Does anyone have to understand AI output when it comes to math? Then that someone has to be trained in math. Yeah, for all intents and purposes that person is a mathematician. Maybe not the one who gets money for that in which case they are not a professional mathematician. Maybe these paid guys will disappear. However if AI keeps churning out new stuff nobody understands humanity will have to create a new category of employment for those who do to make sense of all that. Mathematicians, then, are back in the game again.
One possibility is that AI keeps churning out new math and funnels it into other branches of science and engineering without any human input. At which point math becomes a black box. Maybe in that case human mathematicians might become obsolete. But then other branches will start becoming incomprehensible as well.
Human Mathematics is what lives in the head of all of humanity, not a serialized proof of a theorem or conjecture. Yes the other kinds maybe useful, may even pay the bills, but as long as humans enjoy mathematics the human side will survive.
People still go on runs although that's not what wins wars today.
Well, thank you for the context of (2) and (3), but you’re dead wrong about (1), because Kaczynski was uniquely qualified to accurately predict LLMs, and here is the proof, complete with an analogy of headstone carving.
So this is our battle-cry: “Ted Kaczynski wasn’t wrong!”
Personally, I found that people are impressed with AI for subjects they simply don't understand, and when an expert works with AI, they're often underwhelmed. So while we're seeing some mathematics being automated and proved, I think there's a long way to go before we automate proofs with meaningful human value.
He was a bit ahead of the trend. I think mathematicians may be able to use AI to explore distant areas of maths. It's not like it's finite.
I would probably be more inclined to do serious maths now with AI assistance than before without as I'm not good enough to make decent progress. I've long been curious what the renormalization stuff in quantum mechanics is about and how to combine that with gravitation but it's way beyond my brain cells.
In your letter of December 14, you ask me whether mathematics is a worthwhile endeavor. Mathematics absolutely is not a worthwhile endeavor! I can imagine only three possible reasons for studying mathematics:
(1) Entertainment.
(2) To promote technological progress.
(3) To promote one’s own career.
Reason (1) is harmless; but one doesn’t refer to entertainment as a “worthwhile endeavor”; it’s just a pastime.
As for reason (2), modern technology is the worst thing that ever happened to the world, and to promote its progress is nothing short of criminal. Read Our Final Century, by Martin Rees; or read “Why the Future Doesn’t Need Us,” an article by Bill Joy that appeared in Wired magazine, April, 2000.
As for reason (3), to choose mathematics as one’s career would be very risky. Not long ago I received a letter from a gravestone sculptor whose craft had been rendered obsolete by a laser-guided machine that carved gravestones automatically. He was in his forties, unable to find work, and depressed. Maybe you think that can’t happen to you if you become a mathematician. But you’re wrong. Martin Rees, Bill Joy, and many other distinguished experts believe that within a few decades machines will be developed that will be more intelligent than even the smartest human beings. When that happens, people will be obsolete; they will be phased out and will be replaced by computers and robots. This will happen to everyone eventually, but mathematicians probably will become obsolete before anyone else does, because mathematics is more amenable to computerization than any other field. Hence, computers probably will surpass humans in mathematics before they do so in other areas.
In the same sense as pharmacology is a branch of physics. Technically, yes. Realistically the overlap is small and you don't need one for the other most of the time.
I saw a cryptographer interviewed. She was maybe 20yo and was working onboard a US aircraft carrier. Installing and managing cryptographic systems does not make one a cryptographer. Doing math via computer programing also does not make one a mathematician any more than driving a car makes one a mechanic.
As my mathematical statistics professor told us on the first day, “statistics is not mathematics.” It’s a good idea to remember: if a branch of the subject x is called “mathematical x,” then x in general is not totally mathematical and can be studied to some extent without mathematics.
For instance, in mathematics, we have A ⇒ A (every statement implies itself, for instance "if it rains, then it rains"); and analogously, in programming, we have the identity function of type A → A (which reads a value as input and outputs the same value).
This is the tip of an enormous iceberg identifying, in a certain precise sense, proving with programming (and stating mathematical assertions with specifying the desired behavior of a program).
