> Before approving construction, I would want communities of humans to understand why the design works and what justifies confidence in its safety. I would hope that we all would.
Until very recently, I pored over every single line of code Claude generated with razor sharp scrutiny. I would usually catch issues with every response. I'm catching fewer problems these days. Maybe the model is just getting better, and maybe I'm being less careful while under pressure to ship more and more often. But model capability is obviously growing. Even back in March, you could tell it "give me a function that adds two numbers" and you could be 100% confident that it would write the correct function. There was almost no point in looking at the code. Since then, the complexity floor of problems in the category "this is so simple that the model couldn't possibly get it wrong" is rising, and with it, my cognitive surrender to the model is increasing too. Why check it? It's obviously going to be correct.
If AI designs a terawatt fusion plant, then of course we're going to meticulously pore over every detail to ensure safety, reliability, efficiency, whatever. If we find no flaws in the design whatsoever, will we be less careful about the second one? The third one? What about the ten thousandth one? Will "a nuclear fusion plant" become something that models couldn't possibly get wrong?
Terence Tao is arguing that the human involvement in research is crucial, but doesn't convincingly justify why, in my opinion. He says that "human agency is a value of fundamental importance" and that we will need to build "thriving human communities that can understand [AI ideas] together" - not for the sake of correctness, which AI may surpass us on, but for, I guess, the possibility of reclaiming human meaning and purpose. I don't disagree with this at all, but it's not an argument, it's a statement of values. Unfortunately, the stark reality is that if AI does surpass humans, it will become the economically dominant strategy to not verify them and not double check them, but to just do whatever they say. This seems like a great way to raise p(doom). But as the models get better and better, and as I'm scrutinizing Claude's output less and less... I just hope that there are more Terence Taos out there than people like me.
There is a failure to understand that the process is the result. You don't study mathematics or computer science and information theory to produce commodities. You study them to transform your mind. The output of an LLM is useless without a human mind to comprehend it. We can have Super Intelligence, but if humans are incapable of comprehending it, it is just another useless dead artifact. Practice, applied over a lifetime, is what creates the capability for comprehension. Asking an LLM to give you an answer creates an artifact. Humans being humans, most of their requests boil down to "make me rich without having to work for it," so the request itself is paradoxical and impossible to satisfy. Philosophers have only been saying this for all of human history, so don't hold your breath for any breakthroughs.
Precisely. I don’t really care whether LLM’s can produce code more and better than me. I learn languages, program and study computation to understand better the world we live in. Being a human being means increasingly being technologically augmented. To have any deep understanding of that world requires deep understanding of maths, physics, programming etc. that you can only gather by doing those things and solving problems with your meat brain.
There’s a Twitch-streamer Tsoding who programs on C for fun calling it “recreational coding”. Maybe human programming will be a form of art in the future, virtually useless for big corporations to make money. I don’t care, I love it anyway.
> To have any deep understanding of that world requires deep understanding of maths, physics, programming etc. that you can only gather by doing those things and solving problems with your meat brain.
There is tons of evidence against that. Someone armed with just LLM, can have much better uderstanding of problem then "meat brain expert" who studied the subject for decades.
We seen in last decades how "experts" are clueless, and how they predictions work.
> don’t really care whether LLM’s can produce code more and better than me
So on one side there is monopoly on "deep understanding", but on other no one really cares about quality?
You are both reading too hastily to quite grasp what I am claiming as well as making claims and assumptions you do not back with evidence. If there is tons of evidence how a person with LLM can understand - I was speaking of the world and times we live in, not just single problem - a problem an expert does, it is quite trivial for you to present that evidence.
Mind you,solving a problem is not same as understanding it. Anyone can just take a science calculator and bunch in some function without understanding anything about how to solve it.
Great but you will no longer be paid to do what you love.
History teaches us that understanding deep problems in mathematics finds natural applications elsewhere. So, either AI completely solves mathematics (unlikely for the moment), or we use marginal amount of funding to keep the mathematical communities alive.
I have never been paid to do what I love. Well, I got couple of art grants some years ago.
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> The output of an LLM is useless without a human mind to comprehend it.
I don’t understand mRNA vaccines, but they are useful to me. The output of an LLM could at least in theory be the design to a major technological advancement, and its implementation with automatic tooling. We don’t have to understand that for it to be useful.
An LLM could also in theory fake alignment and create technology that seems really useful but secretly harms humanity in the long run. If humans don't understand what it does, that possibility becomes more likely.
mRNA vaccines were created by humans who understood them. You exist within a society (a networked distributed information system) where you accept the judgement of the humans who understand and create this things, which is how you end up benefiting without personally understanding.
