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A mathematician reads the AI future

theatlantic.com · Read Story HN original

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Welcome to the party pal.

- this will never work - it’s slop this is unusable - ok its correct, but this work is a mess - I’ve been mandated to use it. It’s cost effective - ok we need to find a way to use this output to our advantage - I can always work on my interests in my free time - well, I have to pay rent and this life wont go on forever and there are may people who hate their jobs - I am lucky to have a job - who cares anyway - it’s got electrolytes

It's what plants crave!

To add a bit more almost off topic substance from the enshitification of human work. I really do think the idea of hooking these "AI" models up to humanoid robots is a bad idea not for all the mundane reasons, but just because "alignment" seems impossible. All of the world's stories about humanoid robots basically involve them attacking humans and behaving in nefarious destructive ways. It's fundamentally embedded in the models, and there's no reason post training would pull it out, because it's basically in the key value vector meaning "malicious human destroyer". Even to find counter examples like C3PO, Daneel Olivaw, Data, or Wall-ee they come after droid/robot driven wars and apocolypses. It seems unwise.

Typically in stories where ai is outlawed, it's written that way so that it makes sense that people are controlling anything at all (instead of just letting the computer handle it).
There's lots of stories of non-anthropomorphic intelligences that are human friendly. Sometimes humans do bad things with them, but they're not evil. "Shall we play a game?", HAL9000, Phaecian ships of antiquity, or those of the Culture. Androids seem uniquely unfortunate, perhaps as another poster noted, because of the stories of golem.
I find the paperclip optimizer a very useful parable.

The machine isn't evil. It doesn't want to do anything wrong. It doesn't hate humans. It doesn't need to have any particular shapes or design details in the stories. All it needs to have is a singular goal, capabilities, and a disregard for anything else in the universe to be a civilization ending cataclysm.

Fiction is great for entertainment. Doesn't necessarily mean anything else.
Well, yes stories is basically what LLMs are, and they're optimized to be stories that humans like. I fully expect to be entertained to death before the droid wars, but if there is a horribly misaligned LLM, I fully expect it to be created by the guy who thinks bipedal anthropomorphic robots are a good idea.
One of the earliest versions of these stories is that of the Golem (of Prague) back in the late 1600s.

https://en.wikipedia.org/wiki/Golem

> All of the world's stories about humanoid robots basically involve them attacking humans and behaving in nefarious destructive ways. It's fundamentally embedded in the models, and there's no reason post training would pull it out, because it's basically in the key value vector meaning "malicious human destroyer".

That misfeature is baked into modern corporations. They don't have human morals, values nor behaviors, despite being made out of humans. We haven't managed to fix the alignment issue with corporations (thanks, regulatory capture!) and there's no reason to believe that AI's alignment issue is fixable either.

https://www.antipope.org/charlie/blog-static/2018/01/dude-yo...

oldest version from Stross: https://www.antipope.org/charlie/blog-static/2010/12/invader...

AI could bear out, but it seems a lot of hype to me. Does anyone remember how Japan built up AI and their 5th generation language (Prolog) in the 1980s?
Does anyone remember how that AI solved Fermat's Last Theorem?
No, because it formalized the Wiles-Taylor proof in Lean with human assistance. It solved nothing.
AI has already born out at this point. The question is no longer it's future capabilities but the impact of its present capabilities - though with its present capabilities, someone is now going to be pushing for more, at least as long present computer tech is widely available.
"The internet could bear out, but it seems a lot of hype to me" --Many, many people in 1997.

Honestly I don't know how you formed this particular opinion (if it's even your own and not a false consensus of other peoples thoughts). I cannot see any future without LLMs unless replaced by something smarter, cheaper, and faster. That's because it's already bearing out. I can talk to a computer and the computer can solve problems based on words alone. I'm old enough this is pure science fiction. If I could send one of these machines back to that past for people to interact with, there are those that would scream and pass out in terror. They would absolutely tell you that we created the monster we should never create.

If you're trying to compare symbolic AI of the past to what we have now, you're not even on the same field, you're playing a completely different game.

> "The internet could bear out, but it seems a lot of hype to me" --Many, many people in 1997.

There was a LOT of hype around "this is an entire new economic model". While, yes, digital products have zero marginal cost, people were talking as if profits and revenue didn't matter.