However, programming is a bit more general than proving: Circular proofs are simply of no value, whereas looping programs can still be valuable. For instance, I for sure hope that the main loop of the browser I'm currently using to fill out this textbox does not prematurely stop.
cartographery and translation are vastly smaller professions than they were, that have been altered as to where and how they are practiced and going forward are vulnerable to bieng abused and manipulated if they fall under central controll with closed source software.
It absolutely is. I once read a tiny part one of his manifesto, and it was full of weird leftist boogeymen without any justification. It made sense that he went ahead with terrorism rather than trying to argue his point peacefully.
What does "amenable to computerisation" even mean? Typist used to be a job, but it's become computerised. Stuff like data entry is surely not for away.
The Unabomber had semi-correct problem identification, but completely worthless prescription like else anyone unable to separate reality from fiction basing their ideas on a Hollywood revenge movie or becoming a crazy terrorist with a cause that maybe valid seeing themselves as "good guy freedom-fighters" but alienates and harms many. People might've been interested in helping to counteract the effects or sources of a problem if a change advocate approached them in a manner that was constructive, achievable, rational, and considerate. Instead, evil, lazy actions make the cause a pariah and its supporters enemies to most.
He had infinite options he failed to exercise, like getting involved in the humanities (sociology, philosophy, law) and/or community building to do the groundwork necessary to contribute positive change rather than illusionary shortcuts to fruitless impact, needless suffering, and self-destruction.
AGI is a canard. Too much money in electricity, servers, land, and technological advances would be needed to build and operate sufficiently capable digital reasoning. Domain-specific pseudo-intelligence task automation will continue here and there with LLMs, deep learning, and such, but no one is building just one "brain" for less than $5T and it probably wouldn't be very performant.
Current AI is totally incapable of replacing expert human judgment for almost everything because they lack constraints, predictability, and reliability. Also, most models hallucinate worthless, incorrect answers so often that they should be relegated to glorified creative, entertainment, and task-acceleration work for the foreseeable future and not be given wildly-inappropriate power like giving a toddler a nuke. Furthermore, the appeal to LLM authority fallacy is a dangerous trend of unthinking, laziness of people failing to think skeptically and find sources for themselves. Finally, too many laypeople and wild-eyed techbros are projecting and imagining AI capabilities that aren't really there and may never exist, but then making much bigger mistakes of irrational, risky bets on their preconceived conclusions, and telling us we should worship the billionaires, accept layoffs, accept panopticon surveillance, accept their loud, polluting data centers in our literal backyards.. for what good?
Its already replacing human experts. Watch the bond market self off currently happening in US. Driven by hordes of AI agents doing thousands of things faster than experts can blink. The experts at the Treasury tried to react at traditional human speed. Within a day the agentic horde detected the moves and counter reacted. Its like watching chimps throwing stones at a hurricane. The chimp troupe is quite unconcious about the randomness and surprises ahead.
Replacing people willy-nilly with AI is a stupid fad that won't work the way they think it will in most instances. AI doesn't impart judgment, constraints, reasoning, or correctness so far the way a human can and likely never will because AGI is a fantasy. Owners and managers will only learn this lesson after they suffer failure from their own stupidity and recklessness.
Another angle is excuses for mass layoffs are continuation of the Powell memo neoliberalism agenda of suppressing wages by keep workers desperate and partly a consequence of rising interest rates since there's no more free money.
Workers need to stop depending on megacorps for stability and form worker-owned co-ops that compete with and supplant unstable, mercurial megacorps.
His impact has not been fruitless, to the contrary and case in point, we're now discussing about him in here and in other similar places. Had he chosen the lame road of becoming a humanities thingie nothing of his legacy would have remained.
> People might've been interested in helping to counteract the effects or sources of a problem if a change advocate approached them in a manner that was constructive, achievable, rational, and considerate.
I mean this is just obviously and flagrantly untrue, eg. Greta Thunberg became a culture war boogeyman for half of the political spectrum over significantly more moderate views expressed in exactly the way you describe. If anything, acting like a bitch just emboldens the type who cause problems to cause more problems when they see these signs of weakness and zero will to resist them, as we see happening with acts of complete irrationality like Trump making a war against fucking wind turbines a top priority of the US government's agenda.
When you tell people they're protesting the wrong way, you're really just saying "I don't want to hear your complaints. Make them in a way that doesn't bother me so I can ignore them".
