6 ms·

Is mathematics about to enter the conservatory?

134 points by _alternator_ 28d ago

turtleyacht 28d ago
AI could keep on generating an "observable universe," and mathematicians discover things by way of validating results. This doesn't seem much dissimilar to astronomy.
- hoppyhoppy2 28d ago
  the article is about music conservatories, not astronomical observatories
  - turtleyacht 28d ago
    Right. It's not conservatories, because we will have communities of Lean programmers and hobbyists helping things along, a group effort that is poorly described by relegation to a limited, privileged set of performers.
seibelj 28d ago
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dofm 28d ago
> Our society does not support classical musicians in the same way that we support ‘popular’ musicians. It really really does. Popular/rock/folk/classical musicians all earn much the same way now: a blend of teaching, occasional performance fees, functions performances like weddings and galas, music-related side-gigs (composition, arrangement and recording for commercial music), and non-music-related side gigs — teaching non-musical things, gardening, painting and decorating, bar work, office temp work, even full time jobs (doctors and lawyers, accountants). I know a couple of classical musicians whose actual money-making music is playing other instruments in funk/rock functions bands. Even the "best" or most famous musicians, popular or classical, have side gigs. Approximately nobody makes their money only from performing or from recordings; that ended twenty-five or thirty years ago. Elite soloists, maybe — but that is actually a pretty expensive life to live. I would be surprised if many of them risked a life where they had no other job. The idea that a "conservatory" system exists that meaningfully supports classical musicians is nonsense almost anywhere in the world, I would think. Even the first-chair musicians and conductors have side gigs. (ETA: I can't believe this is a workable model for mathematicians, either. Maybe for a couple of dozen the world over. But there is no performance, no regionality, little in the way of public dissemination, little in the way of reflected glory for benefactors. No, the "conservatory" will perhaps be the intelligence agencies, as it was before.)
- anon291 28d ago
  Modern 'classical' music is a myth. In their day, classical composers were essentially pop performers. Women used to throw their undergarments at mozart... Today classical music is filled with people who want to pretend to be superior to pop musicians because they keep their repertoire confined to academically acceptable areas. And then the LARPers that want to make new music make complete and utter arhythmic and atonal trash that demands humans subdue our own aural feelings of beauty. You'll find classical musicians who complain about this stuff are usually incompetent musicians who really stretch the definition of artist. Sorry spent almost a decade of my young life in a somewhat competitive music school environment. Lots of the other kids were upset I played what I wanted to and people liked it. Actual modern composers in the classical tradition (I.e. people alive today who compose music that is similar in feel to older composers) are well compensated because they're often hired to score films, video games, and other capitalist interests that the supposedly 'real' classical musicians would scoff their noses at.
  - boothby 28d ago
    > Today classical music is filled with people who want to pretend to be superior to pop musicians because they keep their repertoire confined to academically acceptable areas. As somebody with classical training and a brother in the industry, it pains me to read this misinformed opinion of yours. Top-tier symphonies world round are doing crossover concerts with pop artists, play pop songs, modern and experimental music, and regularly feature works by living composers. In my high school orchestra, circa '98, we played stuff like music from Star Wars and West Side Story -- not just the ancients. Down the foodchain, it gets even weirder. The favorite gig I played involved interpretive dance featuring waterboarding, gallons of fake blood, a live chicken race, and more. Where you certainly will find a subset of afficionados of any genre who scoff at anything but their extremely narrow definition of "good music," if you take the time to rub elbows with mature classical musicians you'll find many to most of them quite open minded. Your experience with young artists, finding them to be idealistic and purist, does not extend to the whole field. I know people who only listen to a single narrow genre or decade of pop music. How are they different? Edit to add: > And then the LARPers that want to make new music make complete and utter arhythmic and atonal trash that demands humans subdue our own aural feelings of beauty. Oh, no. No, no no. I've been to a circuit-bent punk show. I recently went to an ambient music festival. I've heard glitch pop. Angine de Poitrine is blowing up because they use a semitonal guitar (though as a bit of a noise snob, I find their use of semitones milquetoast and rather uninspired). Here you are, narrowly defining music, and excluding what you dislike. But it's not just "classical" living composers doing this.
Havoc 28d ago
Presumably it’s just a matter of timing till most knowledge work heads that way. From what I can tell discussions on what to do about it haven’t really advanced much if at all. Still the same mix of new jobs will appear, jobs will change and perhaps some talk of UBI.
marcus_holmes 28d ago
It's a good question. Pure maths has foreshadowed a lot of physics, and a lot of Computer Science. We should probably keep doing it. Does the current model (of highly-talented academics at Universities mostly arguing with each other) change because of AI? Does it invalidate human effort, or does it allow humans to push the boundaries further? Is there no point in training or paying for mathematicians because AI will take over the whole role? Or, as we're finding with so many other areas, does AI do its best work when guided by someone who knows the area and subject well?
- a2ff6eeb0 28d ago
  What do you mean by invalidate? It means we no longer need to understand math, of course. When Claude made progress on the Riemann conjecture, here are the kind of prompts used: > Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress. It seems like the kind of prompts a high schooler could come up with. The prompter is the creator of bun.js, a kind of janky JavaScript execution environment. It seems like we no longer need to know the subject well at all.