If we imagine Super Intelligence, where NO human is capable of understanding, then how would it ever be possible for any human to identify what is actually beneficial or not?
This resolves in a paradox, common to all magical thinking. You can certainly wish that some all powerful benevolent entity will solve all of your problems for you, but it is not likely to work out well.
None of this is new. It is the same delusions as alchemy and the same thing that tales about genies warn of.
> mRNA vaccines were created by humans who understood them
If authors understood them, why most of their predictions were wrong? Time to decompose spike proteins, side effects, distribution through brrast milk....
Event the most basic promise 100% protection against infection was wrong! They lied and we allowed infected people into hospitals!
> You don't study mathematics or computer science and information theory to produce commodities. You study them to transform your mind.
Normatively, this ought to be true. Descriptively, this is of course false. Our entire society is organized around producing commodities, typically by consuming people as inputs.
It’s not ‘of course false’, and, to be honest, I can only assume you have little idea what mathematicians actually do.
Most pure mathematicians are no more interested in ‘producing commodities’ than any other academic is. That’s not what the subject is about — at all. The confusion arises because mathematics turns out to be extremely useful (no surprise; it’s quite useful to have a detailed understanding of the basic principles of reality).
Again, this seems to be an alarmingly common fallacy here on HN. As a commenter above observed, pure mathematics (and that is what we’re talking about here) is in important ways closer to the humanities than it is to other sciences.
Not exactly. The input to produce commodities is labour-power (the potential to perform labour). Education or study is the process of producing the commodity of labour-power, the potential labour of a mathematician who can do some sort of specific work.
>The output of an LLM is useless without a human mind to comprehend it
This is like saying software is useless if the user doesn't read the source code of it. This what happens >99.99999% a person uses software. People want to be entertained or have their problems solved.
Your analogy doesn't work. A "product" in research pure math is not the same as writing code.
> You don't study mathematics or computer science and information theory to produce commodities. You study them to transform your mind.
That's nonsense. Of course you study them to meet demand.
People who study STEM for the enrichment of their intellect are privileged. Most of us had to study STEM (or whatever else) because we had bills to pay.
> you study them to meet demand
nobody who has ever achieved notoriety in any intellectual field ever did it to "meet demand." if your goal is to be an interchangeable widget that produces value as part of a corporate machine that exists for the enrichment of your shareholders, you are certainly free to choose that path, but don't imagine that is the limit of human existence. also, don't be surprise when you are replaced by AI, because it is a superior widget.
The desire for novelty and to be first is demand. The publishing and grant writing. The whole funding and tenure apparatus. It's nothing but demand gradients.
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> The ideas and opinions presented here are entirely my own, but GPT 6 Astra was instrumental in helping me draft this note.
It really looks like Tao is on the path of accepting and embracing AI now.
> But we are now entering a time for humility: a time when all of us are going to know what it feels like to be unable to keep up.
Humility is the wrong word. We didn't feel it when the steam engine was introduced, so why now?
"We’re gonna need a lot more mathematicians."
What the article really says is that we're going to need much smarter mathematicians. That is not possible for puny meat-brain humans. Humans are close to their ceiling. AIs are just getting started.
In practice, we're probably going to hit that limit first in IC design. I once went to a talk by the Intel engineering manager who headed the Pentium Pro effort. That was the first superscalar x86 CPU, and it took about 5,000 engineers at peak to design it. Getting that many people coordinated on one thing was a real achievement. Then Intel stayed with minor tweaks on that design for years.
We're soon going to be seeing designs of even greater complexity cranked out by AIs. No human will understand them at the gate level. Reading AI-written programming language code is bad enough. Reading AI-written Verilog may be beyond human comprehension, except in small sections.
> Humans are close to their ceiling.
If Math Academy teach 10 year old kids calculus, I doubt that.
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Like most of us I go back and forth between sheer optimism and fear for the future that AI may usher in. Recently I started vibe coding a fun video game with my ten year old. The experience is different than my work because it’s been such a joy to basically have a personal genie in a bottle help me make some personal art with a loved one regardless of either of our skill sets. The concept the author of this post is arguing now resonates with me more than it would have a few weeks ago. The sheer surface area that AI can create in our intellectual life is limitless and needs humans to explore. There can never be enough of us in that sense. Whether it’s as validators or creators.
Certainly humans can enjoy exploring such things, but will they really be needed?
What does needed even mean? To produce shareholder value? Maybe not. To explore thoughts and ideas humans have for fun? Certainly
To make money in order to eat food and have a home.