I generally agree with you, but I do think that terrorism is objectively the wrong way to protest. I’d say the Unabomber’s victims and their families were slightly more than “bothered”.
Becoming a lawyer or getting a polisci degree is typically a stepping stone to becoming an elected official by understanding how the system of laws operates in order to change them. Bernie Sanders, for example. People like Darline Graham who don't know anything about anything and are there for feelings of nepotism shouldn't hold office... and I sure hope neither Hunter Biden nor Trump kids ever win office either. Elected office needs competency and requisite experience for the job first.
You're cherrypicking polarization as a counterexample against trying to be better. No one figure is going to appeal to all people, but actively pushing away a sizable fraction with negativity is the surest way to carry water for being divided-and-conquered.
If people aren't willing to listen to constructive feedback that maybe they are protesting or evangelizing a cause less effectively than they could be, then that's their ego and stupidity. Sensible people may have mentors and can evaluate feedback from all sources to pick through it for useful bits.
Does anyone have to understand AI output when it comes to math? Then that someone has to be trained in math. Yeah, for all intents and purposes that person is a mathematician. Maybe not the one who gets money for that in which case they are not a professional mathematician. Maybe these paid guys will disappear. However if AI keeps churning out new stuff nobody understands humanity will have to create a new category of employment for those who do to make sense of all that. Mathematicians, then, are back in the game again.
One possibility is that AI keeps churning out new math and funnels it into other branches of science and engineering without any human input. At which point math becomes a black box. Maybe in that case human mathematicians might become obsolete. But then other branches will start becoming incomprehensible as well.
Human Mathematics is what lives in the head of all of humanity, not a serialized proof of a theorem or conjecture. Yes the other kinds maybe useful, may even pay the bills, but as long as humans enjoy mathematics the human side will survive.
People still go on runs although that's not what wins wars today.
The interesting context: 1) this has nothing to do with LLMs 2) this is a pdf of a handwritten letter and 3) this was written by the unabomber
I would like to also know the date.
Dec 2004
Yup. Few here read the article before jumping to the AI conclusion. Even fewer even know what Freedom Club was all about.
Well, thank you for the context of (2) and (3), but you’re dead wrong about (1), because Kaczynski was uniquely qualified to accurately predict LLMs, and here is the proof, complete with an analogy of headstone carving.
So this is our battle-cry: “Ted Kaczynski wasn’t wrong!”
Personally, I found that people are impressed with AI for subjects they simply don't understand, and when an expert works with AI, they're often underwhelmed. So while we're seeing some mathematics being automated and proved, I think there's a long way to go before we automate proofs with meaningful human value.
He was a bit ahead of the trend. I think mathematicians may be able to use AI to explore distant areas of maths. It's not like it's finite.
I would probably be more inclined to do serious maths now with AI assistance than before without as I'm not good enough to make decent progress. I've long been curious what the renormalization stuff in quantum mechanics is about and how to combine that with gravitation but it's way beyond my brain cells.
Transcribed letter (from chatgpt):
Dear Mr.,
In your letter of December 14, you ask me whether mathematics is a worthwhile endeavor. Mathematics absolutely is not a worthwhile endeavor! I can imagine only three possible reasons for studying mathematics:
(1) Entertainment. (2) To promote technological progress. (3) To promote one’s own career.
Reason (1) is harmless; but one doesn’t refer to entertainment as a “worthwhile endeavor”; it’s just a pastime.
As for reason (2), modern technology is the worst thing that ever happened to the world, and to promote its progress is nothing short of criminal. Read Our Final Century, by Martin Rees; or read “Why the Future Doesn’t Need Us,” an article by Bill Joy that appeared in Wired magazine, April, 2000.
As for reason (3), to choose mathematics as one’s career would be very risky. Not long ago I received a letter from a gravestone sculptor whose craft had been rendered obsolete by a laser-guided machine that carved gravestones automatically. He was in his forties, unable to find work, and depressed. Maybe you think that can’t happen to you if you become a mathematician. But you’re wrong. Martin Rees, Bill Joy, and many other distinguished experts believe that within a few decades machines will be developed that will be more intelligent than even the smartest human beings. When that happens, people will be obsolete; they will be phased out and will be replaced by computers and robots. This will happen to everyone eventually, but mathematicians probably will become obsolete before anyone else does, because mathematics is more amenable to computerization than any other field. Hence, computers probably will surpass humans in mathematics before they do so in other areas.
