Ahhh, epistemology... Does any academic researcher even care about these things anymore?
If you're in academia, you've probably noticed a major shift recently. Research production at an industrial scale through AI.
Grants have "always" been awarded to professors based on quantity multiplied by quality. Now, some professors are churning out 1–3 papers a month with the same group of co-authors. All the grant money goes to them. Grant givers are just only counting the numbers of papers being published.
The Industrial Revolution has hit academia, and some academics are busy arguing for the artisanal value of research while some are creating factories for research.
The problem is the systemic disincentivation of true science, the pursuit of truth and knowledge unencumbered by greed.
When you speak favorably of "factories for research", you adopt the position of a mindless consumer, relishing the prospect of "abundant" products of science.
You fail to notice, livestock lives in abundance as well.
Nobody will speak favourably about the factorization of anything.
The "publish or perish" culture is going through what is essentially the same transformation brought by the invention of the assembly line. Academia, "as an industry", is experiencing what the automobile industry went through a century ago.
Grant approvals are public. Just go through them, and you will see a pattern emerge.
The argument I keep hearing is, "AI is good in the hands of a good researcher."
5–7 papers based on the same dataset? 5–7 papers on the same core topic, published within a six-month period?
They tell me that this is their core specialization and that I simply don't understand how science works.
Science is a self-governed, self-serving, and artificially defined concept.
The article's perspective reminds me of math class when I was a kid. The teacher didn't want the right answer alone, she wanted to see how I got there. In an absolute sense, the right answer is the right answer with or without my understanding, but that's not how the class was graded. We're approaching a point where AI is to science as my old calculator is to elementary school math -- it's capable of leapfrogging to answers faster and more accurately than we can.
Thing is, though, verification is knowledge itself. And if we can get to a point where the important questions have answers, we can surely have the verifiers explain those to us in ways we can understand them.
This is not obvious to me at all. LLMs are capable of amazing feats of reverse engineering but are terrible at explaining and abstracting things well.
I think this is an artefact of how we train them, and they could be trained to be better at this if we focused on it, but at the same time, it shows its possible for these things to be able to do things they cant explain to us (granted, they can't explain them well - you can bash your way to understanding with them anyway but they aren't good at it)
> This is not obvious to me at all. LLMs are capable of amazing feats of reverse engineering but are terrible at explaining and abstracting things well.
It's amazing to me that language models are still such poor writers and communicators. The mathematics community wrestled with this recently, when many solutions dropped into their laps but were not explained very well...
Thing is, (1) generic LLMs will improve, and (2) their lack of ability in this area has a lot to do with the rhetorical and structural habits they pick up during RLHF/instruction-tuning, which trained them for general-purpose comms. Zero-training base models can presumably be trained specifically to communicate scientific concepts. Interesting times.
(Edited to add: With respect to (1), compare Opus 5 to 5.5. 5 was a terrible communicator, even of software/coding concepts, whereas 5.5 is excellent and leaves very little to be desired.)
LLMs are excellent writers in the sense that they get the spelling, grammar, syntax, etc... right. They are certainly way better than I am, and they can compete with the best writers considering how AI-generated prose has winned literary prizes.
Many people don't like the style, probably by association with slop and fatigue more than the style being fundamentally wrong.
Being a good communicator is an entirely different thing, you can have terrible spelling and grammar and still be good at getting ideas across. It is a common situation when the communicator in question is not using his native language.
That LLMs are so good at writing and so bad at communicating is not surprizing. The key to good communication is getting into the other people's mind, LLMs can't do that, because they "think" in a way that is completely alien to us. We use words to express our thoughts, thoughts that are based on a physical world model: touch, movement, sound, light, etc... LLMs have no idea about how the physical world work, everything the see is just words, they have no intuitive idea of, say, objects falling down, just that "falling" and "down" go well together. And for explaining things, they will go "someone asks for an explanation, explanations usually use these words, I will be using the same kind of words".
> 5.5 is excellent and leaves very little to be desired.
Hm, that may have to do with (faking) confidence. I've often enough with 5.5 still run into cases where it confidently explained something, at the surface it kinda made sense, but the more I dug and verified, the more it became apparent that it was entirely wrong with the most crucial core concepts. It has gotten to a point where you really need a domain expert though to realize this, which makes it tough for using it in areas where you are not an expert and don't have easy access to one either.
