> But even if it had solved every problem in the Langlands program, to imagine that would have “solved number theory” would be as naive as saying that the construction of the periodic table solved chemistry.
Of course if you solve any existing problem, new ones appear. That's not the point. The point is that AI will be able to advance on any problem better than any human.
But in a human way? I don't think so. The 700+ solutions that were put out by openAI are in no way accepted as solved until humans say so. It's kind of like saying SC2 was solved when Alpha beat the best players. The professional community just went on playing much the same. Math should do the same. Just with better tools
Mathematics as a field will not cease to exist, and not everyone will be interested in (or qualified to) managing the fields progress and its applications.
Isn't it also possible that the written proofs themselves are incorrect, say, for example, by mis-specification of constraints? Let's say I publish what I claim is a proof that 2+2=4, but in the Lean specification, I proved 1+1=2.
the impression i get is that people don’t per se assert that exploitable bugs exist in Lean, but that the volume of (code) proofs published represent a new magnitude of challenge to the integrity of Lean.
the obverse would be to assert that Lean (or any other theorem prover) is infallible under all circumstances, present and future - an even weightier claim in my opinion.
I keep seeing people point to AI solved games as evidence that AI advancements are less impactful than we might think. Usually it's chess ("today there are more players than ever!"). Most of the time these are bad analogies. Games are played for entertainment, so productivity is meaningless.
I never advanced in math past high school, but my assumption would be that we as a society aren't paying mathematicians to have fun[0]. The discoveries mathematicians make must translate into real improvements in engineering and other life improving fields. So why would we pay mathematicians to work on math much the same way, if a new machine-led way makes these discoveries faster and cheaper?
[0] Being a little facetious. I know I don't know what I don't know.
Mathematicians can have as much fun as they want while working on math problems, they have the skills and the brains, why shouldn't they enjoy their work?
With math you never know up front what 'real improvements in engineering and other life improving fields' will require some key bit of it that someone interested in pure math came up with a decade or two (or 10) before we found an application.
I don’t think we know whether or not that’s true yet. Imagine a problem which requires a paradigm shift or new novel techniques to solve. There is no proof (yet) that an AI could create one.
It's not magical abilities - humans have proved for millenia that they can find novel solutions to problems - we have no idea how that comes to be though (which could be called magic I guess)
At issue with AI is that it's searching an existing corpus for fragments of solutions generated by humans - that's not necessarily novel, and we've not yet worked out how to make the machines actually invent.
LLM agents are perfectly capable of "advancing" my codebase down bizarre, esoteric rabbitholes. Meanwhile, the value remains undelivered.
Many crystals, likewise, are advancing their fantastic complexities in the deep, dark recesses beneath the crust of the earth, but does it make a sound? Who gives a shit.
Many paperclips, indeed, can be churned out. Even we can be converted into paperclips, remember.
> The point is that AI will be able to advance on any problem better than any human.
If that was true it would of course be significant.
If you had no morals, 2 trillion dollars to spend, ability to commit intellectual property theft without consequences, and most of the smartest people in the world actively working to advance your cause... ...you really think you couldn't compete with the clankers?
It’s amazing for me to see math research going from craft to technology.
CS had this moment decades ago, sans some theoretical parts that are joining the bandwagon now.
I did a bit of math research in grad school collaborating with my math postdoc roommate. I found the aversion to any computation making its way into the craft to be odd decades ago.
Well, now the proof’s in the AI generated pudding.
> But even if it had solved every problem in the Langlands program, to imagine that would have “solved number theory” would be as naive as saying that the construction of the periodic table solved chemistry.
This analogy is pants on head stupid. They're talking as though the only thing AI will ever solve is the Langlands program, not as though we have discovered a generic tool.
It's like saying "they drove the car one mile -- and every mile driven leads to more roads that we can trot along, why are you so worried about the future of horses?"
People are allowed to process their anxieties. And processing takes time.
That said publicly doing it on the great modern internet attention/noise factory complicates the story.
Everyone is surprised that a person that some consider to be one of the greatest modern mathematicians can have such obtuse views of technology and its own field.
Sure, or you can think for yourself for five minutes on the implications of a general proof machine, and whether it's likely to continue producing proofs.
