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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.
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.
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.
Terry Tao's actually one of the more vocal proponents of AI-assisted formalization right now, he's not exactly a counterexample here. He's using Lean and AI tools to check proofs faster, not treating it as beneath serious mathematicians.
I think humans will always value human labor in some professions like athletics and some entertainment and service. Consider how chess has not been diminished as a human competition despite computers being much better. We prefer human drama.
High end service will likely be human to distinguish itself from all the cheaper automation. Listening to humans play live music won't go away. Having a human touch when being cared for won't either.
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.
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.
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.
Ran into this arguing with a math PhD once. Told him fine, prove termination of my build script using the Church-Rosser theorem then. He couldn't, obviously, because 90% of my job is fighting flaky APIs and config drift, not logic. Math background helps but it's not what I do all day.
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.
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.
Good point. At least 20+ years until you could see a start of what he describes in the letter. Wondering why this is really the case what he describes...
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?
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.
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.
> 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".
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.
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”.
Read the whole thing back when it circulated on a math blog. The actual argument is narrower than the title suggests, it's about proof verification and automated theorem provers eating the "checking" side of math, not creativity. Coq and Lean are basically living out that prediction now, just slower and messier than he expected.
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.
We ran a shop for 12 years, no AC in summer, dial-up internet till 2009. Nobody signed up for "primitive." The second hot water and a phone showed up, everyone took it and never looked back. That's not oppression, that's just people voting with their feet.
Well, ask any person medical dependent advanced tech on whether they want to go back to a primitive life - and most obviously say no, as they would literally die. And also most other people like hot showers and refrigerators.
So you cannot get far with peaceful discourse - so what do you do, if the self righteous anger is still boiling? Literally blow something up apparently.
I mean I get the anger on careless destruction of wild nature. I feel it too. But bombs don't change that. They make it only worse.
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.
Same argument got made about chess after Deep Blue in 97. Didn't kill chess, just changed what humans bother doing manually. Symbolic math tools (Mathematica, Macsyma) already automated grunt work decades before this letter, mathematicians still employed.