  - piltdownman 27d ago
    What did the Medicis or Guggengheim's do other than be rich and idle at the right time and place in history? The contemporary prompt is a port for patronage, not a point of inflection - with a similarly ludicrous symbiotic relationship defined by impression management on both sides. Same as it ever was.
  - marcus_holmes 26d ago
    OK, but in that scenario the prompter doesn't understand the output and can't judge whether the LLM is going off the rails or not. As we know from coding, this is a vital step in the process. Experienced coders produce better results, faster, from LLMs than inexperienced coders. I'm not a mathematician so I can't judge the results (which is kinda my point).
gpm 28d ago
I like the framing in the headline - really more than the article itself. I think underappreciated in discourse like this is that of course we will still have "mathematicians" - people whose work is mathematics. The job might change, but at the very least someone has to choose where to spend the compute and the dollars, decide what theorems are worth investing in, what definitions matter. Someone still has to serve as the ambassador reminding people at the relevant points to look over at the field for productivity and correctness reasons, presenting fun riddles for entertainment and education, advocating to political bodies for funding. Metalworking looks a lot different than it used to, but the end of a man with a hammer and leather bellows bashing out a nail didn't end the career of metal working either. The work sure looks a lot different though, and there are many fewer of them.
madrox 28d ago
We are largely having a reckoning with whether a discipline is the process or the outcome. Music didn't enter the conservatory so much as the relative interest in various styles have changed over time. I get that the author was implying that by talking about pop music, but what was music doing before Mozart came around? Every field is having this existential crisis right now, from art to math. Especially in art, the anti-AI hate mostly reduces to arguing that art is the process not the outcome. The need for research-level math isn't changing (if anything, it may accelerate), but how we do it is. The languages, systems, and process I used to write code has changed a lot since I wrote my first line of BASIC in 1994. Mathematicians, I expect, have not encountered nearly the same amount of disruption in academia. I feel for them.
- whateverboat 27d ago
  Before Mozart came along, we had folk music, music of the masses, and they continue to exist and will exist today.
  - viccis 27d ago
    Why are you guys talking about Mozart as if you can split the mass adoption of music into pre and post Mozart? Mozart was one of many in an ongoing evolution of European music. The way masses interacted with music varied based on the time and the culture. Some cultures at any given time would vary based on whether they produced much music at all (look at how Calvinism and the way the Dutch aristocracy handled music patronage vs Italy or France impacted Dutch music's dominance before vs after the Renaissance), what kind of music they produced (worship music only or also secular patronage?), etc. Mozart did not significantly overhaul this, rather he spent his latter years desperately trying to keep his reputation and relevance alive with travels.
- Fordec 28d ago
  I like this framing. I know that AI has it's place and in others it doesn't. I recognize I sound like an AI shill in personal conversations, but I'm a very outcome driven person. I simply want multiple, thousands of outcomes even, and those outcomes all coming together is my process/journey, which is different to a developer or musicians process may view their career.
djmips 28d ago
They didn't mention coders but my idea is to have Silicon habitats of programmers recreating nineties professional programming on Pentium PCs in dimly lit cubicles. Tourists shuffle by watching live coding like watching a blacksmith at a Colonial Williamsburg.
- ur-whale 28d ago
  > Silicon habitats of programmers recreating nineties professional programming on Pentium PCs in dimly lit cubicles God I miss those days.
pianopatrick 28d ago
Well, I think one good thing we can conclude from the music world is that there are people out there who want to pay for humans to do things even when the computer could do it better. I.e. when you go to Vegas and go to a bar, you want to have a guy playing piano and singing, and are willing to pay a bit more for that. You don't want just a jukebox, even if the jukebox can play "Don't Stop Believing" better than the dude with the piano. All that to say, there will be certain jobs that people will want to pay humans to do even if the robots can do those things "better".
- VladVladikoff 28d ago
  The big weakness of the analogy from the OP is that music is universally accessible, while high level mathematics is not. The potential audience for the human playing the piano is far larger than the human solving complex mathematical theorems.
  - piltdownman 27d ago
    If fumbling through 'hot cross buns' on the recorder is roughly analogous to recitation of multiplication tables, then Gould playing Shostakovich can certainly be referenced as one would the Feynman Lectures on Physics. Certainly more effort has been put into exploring the relationship between... Bach and Godel than your surmise suggests; SHRDLU, Toy of Man's Designing! https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach
a2ff6eeb0 28d ago
> To be clear, I haven’t fully verified the proof; I worked through it with Claude Fable and it passes the sniff test, but fully digesting it will take a bit more energy than I have right now. As predicted, we no longer need mathematicians for math; the math is being both generated and read by models. We're in for some exciting times, when the pace of mathematical advance can run faster than the constraints of human brains.
- sumanthvepa 28d ago
  We definitely need mathematicians to understand it and verify to us that the math is correct. And it takes a mathematician to even talk to the AI in a way that will be useful. There is no way I could personally get Claude Fable or Opean AI GPT 6 to generate a proof of Fermat's Theorem in LEAN. It actually take mathematical skills. And real depth to understand the work.
  - a2ff6eeb0 28d ago