If you've forgotten how to think for yourself, you can also ask an LLM.
The host of the blog, Tao, was an early booster. He didn't think through the implications, and seems to have expected it to remain unable to do interesting work. Today he's on a "war footing".
I don't think mathematics are uniquely skilled at predicting the future, and the impacts of AI on their profession.
It is weird. From what I can tell, you and I have quite similar expectations on what AI will be able to do in the future, but for some reason you are much more dismissive of Taos opinion.
I perfectly understand his point and it is not about being selfishly frustrated by a machine being better than him. Is that really your interpretation of the discourse?
Logic is logic, you don't need a specialist's opinion on every aspect of a specialist field. I've had eye opening insights delivered to me on problems I'm working on by people who barely know how to use a computer.
> Under a partnership, the Simons Foundation, Anthropic and OpenAI will commit $15 million in combined funding and resources. The foundation will manage and award funding, including through an open call for proposals, to support workshops and initiatives that help researchers evaluate recent AI-assisted results, learn and use new tools, share perspectives and shape collective standards for AI use.
[delayed]
Isn't it the passage of mathematics from the age of craftsmanship to the age of industrial making ?
My recent take on AI is that people haven't adapted to the new huge potential of the tool, and don't dream big enough (yet).
It's like seeing a car engine for the first time, lamenting about the future of horses, and not realizing it'll also help us fly.
> But even if it had solved every problem in the Langlands program, to imagine that would have “solved number theory” would be as naive as saying that the construction of the periodic table solved chemistry.
Of course if you solve any existing problem, new ones appear. That's not the point. The point is that AI will be able to advance on any problem better than any human.
But in a human way? I don't think so. The 700+ solutions that were put out by openAI are in no way accepted as solved until humans say so. It's kind of like saying SC2 was solved when Alpha beat the best players. The professional community just went on playing much the same. Math should do the same. Just with better tools
Math is too boring as a spectator sport. It's funded because of its practical use.
There's going to be some hobbyists doing math in their basements, but there's unlikely to be a future for professional mathematicians.
Haha, the breaks from reality there are two, one professionals do not spend most of their time inventing proofs, and two, practical use? :-)
Mathematics as a field will not cease to exist, and not everyone will be interested in (or qualified to) managing the fields progress and its applications.
The proofs may not yet be understood, but to claim they should not yet be accepted as solved is to claim there is a bug in Lean, which is a big claim.
Isn't it also possible that the written proofs themselves are incorrect, say, for example, by mis-specification of constraints? Let's say I publish what I claim is a proof that 2+2=4, but in the Lean specification, I proved 1+1=2.
the impression i get is that people don’t per se assert that exploitable bugs exist in Lean, but that the volume of (code) proofs published represent a new magnitude of challenge to the integrity of Lean.
the obverse would be to assert that Lean (or any other theorem prover) is infallible under all circumstances, present and future - an even weightier claim in my opinion.
I keep seeing people point to AI solved games as evidence that AI advancements are less impactful than we might think. Usually it's chess ("today there are more players than ever!"). Most of the time these are bad analogies. Games are played for entertainment, so productivity is meaningless.
I never advanced in math past high school, but my assumption would be that we as a society aren't paying mathematicians to have fun[0]. The discoveries mathematicians make must translate into real improvements in engineering and other life improving fields. So why would we pay mathematicians to work on math much the same way, if a new machine-led way makes these discoveries faster and cheaper?
[0] Being a little facetious. I know I don't know what I don't know.
Mathematicians can have as much fun as they want while working on math problems, they have the skills and the brains, why shouldn't they enjoy their work?
With math you never know up front what 'real improvements in engineering and other life improving fields' will require some key bit of it that someone interested in pure math came up with a decade or two (or 10) before we found an application.
I don’t think we know whether or not that’s true yet. Imagine a problem which requires a paradigm shift or new novel techniques to solve. There is no proof (yet) that an AI could create one.
We have to come to terms with the reality, and we must find a way of existing with this new super tool
Why do you believe human brains are magic? We may need some breakthroughs, but trillions of investment tends to produce those.
And it's becoming less clear over time that a breakthrough will be needed.