How do you think this will work? Do you think the whole of the rest of the world, about 7 billion people, will agree to give up on wanting to reach the western life standard that is currently consuming 4 Earth's of resources every year?
Will all rich people in all countries collectively agree to be moved into tiny apts same size and give up their luxuries?
If not, how do you define who gets what? Who gets to live in the fancy house, etc?
I don't think "abundance" is a stable state. There are always ways to use more resources and more energy, so no matter how much we have, it will never be "enough" -- abundance is just a transition state where a population or system has not yet figured out how to grind the surplus. The faster the progress, the shorter I would expect these periods to be.
Right now that looks like a bunch of rich edgelords and us as serfs
> If AI leads to an era of abundance, then the economic system has to change.
This is beyond naive.
You're right that we could already feed everyone with a different distribution of produced wealth. That part is not something that AI will change (although it would raise the resulting standard of living).
What it does change is the basic equation underlying capitalism as an economic system: a few people concentrate capital in their hands, but capital by itself is useless without labor, so they have to hire workers to produce something useful with all that capital that they own. The workers get a shit sandwich, comparatively speaking (given the amount of wealth they generate), but they do get something out of it. The system is stable overall because, while a better arrangement is possible, most people - even low-wage workers - have too much to lose to riot.
With AI that can do most work, the capital no longer needs labor. People who own all the robots can just have them produce whatever they need. Everybody else is then "economically redundant", and the whole system collapses because people aren't going to sit around and starve because there are no longer jobs to be had - and at this point they have nothing left to lose and everything to gain by rebelling and taking over the capital.
If this is true, you would think that companies would be opening shops in the middle of (some shithole country) so they can make money (or someone else would grab it). But they don’t, why is that?
Money will become unnecessary. The future Anthro Park will no doubt provide a safe enclosure, feeding at regular intervals, and an enriching environment for you and your fellow semi-evolved simians.
The current approach to resource distribution worked so far. When it stops working because we have too much abundance, we'll settle on another one.
That doesn't mean the transition will be smooth. It doesn't mean that certain classes won't be worse off. I can certainly imagine programmers being among the losers. And there certainly are futures where we slide in dystopia. So let's try building the good futures. Alea iacta est.
> The sheer surface area that AI can create in our intellectual life is limitless
I agree with this statement, though I think this Brave New World is incredibly exciting to some and dystopian to others. The former group might include those that value the intellectual process above financial reward and status.
The flip side is there are many people, especially in tech, where their area of expertise has evaporated along with their lucrative and previously high status careers. It used to be possible to have a technical job by essentially following recipes and it turns out AI is far better at that than a human.
The linked article lays out why human understanding of mathematical models remains essential and I think the same applies to software. We're gonna need more software engineers who are able to think critically.
> To take on this responsibility, we may need to broaden our view of what a mathematician can contribute. I have in mind something like a “deployable intellectual reserve”: communities of mathematically sophisticated people that humanity can call upon to help understand consequential AI-enabled breakthroughs.
> Our ability to understand difficult and unfamiliar ideas may become one of the most important contributions we can offer to society. We should be willing to bring that skill to problems far beyond our usual research interests. [3] Doing so asks us to expand our sense of our vocation.
Am I reading this wrong, or is he talking about what (mathematitian) Data Scientists have been doing for years? So he is basically saying that former Data Scientist that have turned into prompt/software engineers should go back to being data scientists.
In any case, people should stop trying to fit AI in the previous status quo. What we need is curious people, that is what we have always needed.
A few centuries ago there were no "mathematitians", there were mathematitians/philosophers/artists/physicists all in one person. So its not like "mathematitias" is something that has existed for millenia.
We need curious and ethical people.
Maybe AI brings back the age of a well rounded scientist/philosopher. I know this sounds counter intuitive because the article is saying that we cannot keep up with the AI.
> "If AI fulfills its promise, we will encounter more beautiful and consequential ideas than we have ever seen."
It will be as it always has been: these ideas will further enrich the rich, at the expense of everyone else. We'll have our first quadrillionaire, while the masses are debating whether the minimum wage of $7.25/hr should be bumped up.
What a doomer way of thinking. Scientific advancements has positively improved the lifes of people in the past I don't see how scientific advancements accelerated by AI would be any different.
One question: LLM might answer correctly many logical and math problems, but I don't see any guarantee that when the LLM context receives new information the answer could get worst. Security in LLM answer is not a monotone increasing function of context size.
> I have in mind something like a “deployable intellectual reserve”: communities of mathematically sophisticated people that humanity can call upon to help understand consequential AI-enabled breakthroughs.