    When Claude made progress on the Riemann conjecture, here are the kind of prompts used: > Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress. It seems like the kind of prompts a high schooler could come up with. The prompter is the creator of bun.js, a kind of janky JavaScript execution environment. Math isn't a thing people need to care about any more. AI will soon take care of it. There may be some hobbyists, but progress will not depend on them. AI will come up with new math as needed when it builds for us.
    - Xmd5a 28d ago
      He did a frog's job, not a bird's.
    - ThrowawayR2 27d ago
      You're overlooking the word "mostly" in the quote you trotted out. Ask yourself: what were the prompts that weren't encouragement and would you understand them if you looked them up?
rtpg 28d ago
> Classical music has been institutionalized, sent to the conservatory as a relic. A small segment of society has decided the ability to perform it is worth preserving, and devotes a sliver of capital to that end: training young people, and paying a few of the best players in the biggest cities to do it professionally. I had a whole discussion with a German friend whose husband works in opera (this was after Chalomet's "opera as a dead art" comments) and their view was mostly that this view of the world does not hold for at least chunks of Europe. To their mind, there is still both active input into this space, support in this space, and there's societal support to some degree or another. I don't know the realities on the ground, but that annecdote did make me wonder if I simply assumed that the world of classical music wasn't as dire if you leave the States, at least in terms of job stability. The comparison to popular music is kinda funy too... plenty of pop musicians that don't live off of their music, right? Maybe we're not generating "Taylor Swifts of Oboe"s but I feel like the measure is more about the median (or even the 90th/95th percentile?) when it comes to art, rather than the top of the top.
- sdenton4 28d ago
  The job stability in classical music is great. It's getting a job in the first place that's a problem. My partner, in an earlier life, was one of the best young flautists in Canada. There were about eight jobs in the entire country for orchestral flautists, and about a year before graduating, a few of them turned over, meaning it would probably be another five years before any more jobs opened up. Good time for a career change...
  - jimmydddd 28d ago
    Old joke: What's the difference between a flautist and a flutist? About $50 an hour. :-)
- lokar 28d ago
  I think he agrees it is popular, but in comparison to contemporary styles of music it’s tiny (in skilled performers, listeners, funding and revenue). Right? Even in Europe.
SubiculumCode 28d ago
Does math have an end? Or is it an infinite self-construction?
esafak 28d ago
Conservatories are not going to support the entirety of the white collar market, so something is going to give. Not to mention the blue collar market, as robots take off.
nadermx 28d ago
I haven't done math since college. Now the things I struggled with I was able to grasp. So much so that I was able to prove a conjecture, small one, but nothing in my life I thought I would of, its even getting peer reviewed. Its drudgery to prove these things. But man it feels cool when you do. I now have a better understanding of the entire physical mechanics of life around me, to a gravitational sort of understanding. Simply because I thought I had a conceptual understanding of p vs np. And after weeks I was able to prove myself wrong. People seem to worry that AI is going to take away everything. But my experience is that I feel more able to create even ideas before I would never imagine. It feels more like in HG Wells where he's in the far future talking to the AI about his equations and the AI says "oh your talking about time travel, thats impossible" It feels like that reality is now more likely than any other, anyone can invent anything now and have the math to back it up. You can speak physics into existance. I'm excited for the future
sankhao 28d ago
>Mathematics, especially pure mathematics, has always been about communicating stories that help us understand reality more deeply. I'm pretty sure pure mathematics is the part of math which is not about reality.
- istjohn 28d ago
  Reality encompasses more than the physical universe. Abstract mathematics describe an aspect of reality, too.
  - lioeters 27d ago
    One might argue that mathematics is more fundamental to reality than space and time, which emerge from it.
nxpnsv 28d ago
Our AI system don't just do things. They do it because someone asks. A lot of the boom in AI maths results are solving human formulated problems mostly for PR benefit. Once the novelty passes, would Anthropic or OpenAI keep spending? And without mathematicians to ask the right questions and able to appreciate the results, why would AI driven research continue?
- busyant 28d ago
  > And without mathematicians to ask the right questions Here, I disagree. What makes you think the AI won't be able to ask the right questions without prompting? > and able to appreciate the results, why would AI driven research continue? Here, I think I agree. At some level, there has to be a human in the process that must understand / interpret the results. I gotta say, however, that I'm not certain about my agreement. I'm worried that I'm missing something where the human can be excised from the process entirely.
  - nxpnsv 27d ago
    > Here, I disagree. What makes you think the AI won't be able to ask the right questions without prompting? But why would they ask the right questions without prompting? The LLMs have no intrinsic goal to research math problems, it would just be very costly to run queries without a reason to run them... arguably a human in that loop would be a mathematician, but then we do need them after all.
    - busyant 26d ago
      > But why would they ask the right questions without prompting? What if the models are good enough (maybe even now?) so that all you have to say is "come up with a list of interesting problems overlooked by humans in <insert math discipline>. Then work on those proofs." I don't think that's so far fetched. Especially given the news today about NS.
  - emp17344 27d ago
    I think we know enough about reinforcement learning to tell that it won’t be able to entirely replace human mathematicians. All of the techniques used by these AI firms are well-studied.
kdavis 28d ago
Maybe in the future mathematicians could be the ones proposing different axiomatic foundations (e.g. ZF vs ZF + C vs ZF + C + CH vs ...) and then using computers to examine the consequences of these differing foundations?
- QuesnayJr 28d ago