You point at the exact problem here: people are so used to arguing from ignorance, they don't even notice.
Verification isn't knowledge. Far from it. You can verify statements without knowing why they're true. Variants of that concept are e.g. used in cryptology.
You need humans to truly understand (to know the context) in order to make correct judgements. Without actually knowing the context, you have no way to compare.
An infallible oracle tells Archimedes that the speed of light in vacuum is ~1.08 billion kilometers per hour. Archimedes, with the iron age tools and methods at his disposal, might be able to verify this and make some use of it himself. Maybe. In any case, what he has gained is knowledge itself.
The same goes for our own time. A powerful AI can tell us things at the edge of what we can grasp -- or beyond what we can grasp -- and it would nevertheless be knowledge that we possess. We can work to verify it, we can have it explained to us as though we were schoolchildren, or we can simply accept it as a static fact of the natural world.
In truth, we're going to have to learn to coexist with minds that are more powerful than ours. At least in some respects, if not in all respects. The good scenario is that they share information with us, and we receive it however we can. "Head in the sand" and "mutual disdain" are bad outcomes.
You might want to look up the actual definition of knowledge. It's a pretty interesting topic in epistemology really, far from your simplistic take.
You already live in coexistence with minds more powerful than yours. Society works in a way that you never need to notice that, those minds taking care of things beyond your grasp for you.
The downside of that "convenience" is you developing an over-simplified bubble-view of the world, rendering you prone to arbitrarily hazardous misjudgements.
Here, you align foolishly with interests that cannot possibly be your own. Namely, exploiting scientific knowledge for personalized monetary gain on an unsustainable scale.
When a tiny group of people hogs essentially all scientific knowledge, that renders you what?
Your idea of being graciously provided with some "basic income" or whatever is blind copium. You would live as livestock at best, to be discarded as useless whenever your masters see fit.
I don't think this is the issue. Most people are mediocre mathematicians, too, yet the companies have selected well enough for math literacy in training data (presumably). I think its a matter of training - they are often post trained by other agents (which read everything), human reviewers not paid enough to care (easily wowed by 10 paragraph length essay with correct punctuation), and deterministic scripts (checking for presence of a specific point, so agents are incentivised to write as much as possible to have more chances of hitting the unknown thing the script is looking for)
As far as I know labs try to train the other way, else we'd have monstrously long and useless outputs, but its hard to overcome these natural biases for length
I don't think that's a suitable mental model of how LLMs work. Their output is not just the statistical average of all the training data. If it was then the output would be quite useless.
An LLM trained on the entire internet incorporates essentially all (human-known) aspects of things.
Like a superposition of all kinds of writing styles, all perspectives on every topic and all kinds of ways to do things right and wrong.
In post-training (and of course already by sensibly curating the input data in the first place), people try to select useful submanifolds from that.
Ideally, you get a combination of all the extant strengths of people combined into one model. Self-improvement then leaves the sphere of human capability for good.
And in many cases it is not really the new solution that is important. It is the new techniques, abstractions, or other sense-making or investigative tools that made the solution possible that matter.
And the abstractions do still matter, since in many cases it is an issue of tractability. Perhaps an LLM can force its way to a solution through 3 million mind numbingly boring and convoluted steps, but if the number of steps increases exponentially without the right abstraction that means it can only handle a slightly larger problem than a human with pen and paper.
Meaning requires integration. But I assume AI can make meaning of it, now or in the future. I assume the same with people. However I don’t see the point of knowledge without meaning.
I would prefer relation or context instead of integration. Meaning is contextual. Understanding is the process of attaing the meaning or a meaning. Knowledge in this perspective is the final outcome that can be verified in some way or you assume so.
Relation can be a link. I don’t think that’s sufficient for meaning. It needs to have an effect — and arguably a positive one — on the broader coherence.
I sucked at remembering goniometric identities, but I was superfast with testing out a few options on my calculator to make sure I was using the correct one. Without a calculator I was nowhere.
I don't think we're there yet for science. Perhaps for math proofs, but that's a very different domain ultimately since we know the rules of the game in a way we don't with science.
First math and CS, where formal logic dominate, and AI can check/verify its own answers very quickly. Then physics, downstream of math. Then materials science, which in some cases is practically a branch of physics. Then chemistry more generally. Then biology. Then various social sciences.
A big difference is that in mathematics, you can do all your experimentation purely in theory and at arbitrary speed, while for example chemistry needs a lab and plenty of time.