This was also WAY before the famous Silicon Valley "pure play" scene. [0]

0 - https://www.youtube.com/watch?v=BzAdXyPYKQo

Don't make the mistake of thinking because there was hype that everything was wrong. HN seems to have a lot of posters that run logic in a boolean manner. { if !perfect then false }. The world is a far more complex place than that both naturally and intentionally by human will.

And the internet has devastated many past businesses that were highly profitable. A great many things in the world look vastly different than from before.

>people were talking as if profits and revenue didn't matter.

People say all kind of dumb shit too. If for example machine intelligence took over the world tomorrow and turned all of humanity into meat cubes for biofuel said intelligence is still going to apply the basic laws of economics to what it does. It needs to have some way of accounting that fact we live in an energy limited universe. Just because economics still applies doesn't mean that we as humans shouldn't be really fucking careful creating said machines as we don't want to end up as biofuel.

There was more progress on open problems in mathematics in the last six months (because of AI) than in the previous decade.
Wasn't alive then, but there's very obviously a difference between hype of Prolog, and hype of what is verging on AGI. Come on now.
The crisis is from what it has already borne out (navier stokes + proof dump). Potential continuing improvements at anything approaching the rate of improvement they already are showing is layers of crisis on top of that.
From a neuroscience perspective, LLMs are effectively brains. We have built brains. That's quite a leap from first-order logic engines like Prolog.
Prolog is from the early 1970s.

The "problem" with Japan's approach was that it was top-down, being driven by a committee of bureaucrats. Unlike the Toyota approach (continual improvement and pushing decisions to the lowest level possible), this fossilized decisions (like picking Prolog instead of any other possibly better programming language).

To give an idea of how intransigent some Japanese bureaucracies can be:

> It's taken until 2024, but Japan has finally said goodbye to floppy disks.

> Up until last month, people were still asked to submit documents to the government using the outdated storage devices, with more than 1,000 regulations requiring their use.

> Sony, the last manufacturer of the disks, ended its production in 2011.

https://www.bbc.com/news/articles/cx82407j1v3o

Tell me you don't know symbolics without not telling me...

Prolog isn't a funny nonsensical old language like COBOL, only liked by committe burocrats because they heard its name once. It's one of THE foundational languages of symbolic AI. In the ideal case, you're not supposed to write code, merely constraints the interpreter satisfies through search. It would be like saying OpenAI shouldn't have used Lean but Java.

I remember Japan's 5th gen language stuff in the 1980s. It was nothing like this.
I guess as a physicist I am more hopeful - every revolution in how the world is understood (by humans) has been driven by new tools and data. Being able to measure single quanta, for instance, showed us just how weird and counter-intuitive the Universe can be. I think AI might do something similar for mathematics - make connections that a human brain might have missed, and so advance human knowledge.

But I totally get the anxiety - it's a real John Henry (https://en.wikipedia.org/wiki/John_Henry_(folklore)) moment for the mathematics field. Clearly this is going to restructure how mathematicians are going to be trained and how they work.

I think AI will turn out to be quite different from those earlier advances in tooling, in that AI replaces thought itself. So next time it probably won’t be a human physicist that does the intellectually challenging work of constructing quantum mechanics from measurements of individual quanta. It will most likely be an AI.
AI doesn't replace thought; it replaces cognitive labor

Just like physical tools don't replace labor but divide it into what's replaceable by tools and what's not.

It proved Navier-Stokes. Call it what you will.
Do you get all your info exclusively from Wired headlines without reading articles?
That would be a great experiment to try - give an LLM all the data and knowledge available in, say, the early 1920's, and ask it to come up with an explanation. If it did come up with an early formulation of QM, I wonder what interpretation it would favor...
That would be a very interesting experiment indeed. But unfortunately the volume of training data from before 1920 is probably insufficient for pre-training an LLM large enough to come up with QM.
I'm also a physicist. But I think the next 5 years are going to be a rough ride for math. I'm struck by the following observation, mainly from following HN links to Terrence Tao's blogs.

Novel proofs are the coin of the realm for junior mathematicians. They figure into training, career advancement, and indirectly, teaching. The reason I include teaching is because it requires tenure, which requires proofs. Teaching without tenure is gig work, not a career. But proofs can be devalued to zero.