  I'm sure AI could contribute to this, but this is already a well-developed field of mathematics, and most of the consequences of additional axioms have been worked out. (The most productive hypothesis has been what's called "projective determinacy", if you're curious.) Mathematicians have also gone in the opposite direction, and tried to work out what are the weakest foundations where different results hold. This is called "reverse mathematics".
  - kdavis 28d ago
    What name does this "well-developed field of mathematics" go by? (I just want to get a taste of what the field is like.) I also thought that there are an infinite set of possible extra axioms, e.g. axiomize any statement that's true but not provably so via Gödel's First Incompleteness Theorem, though maybe the vast majority of such axioms are "uninteresting".
    - QuesnayJr 27d ago
      "Descriptive set theory" is a good starting point, though it's the bulk of what set theorists in general do. It's true that there's an infinite possible set of axioms. It does seem that the types of axioms that have consequences that humans are interested in fall into simple families. For example, many seemingly unrelated questions are settled by assume the existence of very large sets (larger than can normally constructed in set theory).
  - kdavis 28d ago
    Looking a bit more into this, it doesn't seem your claim "most of the consequences of additional axioms have been worked out" holds up. Yes, metamathematics is well-developed, but I don't think that most of the consequences of any particular additional set of axioms have been worked out. Each such new set requires re-deriving all of this alternate mathematics from scratch. This is a lot of work! So I think my original claim---mathematicians select interesting axioms and AI figures out their implications---still seems a possible way forward. PS: I'd guess descriptive set theory under determinacy is the one place where projective determinacy, as you stated, pays off.
deleted 28d ago
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raincole 28d ago
I honestly don't get what the author is trying to say. > But pure mathematics is already in a conservatory, better known as the academy. Yes, exactly. So "is mathematics about to enter the conservatory" is a quite weird question. > who deserves funding, tenure, and fame It's always been decided by a very small clique of academic elites and a few big companies who have too much R&D budget to spend. It's not something that can be decided by 'the pop' democratically. If you ask an average person how much we should spend on linguists and philosophers per year, the answer will be ~$0. I don't see how AI changes that.
tpoacher 28d ago
Betteridge's law of headlines says "no".
lukeh 28d ago
It's possible to have a career in classical music (I have one, for some definition of classical). But I suspect that streaming income from passive listeners (i.e. not fans) will disappear once the streaming services can eliminate those pesky songwriters and artists.
fidla 28d ago
and he shows us a pic of a ukulele, hardly a conservatory instrument LOL
pfdietz 27d ago
The analogy seems strained, since math is not (just) entertainment.
whateverboat 27d ago
> Could this model work for mathematicians? It’s easy to imagine: in Euclid’s time, mathematics largely existed as an intellectual pursuit worthy of a few inclined people. NO! Pythagoras discovered his theorems because they wanted to divide up the revenue. While there have been sections of mathematics discovered by leisure, majority of mathematics has been discovered due to an engineering need.
- djeastm 27d ago
  Do we know much at all about Pythagoras or his motivations outside of legendary accounts from many years later?
  - whateverboat 23d ago
    It is quite well known that the culture around Pythagora's time was heavily influence by architecture and engineering like Tunnel of Eupalinos.
chr15m 27d ago
> I haven’t fully verified the proof; I worked through it with Claude Fable and it passes the sniff test, but fully digesting it will take a bit more energy than I have right now. This is overlooked but really important. Nobody wants to watch robots play chess against each other - we watch human chess even though bots are better. Nobody needs math that has not been verified by humans. Human understanding and communication is the important part of mathematics.
- stabbles 27d ago
  > Nobody wants to watch robots play chess against each other - we watch human chess even though bots are better Many humans have studied robots play chess and learned from them. For example the concept of a "thorn pawn" was popularized after Leela played it with great success. > Nobody needs math that has not been verified by humans. There already are proofs that are understood by a handful of humans; without understanding you can still proof corollaries. For example, there are proofs to theorems that are conditional on the Riemann Hypothesis.
  - chr15m 27d ago
    > Many humans have studied robots play chess and learned from them. Yes, robot chess is very useful for chess players. It's a great technology. People don't want to watch robot chess. They want to watch humans, even those who used AI to train. The human part of chess is what matters. > There already are proofs that are understood by a handful of humans Yes, exactly.
    - Mr_Minderbinder 27d ago
      > People don't want to watch robot chess. I do and I have for a number of years. Most people prefer to watch human chess but there are also those who watch computer chess with the same level of enthusiasm: https://tcec-chess.com/ https://tcec-chess.com/ https://en.wikipedia.org/wiki/TCEC https://en.wikipedia.org/wiki/TCEC
- whoarewethen 27d ago
rayiner 27d ago
> Consider classical music. Our society does not support classical musicians in the same way that we support ‘popular’ musicians “Society” is a leaky abstraction here. If you reify society as a thing that is capable of “supporting” or “not supporting” something you mean essentially the government. In that case, “society” probably provides more support to classical music than pop music, through grant programs, public funding of symphonies, etc.
- deleted 27d ago
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kazinator 27d ago
AI told me that the same hex wrench used on bicycle pedal crank bolts would fit the freehub body fixing bolt in the rear wheel. (Spoiler: nope!) Guess it's too busy pushing math off to the conservatory to know the difference between 8mm and 10mm? You can't trust the shit with first order, ground level facts about the world.
oliviayii 27d ago
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134 points by _alternator_ 28d ago