Math is really super suitable for quick iterations by a machine.
Fields medalist and as Tao listed as one of the most important mathematicians of our age.
Scholz is known to find
„precisely the correct and cleanest way to incorporate all the previously done work and find an elegant formulation for that — and then, because he found really the correct framework, go way beyond the known results“
In a way that man is the complement of an AI, he generates understanding rather than just proofs.
Maybe he is the right template for the mathematicians of the future.
Even Peter Scholz is not always sure of correctness of extremely complicated mathematical statements and welcomes computer assistance in verification of his results.
"
I spent much of 2019 obsessed with the proof of this theorem, almost getting crazy over it. In the end, we were able to get an argument pinned down on paper, but I think nobody else has dared to look at the details of this, and so I still have some small lingering doubts.
"
In a sense, mathematics is not very different from software engineering.
One bit stands out to me: to better understand, Scholz will work the problem backwards. Sometimes that strategy is just so spot on.
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To my eternal shame, philosophy (like this OC) makes my head hurt. Pretzels my brain, ouroboros like (aka "head up my own butt").
Caveats covered, here's my cave man cold take on two aspects of this topic.
#1 As we're all trying to paraphrase here: answers are great; understanding is even better. I like the word "legibility" (h/t James Scott). The current models are not very legible.
Which directly leads to:
#2 Understanding enables predictions.
If LLMs are stochastic parrots, then pi.dev (GPT + reasoning + ralph loop) is a drunken sailors walk (thru a solution space). A kind of messy heuristic for optimization. With some kind of gate for declaring "done!" Pretty useful.
However, I don't expect Pi.dev to make predictions. That'd require something else. Maybe that something is being worked on; am noob, so I wouldn't know. (I'm still unclear about whatever Jeff Hawkins is doing, in practical terms.)
--
Wrapping up: Automated prediction would be cool. That's very different from finding solutions to problems. And the current cohort of AI can't even explain why, much less make predictions.
Assuming predictions requires understanding. Maybe there are other strategies to generate predictions. Like a meta drunken sailor's walk, with drunken sailors all the way down.
(Someone please correct me as needed. TIA.)
[Aside: That article has an ad for their podcast They Joy of ₍₎. Perfect. I have no idea if it lives up to its promise.]
Arriving at truth values has limited value in science, obviously (with full understanding being more useful). For example, knowing a chemical reaction will produce heat is useful (cavemen discovered that one), but knowing _why_ unlocks an entire world of useful tools (the combustion engine, space heaters, etc).
However, even getting truth answers will soon be beyond AI. It is of course making impacts in Math and in publishing in "data heavy" subjects where you can just formally verify, program, and/or munge data.
But in "real science" where we actually need to build a lab, buy supplies, hire personnel, get approval, form physical test harnesses, install sensors in proper locations, calibrate everything, then finally make one measurement, question the whole thing, then finally make a conclusion, AI is of limited benefit.
Yes, it can help speed up coming up with some formulas, spitballing, or checking existing research. It can even help write the jank code for sensor calibration, measurement taking, etc. That's not nothing, but we are _very far_ from meaningful contributions to real experimental hard sciences.
As for math, theoretical physics, computer science, and other "logic based" studies, the question becomes one of benefit to cost of true understanding versus simply knowing something is true.
I'd argue that it paints a starkly negative picture of most science. Once answers are easy to obtain, it seems most people are concluding that actually understanding why its true isn't worth the effort, which means that the question maybe wasn't worth asking.
Its the science equivalent to the recent realization in tech: most ideas suck, your product didn't need more bells and whistles. Actually the engineers pushing back on every shower thought from product was a good thing. The friction that stops you from putting every random-ass feature into your already bloated useless SaaS product was good, and now the sales guy is pushing features to prod for a customer demo. We thought "too many ideas, not enough engineers", we now know "not enough meaningful quality ideas".
In the same way we thought "too many questions, not enough scientists", we now know "not enough real study on meaningful topics".
This misses that AI is already designing and carrying out experiments autonomously. This will only explode with the growth of capabilities in robotics.
Surely the way forwards is to take the results obtained by brute force with AI, for example that certain conjectures are true or false, then to use that knowledge to further human understanding.
Knowing that something is true or false will at least stop humans wasting time trying to prove or disprove it, and allow them to find a more elegant proof, or investigate the implications of the true/false result.
