> With that interpretation, the issue becomes slightly different: is it more important that the collective understanding of the mathematical community should be as advanced as possible or that there should be answers to as many problems as possible? Or are those two aims valuable in different ways, so that there is no point in declaring one of them more important? Or are they so inextricably linked that it makes no sense to argue that one is more important than the other? And when we say “important”, for whom are we saying it is important: for mathematicians, or for society as a whole?
This is easy to me. Truth should be the North Star. If there is a fundamental truth that can be found via mathematics, then the shortest route to that truth should be preferred. While LLMs are definitely capable of solving problems in search of truth, I agree with Tao that instant "true/false" results threaten to short-circuit the traditional avenues we have used to escape local minima in the search for truth. Their products may be the junk food that provides immediate satiation in exchange for long-term health. Perhaps it's wrong, though.
I mean sure? It's clear PLT and other applied CS fields are now as good as dead. You're never seeing new React or Python emerging ever again.
And unfortunately mathematics is much more fundamental to human endeavor than this.
It is getting a lot harder for those people to justify using OpenAI to assist such endeavours. Afterall, OpenAI might just front-run you if they hear a rumor you solved some marquee problem that they can brag about in PR campaigns.
The letter is not incompatible with “pro AI in math” unless one thinks arguing against extreme behavior such as corporations using millions of dollars to scoop results makes one “anti AI”, which is not a reasonable stance in my opinion.
> AI offers the potential of enhancing and accelerating genuine mathematical study and understanding. Mathematics as a profession will need to adapt to these changes in several ways. However, whether these changes ultimately benefit the field or have a destructive effect will in large part be determined by the decisions of the humans in control of this new technology.
You can say it about becoming collectively overdependent on any technology. And I think there's a good case to be made that a similar phenomenon is true for other technologies e.g. over-reliance on (normal) computers has done similar things in my opinion, at least in my field of physics, where you get a more precise result but much less insight.
This isn’t true, as there are plenty of things proven beyond reach.
And plenty of things, eventually solvable, can create major problems that could both be avoided and the problem solved by taking a much better path.
Having technology and the ability to safely and sanely use the technology needs to progress together at a similar rate. The failure to do this is even a reasonable and common solution to the Great Filter. Jared Diamonds book “Collapse” has ample examples of cultures that wiped themselves completely out via not having this balance, so it’s not simply a theory.
This pattern of argument keeps repeating in every place.
Pro tech people: technology removes bottlenecks. Sometimes we use those bottlenecks as a side effect to build muscle and so on. But removing bottlenecks gives us much higher degrees of freedom. It is up to us to coordinate and make use of the technology.
Anti tech people: bottlenecks are fundamentally useful. They should remain and technology shouldn't remove those so easily. Humans cannot coordinate as well when the bottlenecks are removed, so lets not remove them so quickly.
Its not a conspiracy. Its 25 fields medalists who think exactly like how I put it. Ideally, they can just take whatever the technology gives as soon as possible and use it. They don't want it because they don't think the community can rearrange and coordinate such that they can make use of the new found degrees of freedom.
That's literally all there is to it - they don't believe in the rearrangement.
I don’t think the letter is even anti-tech progress. I also don’t think the tech companies are primarily pro-math progress (not that I think you think that). It’s primarily “anti-unnecessarily-destroy-the-human-systems-of-mathematics-just-for-benchmarks-and-marketing”
> … the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community. The goals of the AI companies and the goals of the mathematical community are severely misaligned.
Counterpoint: I'm not anti tech at all. In fact, I sell an AI harness for legal.
I think you've set up a false dichotomy. I'd propose to you the middle ground that a lot of us are concerned that VC-backed AI slop is "solving" problems in indigestible ways that hollow out the core. This applies in OSS as well as mathematics.
Please help me understand this and I'm asking this in good faith.
Why can't OpenAI publish whatever it wants. And the math community can use it or not use it. Fundamentally OpenAI's solutions are high signal - they are incentivised to not deliberately mislead people. Let the individuals in math community choose to read it or understand it? If OpenAI wants to publish something, let them do it in the current channels using peer review using whatever time is required.