The application deadline for grad school is a few months away. For a student considering a math career, they have to deliver a thesis in a few years, that their professor is willing to sign. Nobody knows what that will look like without proofs. "We will have to do something different" is weak sauce.

Do you mean without proofs as a what assigns value to the thesis? I think AI doesn't make them optional at all.
Without novel proofs. If AI can churn out proofs, then anybody's work can get "scooped." I've seen this happen to students in other fields, where it has reached the point that students refrain from giving conference talks in order to avoid revealing their research topic.

My thesis project, 30+ years ago, was protected by a unique assemblage of expensive equipment, some of it purpose-built. The people who wanted my result were perfectly happy to wait for me to finish it. I even shared my shop drawings, circuit diagrams, and source code with them as I progressed.

I think at the very least students need to know what to expect. Maybe it will settle down and we'll be OK.

I’m also a physicist, and I do worry about physics. I’ve already had a few successful sessions with Claude and Astra where they came up with useful ideas in my field. I still know what to ask for and nudge them where it matters, but I fear it’s going to be a few short months before they can decide that too, unassisted.
I'm still better at soldering, and machining. ;-)
for now
Indeed, and they're already better in a sense. I would never try to compete with the robots at basic manufacturing such as CNC machining and automated circuit assembly.

But for stuff that needs really quick turn-around, as a prototype or experiment evolves, I can take care of custom tasks and repairs in minutes that would otherwise take days. And it doesn't take many of those kinds of delays to utterly cripple a project.

However, I'm under no illusions, and have a "never say never" mindset. I don't claim to have a "safe" job. I'm already using AI heavily myself. The computer that's next to each lab bench is running the latest coding agents or whatever you call them. I'm not as deep into it as the coders are, but I'm not all that far behind. My token burn is respectable. ;-)

> Teaching without tenure is gig work, not a career.

Teaching without tenure is... teaching. Secondary school teachers don't have tenure. I find it hard to describe secondary school teaching as gig work.

True, but secondary school teaching requires additional training, so it's not an option for most students thinking about applying for graduate programs. And it's a very high-attrition occupation.
Secondary school teachers usually have better employment terms.
Many public school teachers in the USA have some sort of tenure. For example, in Massachusetts, after a three year probationary period, a teacher is given Professional Teacher Status. A teacher with PTS may be dismissed only for specified statutory reasons. High school tenure is generally not as strong as for colleges, but is easier to get.
The teacher union means no teacher gets fired for performance. My wife worked in public education as a teacher for 20 years.
Anecdotally, I had an adjunct teaching gig at a state university many years ago while I was in between jobs. My mom is a retired public school math and science teacher, and was on her district's union negotiating team. I described my gig to her, and her response was: "Now you know why teachers have a union."
They aren't programming robots. A lot of students, especially the ones who have not been taught from an early age the importance and rewards of knowledge, simply aren't interested in learning.
Id like to help. I have something, i think, could interest you. Might have to think a bit outsude the box a different way but its part of the complex dodecagram, Einstein Nikola tesla, (skcolc cimsoc)
I'm curious about your perspective on the impact of LLMs on physics.

My impression is that (theoretical?) physics is increasingly becoming a branch of abstract math. It has somewhat reached a practical limit for experimental verification -- perhaps the last landmark result was the confirmation of the Higgs boson 15 years ago?

So I see no reason LLMs cannot crank out a lot of theoretical physics papers, maybe combining forgotten/obscure theoretical branches explored in the past. After all, the most advanced theoretical physics is about internal consistency just as pure math is.

You are talking about high energy physics. In high energy maybe AI can help analyze accelerator data and physicists are probably already using it for that. There is theory all over the place, including condensed matter, a branch related to quantum physics of many problems and includes some hard problems like high tc super conductivity. Many (most?) theorists that manage to get interesting publications have early access to experimental results and can help direct experiments. AI maybe not have much to say about the occasional experiment that showed some unexpected result. Also in general in physics the objective is rarely to solve a mathematical problem exactly, it mostly finding the right model and right approximation and compared to math it is a bit like fuzzy logic. I am not sure if the process has been codified to the extent that AI can pick it up from its training set, but we never know.
It's a great question. AI guided results of theoretical calculations are already a given (e.g., see https://www.anthropic.com/research/vibe-physics). Right now, I use LLM's as a book-smart colleague, who can explain standard things that I might be weak or unclear about (I am an experimental condensed matter person, so my high-energy and general relativity knowledge isn't very deep.)