Autonomous or human-directed AI agents submit their work to a public repository.
Then the scientific community draws from this pool of results, identifies the important ones, and starts working on adding the results to the greater body of scientific knowledge. This work of interpretation, synthesis and question formation should be recognised and rewarded in peer-reviewed academic journals.
Maybe but it might also be useless. Knowing a very large number is the product of two very large primes doesn’t at all help the reader to understand factorization, for example.
> “The other side argues… human understanding is paramount, because it drives integration of new findings into the canon […] But the first side, those who emphasize correct outputs, dismisses this as gatekeeping or nostalgia.”
Is this description AKA. theory vs praxis? Academia vs Engineering?
Science has been industrialized, it has to change.
I propose a two-part approach.
First, autonomous or human-directed AI agents submit their work to a public repository.
Second, the scientific community draws from this pool of results, identifies the important ones and asks the next set of important questions. This work of interpretation, synthesis and question formation should be recognised and rewarded in peer-reviewed academic journals.
"Is science about humans achieving insight, or the archiving of verifiable solutions?"
I wonder if this dichotomy fully captures the value of scientific discoveries. One could argue that their practical impact can be independent of whether humans fully understand how they were reached.
Practical impact has always been linked but ultimately independent of knowledge. You can have very sophisticated technology based on zero actual knowledge or understanding, like roman concrete or borosillicate glass. And you can have a very deep understanding without practical impact, like lasers for decades or galactic algorithms for multiplication.
Indeed, if a machine had told Heisenberg in 1943 (or whatever?) that "the critical mass for an atomic bomb is much less than you think", we could very well have had a different world today, regardless of Heisenberg understanding it or not.
The problem is trading off short term and long term progress. A solution alone can be useful in the short term, but if humans don't also build up understanding it will probably prevent long term progress from happening. It's much more difficult to build on top of something you don't understand.
I would rephrase it as: "Verification is not human knowledge", but that doesn't really matter. We are going to be several steps behind AI as it reaches a level of intelligence far beyond human capabilities, and we are not going to be able to catch up with it. It's like trying to beat AI at chess: we are bound to be left behind as AI continues to expand its knowledge in mathematics, physics, computer science, and other fields. Eventually, no human being will be able to reach that level of knowledge within their lifetime.
No need to start worrying about AI reaching a level of intelligence far beyond human capabilities until it actually reaches the level of humans and assuming that ever happens it could be a very very long way off. All of the intelligence "AI" has right now comes from the human data that it was trained on. It's been given enough power to crunch numbers better than we do, as any computer can, and more data to play with than any one human can retain, but none of that equals intelligence. Speculating on a sci-fi future however, if AI is ever able to create new and more advanced forms of AI, which can also create new and and more advanced forms of AI we'll be outpaced quickly.
As long as humans are in charge it's vital for us to understand what is going on - be it in science or coding, once you give up all knowledge (yes knowledge = power) not just work to AI, you can be manipulated/controlled/fooled with ease.
I have doubts about that. You don't need AI (understood as the current LLMs) to make a powerful chess engine, or computer vision or anything that reacts faster and better than a human. We've had those forever.
A good word predictor happens to be good with closed systems with very defined rules for which a huge training corpus exists and we are suddendly freaking out about how it's gonna become so much better than us at everything that we are basically obsolete.
When in doubt about where AI stands, ask it to create a poem, a joke or a riddle. And see how little actual intelligence it has.
How do we know if/when that happens if it’s beyond us to comprehend. An open ended and broad claim like this can always become true one day, similar to flying cars.
Ive never heard such drivel in my life. Are you a shill? The current "AI" is not intelligent, it can beat humans in certain areas but weve always had that with things like Deep Blue. I dont believe llms will reach human intelligence and certainly not super intelligence.
Ahhh, epistemology... Does any academic researcher even care about these things anymore?
If you're in academia, you've probably noticed a major shift recently. Research production at an industrial scale through AI.
Grants have "always" been awarded to professors based on quantity multiplied by quality. Now, some professors are churning out 1–3 papers a month with the same group of co-authors. All the grant money goes to them. Grant givers are just only counting the numbers of papers being published.
The Industrial Revolution has hit academia, and some academics are busy arguing for the artisanal value of research while some are creating factories for research.
Yes, true scientists do care about epistemology.