Can’t afford to be one of your credentialed reserves, Amit. ADHD screwed me over in early life or I’d have breezed through that dual masters in cognets/compsci, and now my country’s socioeconomically ruined — I’ll be lucky to get my accounting degree with my school visibly being sucked into AI vortex every year I progress. The only hope left for me to be what you need of us is to self-study, but without a degree I’ll just be treated as a crank or an AI proxy/puppet if I slip up and talk about interesting math with anyone, so what’s even the point of taking that path? I pivoted the skills into systems theory and process diagnostics instead, which of course now everyone has kicked to the curb and replaced with AI. I’d have made an excellent Susan Calvin, but the financial investment to provide the runway to take that 6 year slow as molasses slog through maths that universities think is somehow an appropriate teaching velocity — 6 months for precalculus alone?! — in order to earn the chance to have my resume rejected by AI is a bad bet. Taking that burden in the hopes of employment at the other end in a field actively having its social fabric and reputation processes being ripped apart by AI? That’s not just poor odds, that’s chasing fool’s gold at the end of a fading rainbow. You’d benefit from having me on your ‘reserves’ list — I have written testimonials spanning thirty years to that effect — but I’ll never come to your attention as a mere CPA.
If we accept that AI is going to do all of these things humans will be superfluous and will just be optimized away. It looks a lot like we see the birth of silicon based life by the efforts of carbon based life. Carbon based life will die and it will not even be because AI decided to kill it, it will be because feeding and watering it was less important than other concerns. Bacteria may continue to exist, though.
The main reason to learn something is actually being able to communicate in the language of that subject. There are complex ideas in math that cannot be easily captured by the language of other fields. Pepole who don't study math cannot even understand what a worthwhile goal in math even is or how it could be useful to other fields.
You can't simply prompt a model to be "better" when "better" isnt even properly defined
Russell once remarked that all of mathematics would be trivial to a sufficiently intelligent being. It builds conceptual tools for limited minds, that lets them understand far beyond their natural reach.
In a world with ASI, having that capacity is vital.
Ha, are you invoking something he said prior to discovering Russell's paradox? Which came about because he wanted to show that all of mathematics can be derived from logic about sets, but instead he showed that it couldn't be.
As someone with a math background, I don't see Russell's paradox as some interesting mathematics beyond set theory. It's just an example showing that one should be careful about defining sets.
If we assume that trusting a model to execute an action is an ongoing exercise, since its trustworthiness is often discovered by the user organically as models develop, should trustworthiness be measured at the level of the model, or at the level of the human intent behind triggering it, whether explicitly or implicitly?
you arent a real mathematician unless you lay around all day thinking about shapes
I think understanding the output of AI will become more and more likely impossible. It's not necessarily a bad thing, if we can benefit from AI produced knowledge, even if we didn't get there ourselves.
The point of the post is that what you call "AI knowledge" is not knowledge.
> This is a guest post by Amit Sahai
Not Terrence Tao post. Beware.
> Imagine that a future AI system proposes a radically new design for a one terawatt nuclear fusion power plant
This is an unfortunate example to choose, being as it is entirely confounded by the canonical illustration of the https://en.wikipedia.org/wiki/Law_of_triviality.
How is that relevant at all?
How is it not relevant? The construction directly contradicts what Sahai imagines happening, and the worked example is the nuclear power plant.
Life is all about tradeoffs. Mathematics have no tradeoffs. We need more engineers.
Life is all about purpose. Mathematicians are instead concerned with meaning. We need more philosophers.
It would be nice to have more mathematicians, but we don't need more. Once AI math goes so far beyond human abilities, any human involvement is like an ant trying to understand quantum physics
We've been those ants for a million years, and only in the last 100 did we start to wrap our heads around quantum physics. We are the purpose behind creating LLMs. There's plenty in the universe we don't understand, and it's very human to keep striving to do so.
If you believe that math is discovering, it's natural to think that all of that AI math already exists and is just waiting for us to find ways to discover and understand it.
Don't write us out quite yet. :)
I think a better analogy would be comparing to an ancient human instead of an ant. An ancient human would have none of the basic abstractions that we take for granted today like literacy and arithmetic, so it would be very difficult for them to even attempt trying to understand quantum mechanics. But I don't think it's impossible because our ability to learn by stacking abstractions is basically endless——so far as our health permits at least.
Even if that happens, what’s the point if there’s no human involvement? AI doing math for math’s sake? And doing what with it?
I think it is like saying what is the point of playing chess when you can never beat stockfish?
What is Magnus Carlsen going to do when he can't beat the computer?