Sincerely yours, Ted Kaczynski
He skips over understanding our world which is probably the reason most pure maths is done.
The Joy article mentions is here https://www.wired.com/2000/04/joy-2/ by the way, and includes discussion of Kaczynski.
Remember, programming is a branch of mathematics.
Programming is the mathematical equivalent of brick layers looking at architects and saying "I could do that."
Using GenAI, they certainly can.
Do architects lay bricks often? Wasn't aware.
computer science, yes, 100% a branch of math
programming is more like communicating to a computer to convince them to do some task. has always been like this, and this will not change
In the same sense as pharmacology is a branch of physics. Technically, yes. Realistically the overlap is small and you don't need one for the other most of the time.
>> programming is a branch of mathematics.
I saw a cryptographer interviewed. She was maybe 20yo and was working onboard a US aircraft carrier. Installing and managing cryptographic systems does not make one a cryptographer. Doing math via computer programing also does not make one a mathematician any more than driving a car makes one a mechanic.
so is physics?
Theoretical physics, sure, ok. Not experimental physics though.
That's arguable.
That too. Statistics used to analyze results and turn them into conclusions.
As my mathematical statistics professor told us on the first day, “statistics is not mathematics.” It’s a good idea to remember: if a branch of the subject x is called “mathematical x,” then x in general is not totally mathematical and can be studied to some extent without mathematics.
What’s the mathematical proof of this?
The Curry-Howard correspondence.
For instance, in mathematics, we have A ⇒ A (every statement implies itself, for instance "if it rains, then it rains"); and analogously, in programming, we have the identity function of type A → A (which reads a value as input and outputs the same value).
This is the tip of an enormous iceberg identifying, in a certain precise sense, proving with programming (and stating mathematical assertions with specifying the desired behavior of a program).
However, programming is a bit more general than proving: Circular proofs are simply of no value, whereas looping programs can still be valuable. For instance, I for sure hope that the main loop of the browser I'm currently using to fill out this textbox does not prematurely stop.
>we have the identity function of type A → A (which reads a value as input and outputs the same value)
That only exists in theoretical computer science. In real computer programming, you always have some bounds to the value of A.
I think it is time to repost Against Curry-Howard Mysticism (https://liamoc.net/forest/loc-000S/index.xml)
It's starting to look like the first profession on Earth will also be the last profession ...
Mathematicians can always switch to a career as a worker in a DRAM factory ...
Very prescient from Uncle Ted.
So many things he got right (except you know what)
cartographery and translation are vastly smaller professions than they were, that have been altered as to where and how they are practiced and going forward are vulnerable to bieng abused and manipulated if they fall under central controll with closed source software.
It’s good to know Ted Kaczynski’s thinking is as lazy as every internet shit poster.
It absolutely is. I once read a tiny part one of his manifesto, and it was full of weird leftist boogeymen without any justification. It made sense that he went ahead with terrorism rather than trying to argue his point peacefully.
Maybe the justification is in another part of this manifesto, but you were too lazy to read it.
Just give it a look mate.
What does "amenable to computerisation" even mean? Typist used to be a job, but it's become computerised. Stuff like data entry is surely not for away.
The Unabomber had semi-correct problem identification, but completely worthless prescription like else anyone unable to separate reality from fiction basing their ideas on a Hollywood revenge movie or becoming a crazy terrorist with a cause that maybe valid seeing themselves as "good guy freedom-fighters" but alienates and harms many. People might've been interested in helping to counteract the effects or sources of a problem if a change advocate approached them in a manner that was constructive, achievable, rational, and considerate. Instead, evil, lazy actions make the cause a pariah and its supporters enemies to most.
He had infinite options he failed to exercise, like getting involved in the humanities (sociology, philosophy, law) and/or community building to do the groundwork necessary to contribute positive change rather than illusionary shortcuts to fruitless impact, needless suffering, and self-destruction.
AGI is a canard. Too much money in electricity, servers, land, and technological advances would be needed to build and operate sufficiently capable digital reasoning. Domain-specific pseudo-intelligence task automation will continue here and there with LLMs, deep learning, and such, but no one is building just one "brain" for less than $5T and it probably wouldn't be very performant.