The problem is the systemic disincentivation of true science, the pursuit of truth and knowledge unencumbered by greed.
When you speak favorably of "factories for research", you adopt the position of a mindless consumer, relishing the prospect of "abundant" products of science.
You fail to notice, livestock lives in abundance as well.
Nobody will speak favourably about the factorization of anything.
The "publish or perish" culture is going through what is essentially the same transformation brought by the invention of the assembly line. Academia, "as an industry", is experiencing what the automobile industry went through a century ago.
Grant approvals are public. Just go through them, and you will see a pattern emerge.
The argument I keep hearing is, "AI is good in the hands of a good researcher."
5–7 papers based on the same dataset? 5–7 papers on the same core topic, published within a six-month period?
They tell me that this is their core specialization and that I simply don't understand how science works.
Science is a self-governed, self-serving, and artificially defined concept.
The article's perspective reminds me of math class when I was a kid. The teacher didn't want the right answer alone, she wanted to see how I got there. In an absolute sense, the right answer is the right answer with or without my understanding, but that's not how the class was graded. We're approaching a point where AI is to science as my old calculator is to elementary school math -- it's capable of leapfrogging to answers faster and more accurately than we can.
Thing is, though, verification is knowledge itself. And if we can get to a point where the important questions have answers, we can surely have the verifiers explain those to us in ways we can understand them.
> we can surely have the verifiers explain those
This is not obvious to me at all. LLMs are capable of amazing feats of reverse engineering but are terrible at explaining and abstracting things well.
I think this is an artefact of how we train them, and they could be trained to be better at this if we focused on it, but at the same time, it shows its possible for these things to be able to do things they cant explain to us (granted, they can't explain them well - you can bash your way to understanding with them anyway but they aren't good at it)
> This is not obvious to me at all. LLMs are capable of amazing feats of reverse engineering but are terrible at explaining and abstracting things well.
It's amazing to me that language models are still such poor writers and communicators. The mathematics community wrestled with this recently, when many solutions dropped into their laps but were not explained very well...
Thing is, (1) generic LLMs will improve, and (2) their lack of ability in this area has a lot to do with the rhetorical and structural habits they pick up during RLHF/instruction-tuning, which trained them for general-purpose comms. Zero-training base models can presumably be trained specifically to communicate scientific concepts. Interesting times.
(Edited to add: With respect to (1), compare Opus 5 to 5.5. 5 was a terrible communicator, even of software/coding concepts, whereas 5.5 is excellent and leaves very little to be desired.)
LLMs are excellent writers in the sense that they get the spelling, grammar, syntax, etc... right. They are certainly way better than I am, and they can compete with the best writers considering how AI-generated prose has winned literary prizes.
Many people don't like the style, probably by association with slop and fatigue more than the style being fundamentally wrong.
Being a good communicator is an entirely different thing, you can have terrible spelling and grammar and still be good at getting ideas across. It is a common situation when the communicator in question is not using his native language.
That LLMs are so good at writing and so bad at communicating is not surprizing. The key to good communication is getting into the other people's mind, LLMs can't do that, because they "think" in a way that is completely alien to us. We use words to express our thoughts, thoughts that are based on a physical world model: touch, movement, sound, light, etc... LLMs have no idea about how the physical world work, everything the see is just words, they have no intuitive idea of, say, objects falling down, just that "falling" and "down" go well together. And for explaining things, they will go "someone asks for an explanation, explanations usually use these words, I will be using the same kind of words".
> 5.5 is excellent and leaves very little to be desired.
Hm, that may have to do with (faking) confidence. I've often enough with 5.5 still run into cases where it confidently explained something, at the surface it kinda made sense, but the more I dug and verified, the more it became apparent that it was entirely wrong with the most crucial core concepts. It has gotten to a point where you really need a domain expert though to realize this, which makes it tough for using it in areas where you are not an expert and don't have easy access to one either.
You point at the exact problem here: people are so used to arguing from ignorance, they don't even notice.
Verification isn't knowledge. Far from it. You can verify statements without knowing why they're true. Variants of that concept are e.g. used in cryptology.
You need humans to truly understand (to know the context) in order to make correct judgements. Without actually knowing the context, you have no way to compare.
An infallible oracle tells Archimedes that the speed of light in vacuum is ~1.08 billion kilometers per hour. Archimedes, with the iron age tools and methods at his disposal, might be able to verify this and make some use of it himself. Maybe. In any case, what he has gained is knowledge itself.