What's wrong with this? The math community thinks this will destroy previously unwritten ways of prestige allocation and remove incentives that used to exist. I say that the community can rearrange and allocate prestige and time in different ways to maximally use the technology.
You're describing an improvised surgery on a living organism. Developing a complex system involving humans that is productive and doesn't collapse is extremely hard, so if it ain't broke don't fix it.
Might have to do with the circumstances of Open AIs conduct that was quite sketchy to say the least?
There is 25 people who see it as their responsibility to use their status in the field of maths to weigh in on public discourse regarding that field.
Fields medalists aren't made on some Fields factory. These are 25 people from different backgrounds, generations, educational institutions and countries. It's kind of incredible you guys think they decided to collude against OpenAI rather than simply addressing a concern about their field they believe is important.
Never said they were colluding. I said I have no patience for incumbents asking for restrictions on a technology that threatens the value of their expertise.
The Math community can "not use" a proof? How would that work? It's a little like coloured functions (async etc) - you have 'human proved' vs 'machine proved'?
I'm pointing out that the way Mathematics works as a discipline is that a new proof builds on existing proofs. If we have a bunch of machine-generated proofs, then a human Mathematician has to decide whether to reference any relevant machine proof that has been put out there.
If, as you suggest, human Mathematicians 'choose to ignore' a machine proof, then another human decides not to, what then? Mathematics bifurcates into 'pure human' proofs and 'mixed machine-human' or maybe 'pure machine'?
Consider that 'calculator' used to be a title for a role a human used to do. That went away, which is probably fine as there were other jobs and likely it was tedious.
Then consider that "just adapt" could be "adapt or die", and that maybe, just maybe there is no way to adapt to well-funded corporations churning out millions of proofs a minute.
I don't know, maybe AI companies have "agency" to not break everyone else's stuff, just to get more funding and a higher share price?
They can use the new proofs as foundations for future proofs.
But many folks just won't be motivated to attack or help digest solved problems because there's less extrinsic value in doing so. Tao and others argue that it's this human effort that finds human-relatable abstractions which spurn further investigation. Take the humans out of the loop, and they'll stay there, is the argument as I understand it.
I read this multiple times and also recollected the original letter. You can’t really blame me for thinking this is a straaaange request.
“Don’t help me solve my problems because it removes the incentive to be in this field” is how I hear it. Honestly.
I would say the incentives HAVE to change because of new found capabilities.
Imagine accountants asking companies to reconsider producing calculators because we used to value accountants for how well they did arithmetic!!
Edit: my main point is that the math community has full agency to do what it wants with new found tech. Instead, asking to change external entities like OpenAI to be careful with releases is a strange thing to do. Why not change yourself and adapt?
>Why can't OpenAI publish whatever it wants. And the math community can use it or not use it.
The "math community" is not an isolated entity that is free from the confines of society. It's made up of lots of people who coexist in a system that requires you to assert your right to live.
Furthermore, the "math community" is overwhelmingly supported by outside donations to keep it running. That's not to say people don't practice math for the fun of it, but that if you're researching problems like Navier-Stokes, you almost certainly are being paid by another party to do so. But those parties may hold new forms of technology over the professional mathematicians head in the name of "productivity", or they may even believe in light of this tech that paying a human to practice math is no longer worth it.
Therefore, mathematicians find themselves coerced by the market to adopt new tools in order to get by, even if the mathematical community largely finds it distasteful.
It feels like the scene from Blazing Saddles where Mel Brooks' character says "We've got to protect our phony-baloney jobs, gentlemen."
If the math community was previously not entirely aligned with what society was expecting, and these changes threaten that previous arrangement, that sounds like a "you" problem for math, not a problem for OpenAI.
If they can't align with society's needs and demands then some creative destruction is coming their way.
Next time you devote 20 years to developing the skills to further humanity only for an unethical group of people to replace you with a stolen version of your work let’s talk.