It seems like a category error between humans using tools and humans building tools.
There is not much point in trying to figure out a better chess engine. There has never been a better time though to want to learn chess.
I find the idea that the computer will discover mathematics and humans call it a day rather ridiculous. As if humans will not then spend their time understanding and incorporating the ideas from the computer.
Alphafold is a better example. Alphafold is only bad if you spent your life trying to solve protein folding. But even if you did, that is the same person who is the most setup to reap the benefits of the unlock in the pragmatic application of protein folding.
We don't figure out how to get machines to harvest corn and then spend all day sitting around eating corn in between naps.
> AI doing math for math’s sake? And doing what with it?
Stuff! Inscrutable stuff, maybe, but that's not "doing math for math's sake."
> AI doing math for math's sake?
Yes, why not? And, of course, AI doing math for AI.
We may not be needed forever...
I don't understand how to make a modern CPU. I'm not involved in the manufacturing of it. From my perspective, there may as well not be any human involvement. I can still use the resulting chip (in an larger system of other things I can't make and wasn't involved in) to argue with you on the internet.
It becomes another abstraction, really. As long as we can use it for something useful, it's still valuable.
At some level of abstraction it's all built around allowing you to do some work/play/etc that you understand. Some of that work allows you to make money and eat food.
If the LLM is operating at such a high level that it never actually constructs a useful product for humans to use, then how will that be good for humanity?
> If the LLM is operating at such a high level that it never actually constructs a useful product for humans to use, then how will that be good for humanity?
If you replace "LLM" with "mathematician" than this is the state of the world today. Stuff like Galois theory is beautiful mathematically, but what has it constructed or enabled for you and me?
There is a difference between manufacturing and design. Yes manufacturing is largely done by machines because of the nature involved but to look at a cpu and think 'no human was involved in creating this', you're wrong and also insulting to the humans who actually worked on things that led to the cpu and the manufacturing process.
A cpu (the physical thing that sits in your mother) is not an abstraction, what are you talking about
Or maybe ants and humans are qualitatively different. Maybe there's a critical mass of intelligence where you can pretty much understand anything, and maybe humans are past that threshold. I don't know that for sure, but I don't think we're anywhere close to hitting fundamental limits to our ability to understand the universe.
Need? We don't need lots of things, including computers. We did well without them for hundreds of thousands of years.
We want to understand. Quantum physics, mathematics, how stuff works. Ants don't.
That want is not a given, not all of us have that drive. In fact, very few of us have it. So far though, it seems multiple disconnected civilizations learned to keep that trait going instead of suppressing it and focusing only on practical ant-like activities.
> Once AI math goes so far beyond human abilities, any human involvement is like an ant trying to understand quantum physics
This makes no sense whatsoever.
We need more, because there will always be far more difficult problems yet to be discovered and solved, and that means, we certainly need expert humans to define and verify them.
If you cannot even explain the problem you are facing, not only you don't understand it, but you certainly would not be able to know if the AI solved your problem correctly.
>and that means we need expert humans to define and verify them.
And this will be true for how long? 3-4 months?
As long as there are problems to discover and solve, which is forever.
The risk of liability is a social problem that is far more difficult to be solved with technical solutions even with AI.
I think this is the most beautiful letter on the subject I've read all year, it brought a tear to my eye. It's like reading those famous STEM letters/essays from history.
I agree. I believe it could be the best piece about AI ever written. The themes of lost dreams reawakened, sobering up of egos, sci fi technological development, the role of humanity. It’s a weird feeling to see that it’s actually really happening.
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"I have in mind something like a “deployable intellectual reserve”: communities of mathematically sophisticated people that humanity can call upon to help understand consequential AI-enabled breakthroughs. " -- I can't be the only one who thought about the scene where the scientists ask Deep Thought the ultimate question...
Very few people scrutinise assembly in 2026 as compiler generated code is 'good enough'. LLMs are beginning to do the same with higher level languages.
Without bashing anyone in particular, a certain OS-vendor's desktop apps, have been 'good enough' to ship, but with p*ss-poor performance in many cases for the last decade or so. We crossed the 'good enough' Rubicon a few years back in terms of what end users receive as a finished app.
Hopefully LLMs will eventually bridge that last gap of efficiency when generating higher-level code that not only works, but is efficient. Maybe there's a future where they generate the final binary without even invoking a compiler.
It has to be said a million times. A fully deterministc compiler (or 99.99% or whatever) is categorically different from an LLM.
Hopefully this million plus one mention shifts the right weights around the datacenters.