The same goes for our own time. A powerful AI can tell us things at the edge of what we can grasp -- or beyond what we can grasp -- and it would nevertheless be knowledge that we possess. We can work to verify it, we can have it explained to us as though we were schoolchildren, or we can simply accept it as a static fact of the natural world.
In truth, we're going to have to learn to coexist with minds that are more powerful than ours. At least in some respects, if not in all respects. The good scenario is that they share information with us, and we receive it however we can. "Head in the sand" and "mutual disdain" are bad outcomes.
No, you're wrong.
You might want to look up the actual definition of knowledge. It's a pretty interesting topic in epistemology really, far from your simplistic take.
You already live in coexistence with minds more powerful than yours. Society works in a way that you never need to notice that, those minds taking care of things beyond your grasp for you.
The downside of that "convenience" is you developing an over-simplified bubble-view of the world, rendering you prone to arbitrarily hazardous misjudgements.
Here, you align foolishly with interests that cannot possibly be your own. Namely, exploiting scientific knowledge for personalized monetary gain on an unsustainable scale.
When a tiny group of people hogs essentially all scientific knowledge, that renders you what?
Your idea of being graciously provided with some "basic income" or whatever is blind copium. You would live as livestock at best, to be discarded as useless whenever your masters see fit.
To be fair, most people aren't writers, so the "average" writing the statistical model can produce is mediocre writing.
I don't think this is the issue. Most people are mediocre mathematicians, too, yet the companies have selected well enough for math literacy in training data (presumably). I think its a matter of training - they are often post trained by other agents (which read everything), human reviewers not paid enough to care (easily wowed by 10 paragraph length essay with correct punctuation), and deterministic scripts (checking for presence of a specific point, so agents are incentivised to write as much as possible to have more chances of hitting the unknown thing the script is looking for)
As far as I know labs try to train the other way, else we'd have monstrously long and useless outputs, but its hard to overcome these natural biases for length
I don't think that's a suitable mental model of how LLMs work. Their output is not just the statistical average of all the training data. If it was then the output would be quite useless.
An LLM trained on the entire internet incorporates essentially all (human-known) aspects of things.
Like a superposition of all kinds of writing styles, all perspectives on every topic and all kinds of ways to do things right and wrong.
In post-training (and of course already by sensibly curating the input data in the first place), people try to select useful submanifolds from that.
Ideally, you get a combination of all the extant strengths of people combined into one model. Self-improvement then leaves the sphere of human capability for good.
And in many cases it is not really the new solution that is important. It is the new techniques, abstractions, or other sense-making or investigative tools that made the solution possible that matter.
And the abstractions do still matter, since in many cases it is an issue of tractability. Perhaps an LLM can force its way to a solution through 3 million mind numbingly boring and convoluted steps, but if the number of steps increases exponentially without the right abstraction that means it can only handle a slightly larger problem than a human with pen and paper.
Meaning requires integration. But I assume AI can make meaning of it, now or in the future. I assume the same with people. However I don’t see the point of knowledge without meaning.
I would prefer relation or context instead of integration. Meaning is contextual. Understanding is the process of attaing the meaning or a meaning. Knowledge in this perspective is the final outcome that can be verified in some way or you assume so.
Relation can be a link. I don’t think that’s sufficient for meaning. It needs to have an effect — and arguably a positive one — on the broader coherence.
I sucked at remembering goniometric identities, but I was superfast with testing out a few options on my calculator to make sure I was using the correct one. Without a calculator I was nowhere.
I don't think we're there yet for science. Perhaps for math proofs, but that's a very different domain ultimately since we know the rules of the game in a way we don't with science.
Oh, it's going to move up the old ladder, from bottom to top:
> https://en.wikipedia.org/wiki/Hierarchy_of_the_sciences
First math and CS, where formal logic dominate, and AI can check/verify its own answers very quickly. Then physics, downstream of math. Then materials science, which in some cases is practically a branch of physics. Then chemistry more generally. Then biology. Then various social sciences.
A big difference is that in mathematics, you can do all your experimentation purely in theory and at arbitrary speed, while for example chemistry needs a lab and plenty of time.
Math is really super suitable for quick iterations by a machine.
What makes you believe that it will be such a progression?
We all know Terry Tao, do you know Peter Scholz?