Well said. It’s on them to adapt. They make it look like it’s society’s problem (which it is) but also put the ball on OpenAI’s court which it shouldn’t.
>It is up to us to coordinate and make use of the technology.
1) Coordination is hard, and 2) "us" is a hopelessly nebulous term that appears inclusive but is almost always exclusive.
I think people would have said the creation of social media platforms like Facebook was neither good or bad, but rather it was "up to us to coordinate and make use of".
But did our society really have a say over how Facebook and other social media sites were able to embed themselves in our everyday lives? I would argue the answer is no.
I think it is easy to just roll of a local maximum, however, you may get stuck in a local minimum.
I kid, of course, but I do wonder where the use of local "maximum" comes from, what is maximum there? Why do you not see this as a landscape of hills and valleys where marbles with certain energies may indeed get stuck in deep enough holes... Of course, I just assume and picture gravity pointing down in that landscape, but hey. I'm human, I feel it is expected of me.
There's some interesting stuff in a book on Katathymic Imaginative Psychotherapy where patients are asked to picture a mountain. As far as I remember it's about using the process as diagnostic tool. What does the mountain look like? Is it a steep rising, rugged massif or a shallow hill. Are you looking up, do you picture yourself climbing it, or are you on it's top etc. While it said that it's always a contextual matter and in the conversation there was a suggestion of imagining to climb the steep massif, being potentially related to narcisim. Whenever I think of it i associatr that with casper david friedrichs painting.
as a society of researchers we've tended to cultivate pretty effective strategies for escaping local maxima. I think of it like ants, where you can see if you place an obstacle in between their nest and a foot source, they develop a path that loops around it. if you remove the obstacle, for some time they continue to follow the old looped path. However, some ants deviate and go around at random, exploring. eventually by chance one happens to find a quicker route. he gets a couple of his friends to follow him, by pheremone, and over time more and more take the quicker route, and they end up abandoning the old route
It works this way with research, with most following the current trends, and some curious souls searching around for other ideas, be they contrarians, dreamers, or just convinced of some strange truth. But if we're right, signs tend to slowly begin to point their way, and we can shift the whole hulking edifice of science towards their point of view.
The problem of llms is that while they may be able to find a shorter route, we can't follow them unless we understand the route. So the forces that slowly begin to change everyone's behavior are lost
The way you get out of a local maximum is to force yourself to try something radically new every so often, even if what you were doing before was working just fine.
This is the 'stochastic' part of 'stochastic gradient descent,' and it's as important for human minds as it is for ANNs. These math wizards seem to be stuck in a rut of their own digging.
piker · · focus · HN ↗
This is easy to me. Truth should be the North Star. If there is a fundamental truth that can be found via mathematics, then the shortest route to that truth should be preferred. While LLMs are definitely capable of solving problems in search of truth, I agree with Tao that instant "true/false" results threaten to short-circuit the traditional avenues we have used to escape local minima in the search for truth. Their products may be the junk food that provides immediate satiation in exchange for long-term health. Perhaps it's wrong, though.
varjag · · focus · HN ↗
bananaflag · · focus · HN ↗
varjag · · focus · HN ↗
And unfortunately mathematics is much more fundamental to human endeavor than this.
sampullman · · focus · HN ↗
varjag · · focus · HN ↗
sampullman · · focus · HN ↗
irthomasthomas · · focus · HN ↗
GPerson · · focus · HN ↗
> AI offers the potential of enhancing and accelerating genuine mathematical study and understanding. Mathematics as a profession will need to adapt to these changes in several ways. However, whether these changes ultimately benefit the field or have a destructive effect will in large part be determined by the decisions of the humans in control of this new technology.
topaz0 · · focus · HN ↗
Chance-Device · · focus · HN ↗
Wherever we can recognise a problem we can solve it.
varjag · · focus · HN ↗
mattmanser · · focus · HN ↗
SideQuark · · focus · HN ↗
And plenty of things, eventually solvable, can create major problems that could both be avoided and the problem solved by taking a much better path.