Current AI is totally incapable of replacing expert human judgment for almost everything because they lack constraints, predictability, and reliability. Also, most models hallucinate worthless, incorrect answers so often that they should be relegated to glorified creative, entertainment, and task-acceleration work for the foreseeable future and not be given wildly-inappropriate power like giving a toddler a nuke. Furthermore, the appeal to LLM authority fallacy is a dangerous trend of unthinking, laziness of people failing to think skeptically and find sources for themselves. Finally, too many laypeople and wild-eyed techbros are projecting and imagining AI capabilities that aren't really there and may never exist, but then making much bigger mistakes of irrational, risky bets on their preconceived conclusions, and telling us we should worship the billionaires, accept layoffs, accept panopticon surveillance, accept their loud, polluting data centers in our literal backyards.. for what good?
Its already replacing human experts. Watch the bond market self off currently happening in US. Driven by hordes of AI agents doing thousands of things faster than experts can blink. The experts at the Treasury tried to react at traditional human speed. Within a day the agentic horde detected the moves and counter reacted. Its like watching chimps throwing stones at a hurricane. The chimp troupe is quite unconcious about the randomness and surprises ahead.
High frequency trading has been a reality for decades. What’s different now?
HFT strategies are simple. They are also static (they can re-fit, but fundamentally remain the same).
Putting LLMs in the loop now gives you reactive strategies. The agents can see the reaction of the market and adjust or change direction.
This creates complex feedback loops that can't be understood at human speed.
> HFT strategies are simple. They are also static (they can re-fit, but fundamentally remain the same).
What makes you say this?
Replacing people willy-nilly with AI is a stupid fad that won't work the way they think it will in most instances. AI doesn't impart judgment, constraints, reasoning, or correctness so far the way a human can and likely never will because AGI is a fantasy. Owners and managers will only learn this lesson after they suffer failure from their own stupidity and recklessness.
Another angle is excuses for mass layoffs are continuation of the Powell memo neoliberalism agenda of suppressing wages by keep workers desperate and partly a consequence of rising interest rates since there's no more free money.
Workers need to stop depending on megacorps for stability and form worker-owned co-ops that compete with and supplant unstable, mercurial megacorps.
> o fruitless impact,
His impact has not been fruitless, to the contrary and case in point, we're now discussing about him in here and in other similar places. Had he chosen the lame road of becoming a humanities thingie nothing of his legacy would have remained.
> People might've been interested in helping to counteract the effects or sources of a problem if a change advocate approached them in a manner that was constructive, achievable, rational, and considerate.
I mean this is just obviously and flagrantly untrue, eg. Greta Thunberg became a culture war boogeyman for half of the political spectrum over significantly more moderate views expressed in exactly the way you describe. If anything, acting like a bitch just emboldens the type who cause problems to cause more problems when they see these signs of weakness and zero will to resist them, as we see happening with acts of complete irrationality like Trump making a war against fucking wind turbines a top priority of the US government's agenda.
When you tell people they're protesting the wrong way, you're really just saying "I don't want to hear your complaints. Make them in a way that doesn't bother me so I can ignore them".
I generally agree with you, but I do think that terrorism is objectively the wrong way to protest. I’d say the Unabomber’s victims and their families were slightly more than “bothered”.
He said you can change the world by becoming a lawyer. This is such a funny take.
Becoming a lawyer or getting a polisci degree is typically a stepping stone to becoming an elected official by understanding how the system of laws operates in order to change them. Bernie Sanders, for example. People like Darline Graham who don't know anything about anything and are there for feelings of nepotism shouldn't hold office... and I sure hope neither Hunter Biden nor Trump kids ever win office either. Elected office needs competency and requisite experience for the job first.
You're cherrypicking polarization as a counterexample against trying to be better. No one figure is going to appeal to all people, but actively pushing away a sizable fraction with negativity is the surest way to carry water for being divided-and-conquered.
If people aren't willing to listen to constructive feedback that maybe they are protesting or evangelizing a cause less effectively than they could be, then that's their ego and stupidity. Sensible people may have mentors and can evaluate feedback from all sources to pick through it for useful bits.
> acting like a bitch
Chill out and take your culture war flame bait elsewhere. https://news.ycombinator.com/newsguidelines.html