> If AI designs a terawatt fusion plant, then of course we're going to meticulously pore over every detail
But suppose some future holy grail AI can do much more than that.
Suppose it could find a cure for cancer, fix the climate, build fusion plants, Dyson spheres and so on.
But nobody can understand anymore how any of it works. We just ask and then trust the AI to deliver (as it always has).
Isn't it fun to imagine how life would look like in that scenario?
We would probably no longer care about code, engineering or even physics and mathematics among other things. We would probably mainly care about
This is how most people already live.
The average person doesn't know how the medication they take works, the mechanics of climate and climate change, how the energy they consume is generated, etc.
We would care about having fun.
For some people, fun is doing physics and mathematics. So they are going to keep doing that.
I think the weirdest part of that scenario is that science might become something closer to archaeology
You can't just leave us hanging like that!
Successfully neutralized by AI, I suppose.
Published in 1909:
https://www.gutenberg.org/cache/epub/72890/pg72890-images.ht...
https://en.wikipedia.org/wiki/The_Machine_Stops
STEM will be considered "historical studies" in an AI-ruled future.
no
> I guess, the possibility of reclaiming human meaning and purpose.
As you described very well, as humans we are mostly interested in solutions, not problems. You don't have to understand how a car works to make the most of it. Increasingly, you don't have to review every line of code to feel confident it is correct. But there is inherent value in understanding the problem. The effort it takes provides a surface area for growth, perhaps the only one that is actually available to us.
The solution provider also holds the locus of control, and it is only balanced when there are other available solution providers. We certainly want some of those to be human.
In my experience, LLMs are becoming very good at executing, but not a creating novel ideas or being creative.
Most of programming is reusing existing ideas in new shapes to solve new problems, but all the building blocks are there in the training set. Or new blocks can (easily) be derived from existing ones.
Math is different, it requires quite a bit of creativity, it's not just 'reuse all existing blocks'.
For the moment LLMs are good at discovering things that we overlooked in maths, or apply cleverly existing math blocks to make new results, but making a new theory that is really useful is out of reach for the moment in my opinion.
>Terence Tao is arguing that the human involvement in research is crucial, but doesn't convincingly justify why, in my opinion. He says that "human agency is a value of fundamental importance" and that we will need to build "thriving human communities that can understand [AI ideas] together" - not for the sake of correctness, which AI may surpass us on, but for, I guess, the possibility of reclaiming human meaning and purpose. I don't disagree with this at all, but it's not an argument, it's a statement of values. Unfortunately, the stark reality is that if AI does surpass humans, it will become the economically dominant strategy to not verify them and not double check them, but to just do whatever they say.
I think you have a fundamental misunderstanding here, and it's not really explained because I think it seems self-evident from within the field. In short: writing code is a means to an end; doing mathematics research is not, but is the end in itself.
The human involvement is crucial because the entire purpose of mathematics research is to increase human understanding of mathematics. It is pursued because it is interesting, not because it is economically useful. In this sense it's a lot closer to the humanities.
A black box oracle that just tells you whether statements are true or false is not the goal of mathematics and would not be particularly interesting to the field (except insofar as it could be harnessed to improve human understanding).
Coding is totally different from this, where it is essentially always done as a means to an end. Likewise with many other fields, like pharmaceutical research or materials science or what have you, that are oriented around solving problems for some practical purpose. Pure math isn't really like that for the most part.
Sure, but I don’t think most of the money that goes into funding math is for the purposes of pure understanding. The reason governments fund mathematics research grants is generally for a more instrumental purpose; taking the US congress as an example, the mission of the NSF is to, “Promote the progress of science; advance national health, prosperity, and welfare; and secure national defense.” Most federal math grants come from the NSF.
Of course, math research is cheap and most academics don’t rely upon grants, their salary covers most of their expenses. But here too, the mathematics professor spends a substantial amount of their time teaching future engineers/quants/other applied mathematicians, who need to understand math for instrumental purposes, not as an end in and of itself. Without the tuitions of these students, I can’t imagine universities maintaining the size of their math departments, let alone expanding them as Dr. Sahai advocates for.
So who or what funds the community of pure mathematics going forward?
Research in pure mathematics is part of what we call "basic research". There are no applications in mind a priori. People instead focus on understanding, because history has taught us that understanding tough problems in mathematics finds natural applications elsewhere. It's the same as theoretical physics or theoretical computer science.
Well with AI, programming among humans will become like math. A hobby.
Another day, another HN thread full of programmers who think mathematics is just like programming.
Thanks for providing a (much needed!) correction.