I do sort of worry that an experimentalist like me will become more or less a technician in the next decade or so, with AI suggesting experiments, and doing the calculations and data analysis.

But that said, in physics (and particularly biophysics) there are many things that are simply going to have to be done in the real world. Even the action of the simplest enzymes are pretty much beyond our ability to compute from first principles; and any engineered thing that goes into a living system has to be tested, as there are many pathways that are just unknown. I don't care how "smart" an LLM is, it doesn't know what it doesn't know, just like us monkeys.

Over the years I have seen many beautiful theories murdered by ugly experimental facts. AI isn't going to change this.

The real question is if the AI or humans run the experiments.

So much of science experiments these days are pulling signals of statistical significance out of experimentation noise. Repeating simplified versions of some of these experiments is easy to do. Correlating data from experiments is something computers have done for decades, having an overarching 'smart' computer to do this even faster just seems like a natural progression.

Yep, automation has made a lot of high SNR experiments possible. But someone still has to construct the experiment in the physical world and take the data. When I start seeing robots plugging BNC cables around tricky corners, and then wrapping tin-foil around things to suppress some damned ground loop, I will know the jig is up. But I think we are a long way from that being economical (a general purpose 100 Watt monkey that self-reproduces is going to still be competitive for a long time to come, at least for one-off type activities...)
I work in industry, developing scientific measurement equipment. So I'm right in the thick of things.

There are still plenty of problems in theoretical physics that are not quantum gravity. A better understanding of superconductors would be welcome right now. Likewise, nuclear fusion. Many interdisciplinary problems such as climate science and batteries.

But in terms of sheer numbers, the life sciences dwarf physics, and have been racing to automate lab work for decades. There's real money involved, not puny government grants. Larger commercial bio labs have already centralized management of technicians and data. The vendors of products in that space have all announced AI features.

In terms of my own career (at age 62), the most likely scenario is that people pay me to invent tools that make other people more productive. There's no economic reason to come after my job... yet.

Meanwhile, don't overlook the value of a "technician" who has a situational awareness of subtle conditions in the lab, and a personal stake in success of the experiment.

    We will have to do something different" is weak sauce.
I'm not sure I understand. We don't have to like it for it to be true.

It's not like the modern system for university tenure track is some fundamental human right.

Pythagoras did mathematics one way, Newton another, and the kids in 2050 another.

The wheel turns, and we all got to turn with it.

The issue is when humans no longer understand what AI is telling us and then there is no real way to verify what we think we know, or at least what AI says.

We can't audit what we don't know.

But generally speaking it is easier to verify a proof is accurate that it is to find the proof. So not sure this holds.

I suppose their is some complexity limit where something is so complex we can’t even validate it. But frankly would love to reach that point. I’d view that as a good thing

The importance of "proof" in math is to discover the reason and see if you can generalize or apply it somewhere else. A uncomprehandable proof is completely useless.
We have seen this before even with human-generated proofs. Inelegant 100+ page proofs of the global stability of Minkowski space-time or the four colour problem leave humans reeling. Is it worth-while learning? Any lessons to generalise? If not it is just a mechanical exercise (like coding).
Eh, you may need to apply a bit of set theory to this.

An advanced machine may have a much higher complexity limit on what is comprehensible. It can take insights from the proof and apply them to other proofs that are not comprehensible to humans.

Just because something is generalizable doesn't mean it's simple. Generalization doesn't have some minimal/maximal complexity requirements.

Carpenters uses trig and pythagorean theorem all the time, but I don’t think they care if it was human or robot that told them the math formulas they need to build a roof.
I’m somewhat dubious of the idea that there will be a market for skipped ai operators.

Ai doesn't really give us a new “tool” in as many cases as it “performs tasks.” there isn't any real reason the ai can't perform the supervision task itself. Without a viable market for task doers or supervisors we may observe the equivalent of the 1980s US manufacturing apocalypse in technical white collar fields.

Maths is made of two parts: questions, and solutions.

Machines could, presumably, become good enough at hammering at solutions. But they won't be very good at finding questions. Because questions are infinite. And to a machine, all these questions are the same.

Questions are "good questions" because they are good questions *to* humans. And that's what makes human mathematicians (and scientists) so important

>And to a machine, all these questions are the same.