AI could keep on generating an "observable universe," and mathematicians discover things by way of validating results. This doesn't seem much dissimilar to astronomy.

hoppyhoppy2 28d ago
the article is about music conservatories, not astronomical observatories
- turtleyacht 28d ago
  Right. It's not conservatories, because we will have communities of Lean programmers and hobbyists helping things along, a group effort that is poorly described by relegation to a limited, privileged set of performers.

seibelj 28d ago

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dofm 28d ago

> Our society does not support classical musicians in the same way that we support ‘popular’ musicians. It really really does. Popular/rock/folk/classical musicians all earn much the same way now: a blend of teaching, occasional performance fees, functions performances like weddings and galas, music-related side-gigs (composition, arrangement and recording for commercial music), and non-music-related side gigs — teaching non-musical things, gardening, painting and decorating, bar work, office temp work, even full time jobs (doctors and lawyers, accountants). I know a couple of classical musicians whose actual money-making music is playing other instruments in funk/rock functions bands. Even the "best" or most famous musicians, popular or classical, have side gigs. Approximately nobody makes their money only from performing or from recordings; that ended twenty-five or thirty years ago. Elite soloists, maybe — but that is actually a pretty expensive life to live. I would be surprised if many of them risked a life where they had no other job. The idea that a "conservatory" system exists that meaningfully supports classical musicians is nonsense almost anywhere in the world, I would think. Even the first-chair musicians and conductors have side gigs. (ETA: I can't believe this is a workable model for mathematicians, either. Maybe for a couple of dozen the world over. But there is no performance, no regionality, little in the way of public dissemination, little in the way of reflected glory for benefactors. No, the "conservatory" will perhaps be the intelligence agencies, as it was before.)

anon291 28d ago
Modern 'classical' music is a myth. In their day, classical composers were essentially pop performers. Women used to throw their undergarments at mozart... Today classical music is filled with people who want to pretend to be superior to pop musicians because they keep their repertoire confined to academically acceptable areas. And then the LARPers that want to make new music make complete and utter arhythmic and atonal trash that demands humans subdue our own aural feelings of beauty. You'll find classical musicians who complain about this stuff are usually incompetent musicians who really stretch the definition of artist. Sorry spent almost a decade of my young life in a somewhat competitive music school environment. Lots of the other kids were upset I played what I wanted to and people liked it. Actual modern composers in the classical tradition (I.e. people alive today who compose music that is similar in feel to older composers) are well compensated because they're often hired to score films, video games, and other capitalist interests that the supposedly 'real' classical musicians would scoff their noses at.
- boothby 28d ago
  > Today classical music is filled with people who want to pretend to be superior to pop musicians because they keep their repertoire confined to academically acceptable areas. As somebody with classical training and a brother in the industry, it pains me to read this misinformed opinion of yours. Top-tier symphonies world round are doing crossover concerts with pop artists, play pop songs, modern and experimental music, and regularly feature works by living composers. In my high school orchestra, circa '98, we played stuff like music from Star Wars and West Side Story -- not just the ancients. Down the foodchain, it gets even weirder. The favorite gig I played involved interpretive dance featuring waterboarding, gallons of fake blood, a live chicken race, and more. Where you certainly will find a subset of afficionados of any genre who scoff at anything but their extremely narrow definition of "good music," if you take the time to rub elbows with mature classical musicians you'll find many to most of them quite open minded. Your experience with young artists, finding them to be idealistic and purist, does not extend to the whole field. I know people who only listen to a single narrow genre or decade of pop music. How are they different? Edit to add: > And then the LARPers that want to make new music make complete and utter arhythmic and atonal trash that demands humans subdue our own aural feelings of beauty. Oh, no. No, no no. I've been to a circuit-bent punk show. I recently went to an ambient music festival. I've heard glitch pop. Angine de Poitrine is blowing up because they use a semitonal guitar (though as a bit of a noise snob, I find their use of semitones milquetoast and rather uninspired). Here you are, narrowly defining music, and excluding what you dislike. But it's not just "classical" living composers doing this.