Fields medalist and as Tao listed as one of the most important mathematicians of our age.
Scholz is known to find „precisely the correct and cleanest way to incorporate all the previously done work and find an elegant formulation for that — and then, because he found really the correct framework, go way beyond the known results“
In a way that man is the complement of an AI, he generates understanding rather than just proofs.
Maybe he is the right template for the mathematicians of the future.
https://www.quantamagazine.org/peter-scholze-and-the-future-...
Even Peter Scholz is not always sure of correctness of extremely complicated mathematical statements and welcomes computer assistance in verification of his results.
See the Liquid tensor experiment:
https://xenaproject.wordpress.com/2020/12/05/liquid-tensor-e...
https://www.ma.imperial.ac.uk/~buzzard/xena/pdfs/liquid_tens...
" I spent much of 2019 obsessed with the proof of this theorem, almost getting crazy over it. In the end, we were able to get an argument pinned down on paper, but I think nobody else has dared to look at the details of this, and so I still have some small lingering doubts. "
In a sense, mathematics is not very different from software engineering.
More precisely: Curry–Howard correspondence
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...
I did not; thank you.
One bit stands out to me: to better understand, Scholz will work the problem backwards. Sometimes that strategy is just so spot on.
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To my eternal shame, philosophy (like this OC) makes my head hurt. Pretzels my brain, ouroboros like (aka "head up my own butt").
Caveats covered, here's my cave man cold take on two aspects of this topic.
#1 As we're all trying to paraphrase here: answers are great; understanding is even better. I like the word "legibility" (h/t James Scott). The current models are not very legible.
Which directly leads to:
#2 Understanding enables predictions.
If LLMs are stochastic parrots, then pi.dev (GPT + reasoning + ralph loop) is a drunken sailors walk (thru a solution space). A kind of messy heuristic for optimization. With some kind of gate for declaring "done!" Pretty useful.
However, I don't expect Pi.dev to make predictions. That'd require something else. Maybe that something is being worked on; am noob, so I wouldn't know. (I'm still unclear about whatever Jeff Hawkins is doing, in practical terms.)
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Wrapping up: Automated prediction would be cool. That's very different from finding solutions to problems. And the current cohort of AI can't even explain why, much less make predictions.
Assuming predictions requires understanding. Maybe there are other strategies to generate predictions. Like a meta drunken sailor's walk, with drunken sailors all the way down.
(Someone please correct me as needed. TIA.)
[Aside: That article has an ad for their podcast They Joy of ₍₎. Perfect. I have no idea if it lives up to its promise.]
Arriving at truth values has limited value in science, obviously (with full understanding being more useful). For example, knowing a chemical reaction will produce heat is useful (cavemen discovered that one), but knowing _why_ unlocks an entire world of useful tools (the combustion engine, space heaters, etc).
However, even getting truth answers will soon be beyond AI. It is of course making impacts in Math and in publishing in "data heavy" subjects where you can just formally verify, program, and/or munge data.
But in "real science" where we actually need to build a lab, buy supplies, hire personnel, get approval, form physical test harnesses, install sensors in proper locations, calibrate everything, then finally make one measurement, question the whole thing, then finally make a conclusion, AI is of limited benefit.
Yes, it can help speed up coming up with some formulas, spitballing, or checking existing research. It can even help write the jank code for sensor calibration, measurement taking, etc. That's not nothing, but we are _very far_ from meaningful contributions to real experimental hard sciences.
As for math, theoretical physics, computer science, and other "logic based" studies, the question becomes one of benefit to cost of true understanding versus simply knowing something is true.
I'd argue that it paints a starkly negative picture of most science. Once answers are easy to obtain, it seems most people are concluding that actually understanding why its true isn't worth the effort, which means that the question maybe wasn't worth asking.
Its the science equivalent to the recent realization in tech: most ideas suck, your product didn't need more bells and whistles. Actually the engineers pushing back on every shower thought from product was a good thing. The friction that stops you from putting every random-ass feature into your already bloated useless SaaS product was good, and now the sales guy is pushing features to prod for a customer demo. We thought "too many ideas, not enough engineers", we now know "not enough meaningful quality ideas".
In the same way we thought "too many questions, not enough scientists", we now know "not enough real study on meaningful topics".
This misses that AI is already designing and carrying out experiments autonomously. This will only explode with the growth of capabilities in robotics.