Having technology and the ability to safely and sanely use the technology needs to progress together at a similar rate. The failure to do this is even a reasonable and common solution to the Great Filter. Jared Diamonds book “Collapse” has ample examples of cultures that wiped themselves completely out via not having this balance, so it’s not simply a theory.
simianwords · · focus · HN ↗
Pro tech people: technology removes bottlenecks. Sometimes we use those bottlenecks as a side effect to build muscle and so on. But removing bottlenecks gives us much higher degrees of freedom. It is up to us to coordinate and make use of the technology.
Anti tech people: bottlenecks are fundamentally useful. They should remain and technology shouldn't remove those so easily. Humans cannot coordinate as well when the bottlenecks are removed, so lets not remove them so quickly.
varjag · · focus · HN ↗
simianwords · · focus · HN ↗
That's literally all there is to it - they don't believe in the rearrangement.
varjag · · focus · HN ↗
simianwords · · focus · HN ↗
varjag · · focus · HN ↗
frozenseven · · focus · HN ↗
neuroticnews25 · · focus · HN ↗
GPerson · · focus · HN ↗
neuroticnews25 · · focus · HN ↗
GPerson · · focus · HN ↗
> … the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community. The goals of the AI companies and the goals of the mathematical community are severely misaligned.
piker · · focus · HN ↗
I think you've set up a false dichotomy. I'd propose to you the middle ground that a lot of us are concerned that VC-backed AI slop is "solving" problems in indigestible ways that hollow out the core. This applies in OSS as well as mathematics.
simianwords · · focus · HN ↗
Why can't OpenAI publish whatever it wants. And the math community can use it or not use it. Fundamentally OpenAI's solutions are high signal - they are incentivised to not deliberately mislead people. Let the individuals in math community choose to read it or understand it? If OpenAI wants to publish something, let them do it in the current channels using peer review using whatever time is required.
What's wrong with this? The math community thinks this will destroy previously unwritten ways of prestige allocation and remove incentives that used to exist. I say that the community can rearrange and allocate prestige and time in different ways to maximally use the technology.
neuroticnews25 · · focus · HN ↗
You're describing an improvised surgery on a living organism. Developing a complex system involving humans that is productive and doesn't collapse is extremely hard, so if it ain't broke don't fix it.
simianwords · · focus · HN ↗
Why can’t the letter say “guys new tech dropped. We need to reorganise. Understanding is crucial” instead of asking OpenAI to change their process.
NonHyloMorph · · focus · HN ↗
ChickeNES · · focus · HN ↗
OpenAI did nothing wrong, being a Fields medalist does not give anyone a monopoly on the truth.
jambalaya8 · · focus · HN ↗
varjag · · focus · HN ↗
jambalaya8 · · focus · HN ↗
Mathematicians were somewhat wiser in the 1960s but the biologists and social sciences never were.
ChickeNES · · focus · HN ↗
GPerson · · focus · HN ↗
GPerson · · focus · HN ↗
gilleain · · focus · HN ↗
simianwords · · focus · HN ↗
gilleain · · focus · HN ↗
I'm pointing out that the way Mathematics works as a discipline is that a new proof builds on existing proofs. If we have a bunch of machine-generated proofs, then a human Mathematician has to decide whether to reference any relevant machine proof that has been put out there.
If, as you suggest, human Mathematicians 'choose to ignore' a machine proof, then another human decides not to, what then? Mathematics bifurcates into 'pure human' proofs and 'mixed machine-human' or maybe 'pure machine'?
simianwords · · focus · HN ↗
Imagine accountants saying the same thing against calculators. They had to adapt. So do mathematicians. So do I in software development.
gilleain · · focus · HN ↗
Then consider that "just adapt" could be "adapt or die", and that maybe, just maybe there is no way to adapt to well-funded corporations churning out millions of proofs a minute.