It's not magical abilities - humans have proved for millenia that they can find novel solutions to problems - we have no idea how that comes to be though (which could be called magic I guess)
At issue with AI is that it's searching an existing corpus for fragments of solutions generated by humans - that's not necessarily novel, and we've not yet worked out how to make the machines actually invent.
Why do you believe that LLMs are good at the same things humans are?
I believe that we're investing trillions into making it so.
Did any ai made any new interesting question or conjecture?
> The point is that AI will be able to advance on any problem better than any human.
Define "better".
Define "advance"!
LLM agents are perfectly capable of "advancing" my codebase down bizarre, esoteric rabbitholes. Meanwhile, the value remains undelivered.
Many crystals, likewise, are advancing their fantastic complexities in the deep, dark recesses beneath the crust of the earth, but does it make a sound? Who gives a shit.
Many paperclips, indeed, can be churned out. Even we can be converted into paperclips, remember.
All but a negligible amount of novel mathematical results going forward will have had substantial LLM involvement
But how do you know which problems are worth making progress on? Traditionally, you'd find those by working on solving previous problems.
ANY problem?
> The point is that AI will be able to advance on any problem better than any human.
If that was true it would of course be significant.
If you had no morals, 2 trillion dollars to spend, ability to commit intellectual property theft without consequences, and most of the smartest people in the world actively working to advance your cause... ...you really think you couldn't compete with the clankers?
It’s amazing for me to see math research going from craft to technology.
CS had this moment decades ago, sans some theoretical parts that are joining the bandwagon now.
I did a bit of math research in grad school collaborating with my math postdoc roommate. I found the aversion to any computation making its way into the craft to be odd decades ago.
Well, now the proof’s in the AI generated pudding.
Have the pro-AI people finally found a new mathematician? Otherwise it is always the same 10 people on Tao's blog citing each other.
This guest author runs a seminar to lure people into AI:
https://math.uchicago.edu/~fcale/AI.html
> But even if it had solved every problem in the Langlands program, to imagine that would have “solved number theory” would be as naive as saying that the construction of the periodic table solved chemistry.
This analogy is pants on head stupid. They're talking as though the only thing AI will ever solve is the Langlands program, not as though we have discovered a generic tool.
It's like saying "they drove the car one mile -- and every mile driven leads to more roads that we can trot along, why are you so worried about the future of horses?"
People are allowed to process their anxieties. And processing takes time. That said publicly doing it on the great modern internet attention/noise factory complicates the story.
Everyone is surprised that a person that some consider to be one of the greatest modern mathematicians can have such obtuse views of technology and its own field.
I think I’ll take the professional mathematician perception of how AI affects his field over random HN commenter saying it’s “pants on head stupid”
Sure, or you can think for yourself for five minutes on the implications of a general proof machine, and whether it's likely to continue producing proofs.
If you've forgotten how to think for yourself, you can also ask an LLM.
The host of the blog, Tao, was an early booster. He didn't think through the implications, and seems to have expected it to remain unable to do interesting work. Today he's on a "war footing".
I don't think mathematics are uniquely skilled at predicting the future, and the impacts of AI on their profession.
It is weird. From what I can tell, you and I have quite similar expectations on what AI will be able to do in the future, but for some reason you are much more dismissive of Taos opinion.
I perfectly understand his point and it is not about being selfishly frustrated by a machine being better than him. Is that really your interpretation of the discourse?
Neither are mindless AI boosters
https://fortune.com/article/ai-godfather-radiologists-obsole...
Ironic that you resort to “think for yourself” as your silly name calling go to btw
Logic is logic, you don't need a specialist's opinion on every aspect of a specialist field. I've had eye opening insights delivered to me on problems I'm working on by people who barely know how to use a computer.
You are welcome to opine on anything but there’s a reason we’re reading his blog and you’re down here in the comments
[flagged]
> Under a partnership, the Simons Foundation, Anthropic and OpenAI will commit $15 million in combined funding and resources. The foundation will manage and award funding, including through an open call for proposals, to support workshops and initiatives that help researchers evaluate recent AI-assisted results, learn and use new tools, share perspectives and shape collective standards for AI use.
"Normal technology"?