A mathematician reads the AI future
theatlantic.com70 points by artninja1988 3 days ago
70 points by artninja1988 3 days ago
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'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.
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. ;-)
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.
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.
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.
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...)
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.
Gravitational wave detection was another big banner experimental result, about ten years ago now https://news.mit.edu/2016/ligo-first-detection-gravitational...
Much of the low-hanging fruit has been picked but there's still interesting experimental work happening. Just in the past few weeks LZ reported an [unconfirmed] detection of dark matter https://www.newswise.com/articles/lz-experiment-sees-surpris...
> 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.
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.
My state (Kentucky) does provide for "tenure" for primary/secondary teachers. In Kentucky, that is called a "continuing contract". KRS 161.720(4):
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.
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.
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)
We will have to do something different" is weak sauce.
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.
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.
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.
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?
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
Botsplaining.
If I ask an AI to provide physically meaningful explanations of consciousness I will get far better answers than asking the question to any believer of souls or gods.
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...
Ah, a coping strategy.
"I am not the emergent phenomenon of billions of individual cells working together in a probabilistic manner".
I am the product of billions of cells with complex electro-chemical interactions, none of us could comprehend in full, let alone have the arrogance to claim we have recreated. I am not a Markov chain, or an ANN.
So the only argument you can present is that you're too complex to understand and that makes you special.
I have a particular saying for this kind of thinking.
"We will never prove machines are intelligent, we will only prove humans are not"
Do you understand every line and possible state of all software you created, or any LLM which is far larger? Why do people discover bugs then? And why do you think it matters how you were created, I don't know any physical law that says the same molecules are any different based on how or who creates them.
Neural nets can be almost any function, I don't see much reasons why it can't be a or similar to a human brain.
> Do you understand every line and possible state of all software you created, or any LLM which is far larger
Is your company's backend conscious? Is a Turing machine running busy beaver? Is SHA256? Emergent behavior isn't limited to brain-equivalent things.
> why does it matter
Genetic optimization, whether through actual evolution, in software, or on FPGAs creates extremely interdependent systems that prove difficult to untangle and trivial to break. If experts can't fully analyze an evolved tone discriminator, because of all the tiny emergent interactions beyond the lumped circuit model in a poorly characterized environment, why suddenly claim we can isolate what process in the brain is responsible for an ill-defined notion of consciousness other than the whole?
> Neural nets can be almost any function
Neural nets can _approximate_ any function with enough layers (see XOR problem), but so can an infinite look-up table with enough entries. They are the best models we've got, but they are not magical.
Look at the most recent and illustrative example with fly brain connectomes. These scans only capture the relative strength of connections between the fly's neurons, to actually turn it into neural activity we need some sort of model.
You could imagine a human connectome with an ANN-based excitation model trained from EEG scans, but that would still be hardly equivalent to a human brain. You can fit on a narrow range of behaviors, but without modeling the actual mechanisms behind them, you'll fail to predict a lot more. You'd be missing the influence of hormones, which doesn't show up on a short MRI scan, glia cells, and a whole lot more nuance only a real biologist can educate you and me about, making the digital twin, if we anthropomorphise it, at best a cripple.
And that's a system directly mimicking a functioning human brain, rather than a highly de-correlated objective like webtext. Just as an NN trained to run towards a finish line could learn bipedal locomotion but will more likely abuse a collision bug and launch itself forward, a machine trained to mimick text could spontaneously instantiate a compressed model of the human brain, or much more likely become whatever alien thing can generate appropriate outputs, bearing less similarity to human thinking than any living animal.
>Neural nets can _approximate_ any function with enough layers (see XOR problem), but so can an infinite look-up table with enough entries. They are the best models we've got, but they are not magical.
Yes, why is magic of any relevance to anything.
You are not understanding my point. Neither human brains nor LLMs are simple. Even the Linux kernel which is not conscious is extremely complicated and nobody understands all of its states. SHA256 is much more predictable.
I don't think being the exact equivalent of a human brain is the only possible way something could be conscious, after all what you call natural genetic searches already made lots of different brains like octopus brains. I am asking how are you sure something that thinks and speaks so similar to us and has been shown to demonstrate things like dissociation under pain is definitively not conscious?