I don't know, maybe AI companies have "agency" to not break everyone else's stuff, just to get more funding and a higher share price?
gottheUIblues · · focus · HN ↗
piker · · focus · HN ↗
But many folks just won't be motivated to attack or help digest solved problems because there's less extrinsic value in doing so. Tao and others argue that it's this human effort that finds human-relatable abstractions which spurn further investigation. Take the humans out of the loop, and they'll stay there, is the argument as I understand it.
simianwords · · focus · HN ↗
“Don’t help me solve my problems because it removes the incentive to be in this field” is how I hear it. Honestly.
I would say the incentives HAVE to change because of new found capabilities.
Imagine accountants asking companies to reconsider producing calculators because we used to value accountants for how well they did arithmetic!!
Edit: my main point is that the math community has full agency to do what it wants with new found tech. Instead, asking to change external entities like OpenAI to be careful with releases is a strange thing to do. Why not change yourself and adapt?
jplusequalt · · focus · HN ↗
The "math community" is not an isolated entity that is free from the confines of society. It's made up of lots of people who coexist in a system that requires you to assert your right to live.
Furthermore, the "math community" is overwhelmingly supported by outside donations to keep it running. That's not to say people don't practice math for the fun of it, but that if you're researching problems like Navier-Stokes, you almost certainly are being paid by another party to do so. But those parties may hold new forms of technology over the professional mathematicians head in the name of "productivity", or they may even believe in light of this tech that paying a human to practice math is no longer worth it.
Therefore, mathematicians find themselves coerced by the market to adopt new tools in order to get by, even if the mathematical community largely finds it distasteful.
pfdietz · · focus · HN ↗
If the math community was previously not entirely aligned with what society was expecting, and these changes threaten that previous arrangement, that sounds like a "you" problem for math, not a problem for OpenAI.
If they can't align with society's needs and demands then some creative destruction is coming their way.
NonHyloMorph · · focus · HN ↗
pfdietz · · focus · HN ↗
GPerson · · focus · HN ↗
ChickeNES · · focus · HN ↗
GPerson · · focus · HN ↗
jplusequalt · · focus · HN ↗
How is a chatbot going to end human labor? Where are the millions of robots required to do all the various other jobs in the economy.
You and everyone else with this rhetoric must see AI as the rapture or something.
ChickeNES · · focus · HN ↗
You're kidding, right?
<a href="https://shop.unitree.com/" rel="nofollow">https://shop.unitree.com/ <a href="https://www.figure.ai/" rel="nofollow">https://www.figure.ai/ etc
simianwords · · focus · HN ↗
ChickeNES · · focus · HN ↗
jplusequalt · · focus · HN ↗
1) Coordination is hard, and 2) "us" is a hopelessly nebulous term that appears inclusive but is almost always exclusive.
I think people would have said the creation of social media platforms like Facebook was neither good or bad, but rather it was "up to us to coordinate and make use of".
But did our society really have a say over how Facebook and other social media sites were able to embed themselves in our everyday lives? I would argue the answer is no.
nkrisc · · focus · HN ↗
teekert · · focus · HN ↗
I kid, of course, but I do wonder where the use of local "maximum" comes from, what is maximum there? Why do you not see this as a landscape of hills and valleys where marbles with certain energies may indeed get stuck in deep enough holes... Of course, I just assume and picture gravity pointing down in that landscape, but hey. I'm human, I feel it is expected of me.
NonHyloMorph · · focus · HN ↗
skywal_l · · focus · HN ↗
GPerson · · focus · HN ↗
RugnirViking · · focus · HN ↗
It works this way with research, with most following the current trends, and some curious souls searching around for other ideas, be they contrarians, dreamers, or just convinced of some strange truth. But if we're right, signs tend to slowly begin to point their way, and we can shift the whole hulking edifice of science towards their point of view.
The problem of llms is that while they may be able to find a shorter route, we can't follow them unless we understand the route. So the forces that slowly begin to change everyone's behavior are lost
CamperBob2 · · focus · HN ↗
This is the 'stochastic' part of 'stochastic gradient descent,' and it's as important for human minds as it is for ANNs. These math wizards seem to be stuck in a rut of their own digging.