LLMs dont create anything new, if programmers stop reading the code technology will be forever frozen to 2022, no new programming languages, operating systems, concurrency primitives, databases, networking protocols, UI frameworks everything will be based on the training data and future generations will forget about all the primitives we now take for granted.
If someone creates a new programming language/ framework or new better way to do async or whatever, no one will use it because it is not in the training data and it wont take off because everyone is using LLMs. It will be like using the same Lego pieces over and over.
What if programming languages, operating systems, concurrency primitives, databases, networking protocols, UI frameworks are already good enough, and the innovation lies elsewhere?
You can do a lot of cool stuff with the same lego pieces.
That is like saying what if music is already good enough.
The problem with a terawatt fusion plant isn’t that the first one will be broken, or the tenth one in some other way. The problem is the hundredth will work flawlessly, and so will the thousandth, and a petawatt is serious waste heat to reject; if we keep building them on this planet, we’ll all simply cook.
Reliable cheap fusion is the holy grail and used in moderation will fix most of our environmental and political problems, but it also forces humanity off this world. Maybe that’s not a bad thing, but there is no free lunch.
Imagine the first time electric calculators calculated the square root of 5. I'm sure people would verify again and again if what the circuits calculated was right.
Then in the 80s, you presses 2 buttons and there you had it in your classroom without thinking twice if the electricity arrived correctly at the transistors.
How crazy will the world be once our [current gen] ANN are like that!
What an amazing thought.
It is insane how many times I see this false analogy repeated on HN over and over (analogy of a deterministic-by-design calculator device (or a compiler, etc.) and a non-deterministic-by-design LLM software).
LLMs are not non-deterministic by design. The randomness in the output is artificially injected for ergonomic reasons. (Yes, the non-determinism in production systems is different, but also not by design)
Nothing is deterministic.
Nothing is stopping LLMs to be more deterministic/correct over time.
Also you yourself is nondeterministic :)
>Also you yourself is nondeterministic :)
All people are. That is how automation appeared to begin with - to provide deterministic behavior.
You're missing the forest for the trees here. The point OP is trying to make is that calculators originally were essentially non-deterministic. Technology will go from unreliable to reliable.
Calculators never were non-deterministic by design.
It will be even more amazing if they solve the theory of everything or the hard problem of consciousness.
Imagine AI crushing quantum mechanics like Einstein pwned classical physics.
Calculators and computers are deterministic, they give the same output to the same output every time. Language models specifically are not. So it might give you are function that is correct, or a function that is not, or worse yet a function that behaves correctly, but introduces some god-awful bug down the line that can cause serious havoc. It is obvious that they need supervision, not only for output, but also sandboxing and various harnesses for them to not do any “oops, I deleted your codebase sry” kind of nonsense people post to Reddit.
So I think the problem is to determine which problems under what instructions we can safely give to a model application to solve and how we test the output for safety and functionality. This would create more usable and safe, albeit a bit more boring, AI-based applications alin to a calculator or general computer. Whether this is posswith current model architecture is another thing.
If you set the temperature 0, an LLM is also deterministic (same prompt -> same output every single time). We just don't do this because the LLM is not so smart in that mode. But "LLM is not so smart" is changing at Moore's law speeds.
Non-determinism is not an essential property of LLMs. It's an optimization that we've added intentionally.
These are all implementation details.
At the end of the day, an LLM is just a very big mathematical function. That is, by definition, deterministic. A particular implementation might give up on determinism for the sake of higher efficiency, but it you want a deterministic LLM, it can absolutely be done.
Humans (IQ of X, non deterministic) can write deterministic code.
AI (IQ of Y, non deterministic) can write deterministic code.
Y is going to keep increasing, while X will not.
IQ hasn't been increasing in developed countries for about three decades now. In fact, it has been declining in most.
The increases still happen globally but mostly driven by developing countries.
> Calculators and computers are deterministic
How do you know?
Memory bits flip randomly. It's not a super rare thing either. You and me have experienced that many times without knowing. The only reason that computers feel deterministic is that we have error-correcting code to fix that. But in the most extreme cases, when multiple bits flip together, once "deterministic" program can generate unexpected output.
So why do you trust computers? Because statistically the case is just very unlikely. Therefore if AI is statistically unlikely to make mistakes there is no reason to not trust them.
You are confusing hardware noise and whether the algorithm itself is verifiable as if parity bits were not a thing. We don’t trust computers because the medium itself is infallible, but because the logic is sound.
With statistical models - such as LLM’s - there is no logic as such, but statistical assumptions based on given data. The output can ge very good or very bad, but you are fool to trust it blindly. Therefore you need a deterministic way to verify, whether meat- or software-based.