Havoc 28d ago

Presumably it’s just a matter of timing till most knowledge work heads that way. From what I can tell discussions on what to do about it haven’t really advanced much if at all. Still the same mix of new jobs will appear, jobs will change and perhaps some talk of UBI.

marcus_holmes 28d ago

It's a good question. Pure maths has foreshadowed a lot of physics, and a lot of Computer Science. We should probably keep doing it. Does the current model (of highly-talented academics at Universities mostly arguing with each other) change because of AI? Does it invalidate human effort, or does it allow humans to push the boundaries further? Is there no point in training or paying for mathematicians because AI will take over the whole role? Or, as we're finding with so many other areas, does AI do its best work when guided by someone who knows the area and subject well?

a2ff6eeb0 28d ago
What do you mean by invalidate? It means we no longer need to understand math, of course. When Claude made progress on the Riemann conjecture, here are the kind of prompts used: > Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress. It seems like the kind of prompts a high schooler could come up with. The prompter is the creator of bun.js, a kind of janky JavaScript execution environment. It seems like we no longer need to know the subject well at all.
- piltdownman 27d ago
  What did the Medicis or Guggengheim's do other than be rich and idle at the right time and place in history? The contemporary prompt is a port for patronage, not a point of inflection - with a similarly ludicrous symbiotic relationship defined by impression management on both sides. Same as it ever was.
- marcus_holmes 26d ago
  OK, but in that scenario the prompter doesn't understand the output and can't judge whether the LLM is going off the rails or not. As we know from coding, this is a vital step in the process. Experienced coders produce better results, faster, from LLMs than inexperienced coders. I'm not a mathematician so I can't judge the results (which is kinda my point).

gpm 28d ago

I like the framing in the headline - really more than the article itself. I think underappreciated in discourse like this is that of course we will still have "mathematicians" - people whose work is mathematics. The job might change, but at the very least someone has to choose where to spend the compute and the dollars, decide what theorems are worth investing in, what definitions matter. Someone still has to serve as the ambassador reminding people at the relevant points to look over at the field for productivity and correctness reasons, presenting fun riddles for entertainment and education, advocating to political bodies for funding. Metalworking looks a lot different than it used to, but the end of a man with a hammer and leather bellows bashing out a nail didn't end the career of metal working either. The work sure looks a lot different though, and there are many fewer of them.

madrox 28d ago

We are largely having a reckoning with whether a discipline is the process or the outcome. Music didn't enter the conservatory so much as the relative interest in various styles have changed over time. I get that the author was implying that by talking about pop music, but what was music doing before Mozart came around? Every field is having this existential crisis right now, from art to math. Especially in art, the anti-AI hate mostly reduces to arguing that art is the process not the outcome. The need for research-level math isn't changing (if anything, it may accelerate), but how we do it is. The languages, systems, and process I used to write code has changed a lot since I wrote my first line of BASIC in 1994. Mathematicians, I expect, have not encountered nearly the same amount of disruption in academia. I feel for them.

whateverboat 27d ago
Before Mozart came along, we had folk music, music of the masses, and they continue to exist and will exist today.
- viccis 27d ago
  Why are you guys talking about Mozart as if you can split the mass adoption of music into pre and post Mozart? Mozart was one of many in an ongoing evolution of European music. The way masses interacted with music varied based on the time and the culture. Some cultures at any given time would vary based on whether they produced much music at all (look at how Calvinism and the way the Dutch aristocracy handled music patronage vs Italy or France impacted Dutch music's dominance before vs after the Renaissance), what kind of music they produced (worship music only or also secular patronage?), etc. Mozart did not significantly overhaul this, rather he spent his latter years desperately trying to keep his reputation and relevance alive with travels.
Fordec 28d ago
I like this framing. I know that AI has it's place and in others it doesn't. I recognize I sound like an AI shill in personal conversations, but I'm a very outcome driven person. I simply want multiple, thousands of outcomes even, and those outcomes all coming together is my process/journey, which is different to a developer or musicians process may view their career.

djmips 28d ago

They didn't mention coders but my idea is to have Silicon habitats of programmers recreating nineties professional programming on Pentium PCs in dimly lit cubicles. Tourists shuffle by watching live coding like watching a blacksmith at a Colonial Williamsburg.

ur-whale 28d ago
> Silicon habitats of programmers recreating nineties professional programming on Pentium PCs in dimly lit cubicles God I miss those days.

pianopatrick 28d ago

Well, I think one good thing we can conclude from the music world is that there are people out there who want to pay for humans to do things even when the computer could do it better. I.e. when you go to Vegas and go to a bar, you want to have a guy playing piano and singing, and are willing to pay a bit more for that. You don't want just a jukebox, even if the jukebox can play "Don't Stop Believing" better than the dude with the piano. All that to say, there will be certain jobs that people will want to pay humans to do even if the robots can do those things "better".

VladVladikoff 28d ago
The big weakness of the analogy from the OP is that music is universally accessible, while high level mathematics is not. The potential audience for the human playing the piano is far larger than the human solving complex mathematical theorems.
- piltdownman 27d ago
  If fumbling through 'hot cross buns' on the recorder is roughly analogous to recitation of multiplication tables, then Gould playing Shostakovich can certainly be referenced as one would the Feynman Lectures on Physics. Certainly more effort has been put into exploring the relationship between... Bach and Godel than your surmise suggests; SHRDLU, Toy of Man's Designing! https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach

a2ff6eeb0 28d ago

> To be clear, I haven’t fully verified the proof; I worked through it with Claude Fable and it passes the sniff test, but fully digesting it will take a bit more energy than I have right now. As predicted, we no longer need mathematicians for math; the math is being both generated and read by models. We're in for some exciting times, when the pace of mathematical advance can run faster than the constraints of human brains.