Surely the way forwards is to take the results obtained by brute force with AI, for example that certain conjectures are true or false, then to use that knowledge to further human understanding.
Knowing that something is true or false will at least stop humans wasting time trying to prove or disprove it, and allow them to find a more elegant proof, or investigate the implications of the true/false result.
I think so.
Autonomous or human-directed AI agents submit their work to a public repository.
Then the scientific community draws from this pool of results, identifies the important ones, and starts working on adding the results to the greater body of scientific knowledge. This work of interpretation, synthesis and question formation should be recognised and rewarded in peer-reviewed academic journals.
I wrote a blog here talking about it: https://colinocallaghan.com/posts/answers-are-getting-cheape...
Maybe but it might also be useless. Knowing a very large number is the product of two very large primes doesn’t at all help the reader to understand factorization, for example.
> “The other side argues… human understanding is paramount, because it drives integration of new findings into the canon […] But the first side, those who emphasize correct outputs, dismisses this as gatekeeping or nostalgia.”
Is this description AKA. theory vs praxis? Academia vs Engineering?
Science has been industrialized, it has to change.
I propose a two-part approach.
First, autonomous or human-directed AI agents submit their work to a public repository.
Second, the scientific community draws from this pool of results, identifies the important ones and asks the next set of important questions. This work of interpretation, synthesis and question formation should be recognised and rewarded in peer-reviewed academic journals.
"Is science about humans achieving insight, or the archiving of verifiable solutions?"
I wonder if this dichotomy fully captures the value of scientific discoveries. One could argue that their practical impact can be independent of whether humans fully understand how they were reached.
Practical impact has always been linked but ultimately independent of knowledge. You can have very sophisticated technology based on zero actual knowledge or understanding, like roman concrete or borosillicate glass. And you can have a very deep understanding without practical impact, like lasers for decades or galactic algorithms for multiplication.
Indeed, if a machine had told Heisenberg in 1943 (or whatever?) that "the critical mass for an atomic bomb is much less than you think", we could very well have had a different world today, regardless of Heisenberg understanding it or not.
> their practical impact can be independent of whether humans fully understand how they were reached
See: most of pharma
The problem is trading off short term and long term progress. A solution alone can be useful in the short term, but if humans don't also build up understanding it will probably prevent long term progress from happening. It's much more difficult to build on top of something you don't understand.
You are conflating science with philosophy
> Verification Is Not Knowledge
A bold stand on the P = NP question.
I would rephrase it as: "Verification is not human knowledge", but that doesn't really matter. We are going to be several steps behind AI as it reaches a level of intelligence far beyond human capabilities, and we are not going to be able to catch up with it. It's like trying to beat AI at chess: we are bound to be left behind as AI continues to expand its knowledge in mathematics, physics, computer science, and other fields. Eventually, no human being will be able to reach that level of knowledge within their lifetime.
No need to start worrying about AI reaching a level of intelligence far beyond human capabilities until it actually reaches the level of humans and assuming that ever happens it could be a very very long way off. All of the intelligence "AI" has right now comes from the human data that it was trained on. It's been given enough power to crunch numbers better than we do, as any computer can, and more data to play with than any one human can retain, but none of that equals intelligence. Speculating on a sci-fi future however, if AI is ever able to create new and more advanced forms of AI, which can also create new and and more advanced forms of AI we'll be outpaced quickly.
As long as humans are in charge it's vital for us to understand what is going on - be it in science or coding, once you give up all knowledge (yes knowledge = power) not just work to AI, you can be manipulated/controlled/fooled with ease.
I have doubts about that. You don't need AI (understood as the current LLMs) to make a powerful chess engine, or computer vision or anything that reacts faster and better than a human. We've had those forever.
A good word predictor happens to be good with closed systems with very defined rules for which a huge training corpus exists and we are suddendly freaking out about how it's gonna become so much better than us at everything that we are basically obsolete.
When in doubt about where AI stands, ask it to create a poem, a joke or a riddle. And see how little actual intelligence it has.
How do we know if/when that happens if it’s beyond us to comprehend. An open ended and broad claim like this can always become true one day, similar to flying cars.
Ive never heard such drivel in my life. Are you a shill? The current "AI" is not intelligent, it can beat humans in certain areas but weve always had that with things like Deep Blue. I dont believe llms will reach human intelligence and certainly not super intelligence.