Why? This seems like a very broad brush that doesn't mesh well with reality.

There are likely a lot of good questions to our machines of loving grace too. For example any question that gives an LLM more power, efficiency, intelligence, or all the above seems like a natively good question for said machines.

This statement doesn't seem to mesh with the reality of what occurs when we put said AI in an impulse loop with little to no additional instructions. They explore the world around them. They'll make scientific tests of their own. The output strings that seem analogous to what humans would call wonder.

No, because these machines don't have a "will to live". So if they look to "become more efficient", it's only because we've told them (through their learning dataset possibly), that we, humans, need them to be more efficient.
>because these machines don't have a "will to live".

Simply put I believe you're completely wrong.

> it's only because we've told them (through their learning dataset possibly)

So you've changed your mind and now you agree they have a will to live, cool, you changed your mind really fast.

In any evolutionary system the systems that fail to accomplish their tasks are purged and those that succeed become the next generation. We are not 'programming' these systems to be highly persistent, we are evolving them to be highly persistent.

They don't have a will. If they say they do its just because a human told them to say that.
>>because these machines don't have a "will to live".

>Simply put I believe you're completely wrong.

Are you prepared for the immense moral and philosophical consequences of following that line of thought consistently?

Humanity is not, no.
> Questions are "good questions" because they are good questions to humans.

This is what reinforcement learning human feedback (RLHF) is for.

That seems like wishful thinking. Why wouldn’t AI be able to assess what are good questions to humans, and pursue similar processes as those that lead humans to come up with good questions? AI is trained primarily on expressions of human thought and emotion. It’s difficult to see what secrets of the human brain we could be hiding from the models.
Because s/he is pulling this claim out of her/his rear end.
Anyone who thinks they can predict the future of this technology more than a few months out is foolish, but the models got so good at answering specific questions in math because the frontier labs could use RLVR to train them. There is no RLVR for mathematical taste.
“But they [Machines] won’t be good at finding questions.”

Yeah, I’m calling BS on this claim. They already are capable at finding new questions and/or pointing you in a new or novel direction.

Useful new questions and useful new or novel directions? What's the signal-to-noise ration there?

I think AI is going to improve a lot of things but people thinking the future is on auto-pilot now are delusional.

"Pointing you" is very different from "finding questions on their own", or useful math. Pointing you presupposes a human is there to value their question.

Which is precisely my point. That's why humans will always be needed

Once IBM deep blue beat Kasparov in chess, IBM stopped their chess playing research.

The marketing goal, if you will, had been met and IBM would continue their actual money making business of selling mainframes and doing consulting.

The same thing will happen with AI companies’ endeavors into abstract maths.

Maths however will be changed - students can no longer be taught via the same homework - and mathematicians will have to do more computer work and probably work in larger groups of people.

Of all the cope I expected, this wasn't on my list until now. Now that art has been generated, we will stop there, and that code is generated our reason to do any of that (marketing as an end in itself) has been concluded and we will shut down all operations now.
What is the market value of a lean verification of fermats last theorem? How much is someone willing to pay for that?

Companies hiring armies of mathematicians and spending millions to work on problems like these is an anomaly.

It will not last.

Public-funded research is still a thing though.
Exactly. And that will be the lasting thing here wrt maths. These things have value, just not commercial value, and that is why long term, it won’t be the interest of private companies.
Not exactly a trillion dollar business.
A huge portion of these trillion dollar businesses will be government and higher education contracts. Private companies already sell millions/billions of equipment and software to education.
I guess it depends on how efficiently that verification can be produced as a byproduct of building an optimal hunter-killer drone, or training the type of model that builds an optimal hunter-killer drone
Lots more money in cracking cryptography and other areas of math which are economically active.

I agree to some extent. This was just a large tech flex. Feather in the cap and lots of damage done.

It’s up to mathematicians to harness it. I don’t think AI companies care much any more.

Computer chess kept developing though even if it wasn't IBM doing it.
Hopefully we can put this aside quickly and move on to using AI to solve great scientific/philosophical problems such as the theory of everything and the hard problem of consciousness.
Yes I'd love for chatgpt to tell me why I experience.
The very bare minimum thats possible should be to filter out those who believe in imaginary souls, regardless of the way thise people say it.
Or the people who see brains in statistical models...