sumanthvepa 28d ago
We definitely need mathematicians to understand it and verify to us that the math is correct. And it takes a mathematician to even talk to the AI in a way that will be useful. There is no way I could personally get Claude Fable or Opean AI GPT 6 to generate a proof of Fermat's Theorem in LEAN. It actually take mathematical skills. And real depth to understand the work.
- a2ff6eeb0 28d ago
  When Claude made progress on the Riemann conjecture, here are the kind of prompts used: > Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress. It seems like the kind of prompts a high schooler could come up with. The prompter is the creator of bun.js, a kind of janky JavaScript execution environment. Math isn't a thing people need to care about any more. AI will soon take care of it. There may be some hobbyists, but progress will not depend on them. AI will come up with new math as needed when it builds for us.
  - Xmd5a 28d ago
    He did a frog's job, not a bird's.
  - ThrowawayR2 27d ago
    You're overlooking the word "mostly" in the quote you trotted out. Ask yourself: what were the prompts that weren't encouragement and would you understand them if you looked them up?

rtpg 28d ago

> Classical music has been institutionalized, sent to the conservatory as a relic. A small segment of society has decided the ability to perform it is worth preserving, and devotes a sliver of capital to that end: training young people, and paying a few of the best players in the biggest cities to do it professionally. I had a whole discussion with a German friend whose husband works in opera (this was after Chalomet's "opera as a dead art" comments) and their view was mostly that this view of the world does not hold for at least chunks of Europe. To their mind, there is still both active input into this space, support in this space, and there's societal support to some degree or another. I don't know the realities on the ground, but that annecdote did make me wonder if I simply assumed that the world of classical music wasn't as dire if you leave the States, at least in terms of job stability. The comparison to popular music is kinda funy too... plenty of pop musicians that don't live off of their music, right? Maybe we're not generating "Taylor Swifts of Oboe"s but I feel like the measure is more about the median (or even the 90th/95th percentile?) when it comes to art, rather than the top of the top.

sdenton4 28d ago
The job stability in classical music is great. It's getting a job in the first place that's a problem. My partner, in an earlier life, was one of the best young flautists in Canada. There were about eight jobs in the entire country for orchestral flautists, and about a year before graduating, a few of them turned over, meaning it would probably be another five years before any more jobs opened up. Good time for a career change...
- jimmydddd 28d ago
  Old joke: What's the difference between a flautist and a flutist? About $50 an hour. :-)
lokar 28d ago
I think he agrees it is popular, but in comparison to contemporary styles of music it’s tiny (in skilled performers, listeners, funding and revenue). Right? Even in Europe.

SubiculumCode 28d ago

Does math have an end? Or is it an infinite self-construction?

esafak 28d ago

Conservatories are not going to support the entirety of the white collar market, so something is going to give. Not to mention the blue collar market, as robots take off.

nadermx 28d ago

I haven't done math since college. Now the things I struggled with I was able to grasp. So much so that I was able to prove a conjecture, small one, but nothing in my life I thought I would of, its even getting peer reviewed. Its drudgery to prove these things. But man it feels cool when you do. I now have a better understanding of the entire physical mechanics of life around me, to a gravitational sort of understanding. Simply because I thought I had a conceptual understanding of p vs np. And after weeks I was able to prove myself wrong. People seem to worry that AI is going to take away everything. But my experience is that I feel more able to create even ideas before I would never imagine. It feels more like in HG Wells where he's in the far future talking to the AI about his equations and the AI says "oh your talking about time travel, thats impossible" It feels like that reality is now more likely than any other, anyone can invent anything now and have the math to back it up. You can speak physics into existance. I'm excited for the future

sankhao 28d ago

>Mathematics, especially pure mathematics, has always been about communicating stories that help us understand reality more deeply. I'm pretty sure pure mathematics is the part of math which is not about reality.

istjohn 28d ago
Reality encompasses more than the physical universe. Abstract mathematics describe an aspect of reality, too.
- lioeters 27d ago
  One might argue that mathematics is more fundamental to reality than space and time, which emerge from it.

nxpnsv 28d ago

Our AI system don't just do things. They do it because someone asks. A lot of the boom in AI maths results are solving human formulated problems mostly for PR benefit. Once the novelty passes, would Anthropic or OpenAI keep spending? And without mathematicians to ask the right questions and able to appreciate the results, why would AI driven research continue?

busyant 28d ago
> And without mathematicians to ask the right questions Here, I disagree. What makes you think the AI won't be able to ask the right questions without prompting? > and able to appreciate the results, why would AI driven research continue? Here, I think I agree. At some level, there has to be a human in the process that must understand / interpret the results. I gotta say, however, that I'm not certain about my agreement. I'm worried that I'm missing something where the human can be excised from the process entirely.
- nxpnsv 27d ago
  > Here, I disagree. What makes you think the AI won't be able to ask the right questions without prompting? But why would they ask the right questions without prompting? The LLMs have no intrinsic goal to research math problems, it would just be very costly to run queries without a reason to run them... arguably a human in that loop would be a mathematician, but then we do need them after all.
  - busyant 26d ago
    > But why would they ask the right questions without prompting? What if the models are good enough (maybe even now?) so that all you have to say is "come up with a list of interesting problems overlooked by humans in <insert math discipline>. Then work on those proofs." I don't think that's so far fetched. Especially given the news today about NS.
- emp17344 27d ago
  I think we know enough about reinforcement learning to tell that it won’t be able to entirely replace human mathematicians. All of the techniques used by these AI firms are well-studied.

kdavis 28d ago

Maybe in the future mathematicians could be the ones proposing different axiomatic foundations (e.g. ZF vs ZF + C vs ZF + C + CH vs ...) and then using computers to examine the consequences of these differing foundations?

