something.
I think the difference is in math the problem is fully specified and easily verifiable and in programming it's not. I don't agree that we always know we can solve the problem.
Not always, sure but 90% of the time yes.
For example, create a DFA for a regex, not too bad just use Thompson's algorithm and then NFA->DFA. But now we have to care about efficiency, user API, maintainability of definitions etc.
Coding is more of a human problem than math
> So I'll say it again, AI will win a fields medal for before managing a McDonald's simply because there are enough big problems within arms reach than their current capacity to plan over time
AI can manage a McDonald’s already. If manage means directing humans to do something to ensure the store is running. If manage means running robots, then yes maybe that is 5 years away but just directing humans to run a store, that is possible right now.
No it can't. Show me a business which uses in context learning to manage a McDonald's
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Have you not seen vend bench?