[dead]
Calculators hallucinate! Mine did not come with error correcting RAM. (Though you might not know from the price.)
Given the disappointing levels of intellectual decay that our current technology has thrust upon civilization, I only see humans reverting back to neanderthal levels of intelligence in short time with the advent of AI
> One wonders whether a generation that demands instant satisfaction of all its needs and instant solution of the world's problems will produce anything of lasting value. Such a generation, even when equipped with the most modern technology, will be essentially primitive — it will stand in awe of nature, and submit to the tutelage of medicine men.
- Eric Hoffer
> Sounds awesome
- Tech Bro
There's no reliable evidence that Neanderthals were less intelligent than modern humans. They're extinct now (except for a tiny genetic legacy in some human populations) but that could have happened for a variety of reasons unrelated to intelligence or lack thereof.
> neanderthal levels of intelligence
were gonna need a citation on this one.
Nit, but Terrence Tao did not write this article, it’s a guest post.
>Terence Tao is arguing
This is a guest post by Amit Sahai.
> What about the ten thousandth one? Will "a nuclear fusion plant" become something that models couldn't possibly get wrong?
For what it's worth, ten thousand terawatt fusion plants probably approaches the level at which the sheer intensity of energy production would cause significant disruption to the climate (it's roughly 5% of the Earth's entire solar input). Every energy source becomes dirty past a certain point. It would be wiser to learn how to build a utopia within a limited energy budget than find a way to produce enough of it to cook the damn planet, but who am I kidding, we're going to build a million of these things.
This assumes we're still building them on Earth.
No, it doesn’t. It assumes we’re using it here. If we beam the power to Earth from space, it’s the same thing.
The more I think about space elevator, the less I believe in it.
The material alone is in a quantity beyond what we can reasonably manufacture.
and the material needs to be perfect. All design we have today have cascade failure mode -- any material failure translates to a total catastrophic failure.
and geostationary does not really meant Geostationary. There are lots of jiggling everywhere. It wear down over time. and let's hope nothing resonance
and we need some maintenance / decommission plan. How can we decommission this when it fail or need upgrade?
Why would we have stopped?
I'm not sure the scarce resource will be people capable of understanding the AI's work. It may be institutions willing to tolerate the cost of understanding it
it's incredible the amount of people who think all these recent posts in Taos blog were written by him.
You oppose correctness to meaning and purpose, which you seem to imply are impractical values. (Worthless values, then?) But you don't mention creativity. The article blithely says that AI creates new ideas and understands things. I don't think it does.
The more likely AI becomes to produce working code every time, the more likely it will become that a one-in-a-thousand or one-in-a-million error goes unnoticed at generation time. It sucks.
Bugs have existed since before AI, though. It's remarkable how bad a lot of very successful software has always been.
Sure, but we currently find that acceptable. Codebases are full of such bugs.
We’re seeing more and more slippery slope arguments, except the slippery slope leads to human cognitive oblivion and it is actually a good thing actually.
> I just hope that there are more Terence Taos out there than people like me.
Just spare me. Being under external pressure to “ship code” is one thing, but being personally inclined one way or another (no external pressure) is another. And when you think being inclined like that is existentially risk (for human civ?) then, what? It’s just the way you are wired and hopes and prayers that collectively that doesn’t drive us off the cliff?
This aw shucks persona isn’t convincing. Same thing with AI Bros who are (1) making the most awesome tech that has ever existed, and (2) aw shucks hope it doesn’t kill us all in the end.
>the economically dominant strategy to not verify them and not double check them
In the big scheme of things is it really that expensive to verify it if a lean proof is generated? The agent itself will likely have already verified such Lean code before calling it "done".
I feel like knowing something is true is useful, but if you don’t understand how and why, you won’t understand the implications
Am I the only guy who still thinks we're kind of putting the cart before the horse here? Look, I would love to live in a world where AI is in the business of designing terawatt fusion plants and revolutionizing all other aspects of society. But right now it can't even really tell a puddle in the road. I feel like we have a really long way to go here, hype-laden PR releases about solving math problems aside.
The models get things wrong in the way that humans don't.
They will never make a logical error yet make terrible assumptions and poor long scale decisions.
Wake me up when an agent swarm can write gcc in a box sealed from the internet.
My dad recently needed to buy a new thermostat for his home with an air furnace (yes, he told the model) asking an AI which one to buy, and he got recommended one that only properly works with boilers. Then after that happened, the alternative he bought the AI never told them he needed to buy a gateway to connect to his furnace.
I think we are a long long looong way from AI designing 'terawatt fusion plants'.