QuesnayJr 28d ago
I'm sure AI could contribute to this, but this is already a well-developed field of mathematics, and most of the consequences of additional axioms have been worked out. (The most productive hypothesis has been what's called "projective determinacy", if you're curious.) Mathematicians have also gone in the opposite direction, and tried to work out what are the weakest foundations where different results hold. This is called "reverse mathematics".
- kdavis 28d ago
  What name does this "well-developed field of mathematics" go by? (I just want to get a taste of what the field is like.) I also thought that there are an infinite set of possible extra axioms, e.g. axiomize any statement that's true but not provably so via Gödel's First Incompleteness Theorem, though maybe the vast majority of such axioms are "uninteresting".
  - QuesnayJr 27d ago
    "Descriptive set theory" is a good starting point, though it's the bulk of what set theorists in general do. It's true that there's an infinite possible set of axioms. It does seem that the types of axioms that have consequences that humans are interested in fall into simple families. For example, many seemingly unrelated questions are settled by assume the existence of very large sets (larger than can normally constructed in set theory).
- kdavis 28d ago
  Looking a bit more into this, it doesn't seem your claim "most of the consequences of additional axioms have been worked out" holds up. Yes, metamathematics is well-developed, but I don't think that most of the consequences of any particular additional set of axioms have been worked out. Each such new set requires re-deriving all of this alternate mathematics from scratch. This is a lot of work! So I think my original claim---mathematicians select interesting axioms and AI figures out their implications---still seems a possible way forward. PS: I'd guess descriptive set theory under determinacy is the one place where projective determinacy, as you stated, pays off.

deleted 28d ago

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raincole 28d ago

I honestly don't get what the author is trying to say. > But pure mathematics is already in a conservatory, better known as the academy. Yes, exactly. So "is mathematics about to enter the conservatory" is a quite weird question. > who deserves funding, tenure, and fame It's always been decided by a very small clique of academic elites and a few big companies who have too much R&D budget to spend. It's not something that can be decided by 'the pop' democratically. If you ask an average person how much we should spend on linguists and philosophers per year, the answer will be ~$0. I don't see how AI changes that.

tpoacher 28d ago

Betteridge's law of headlines says "no".

lukeh 28d ago

It's possible to have a career in classical music (I have one, for some definition of classical). But I suspect that streaming income from passive listeners (i.e. not fans) will disappear once the streaming services can eliminate those pesky songwriters and artists.

fidla 28d ago

and he shows us a pic of a ukulele, hardly a conservatory instrument LOL

pfdietz 27d ago

The analogy seems strained, since math is not (just) entertainment.

whateverboat 27d ago

> Could this model work for mathematicians? It’s easy to imagine: in Euclid’s time, mathematics largely existed as an intellectual pursuit worthy of a few inclined people. NO! Pythagoras discovered his theorems because they wanted to divide up the revenue. While there have been sections of mathematics discovered by leisure, majority of mathematics has been discovered due to an engineering need.

djeastm 27d ago
Do we know much at all about Pythagoras or his motivations outside of legendary accounts from many years later?
- whateverboat 23d ago
  It is quite well known that the culture around Pythagora's time was heavily influence by architecture and engineering like Tunnel of Eupalinos.

chr15m 27d ago

> I haven’t fully verified the proof; I worked through it with Claude Fable and it passes the sniff test, but fully digesting it will take a bit more energy than I have right now. This is overlooked but really important. Nobody wants to watch robots play chess against each other - we watch human chess even though bots are better. Nobody needs math that has not been verified by humans. Human understanding and communication is the important part of mathematics.

stabbles 27d ago
> Nobody wants to watch robots play chess against each other - we watch human chess even though bots are better Many humans have studied robots play chess and learned from them. For example the concept of a "thorn pawn" was popularized after Leela played it with great success. > Nobody needs math that has not been verified by humans. There already are proofs that are understood by a handful of humans; without understanding you can still proof corollaries. For example, there are proofs to theorems that are conditional on the Riemann Hypothesis.
- chr15m 27d ago
  > Many humans have studied robots play chess and learned from them. Yes, robot chess is very useful for chess players. It's a great technology. People don't want to watch robot chess. They want to watch humans, even those who used AI to train. The human part of chess is what matters. > There already are proofs that are understood by a handful of humans Yes, exactly.
  - Mr_Minderbinder 27d ago
    > People don't want to watch robot chess. I do and I have for a number of years. Most people prefer to watch human chess but there are also those who watch computer chess with the same level of enthusiasm: https://tcec-chess.com/ https://tcec-chess.com/ https://en.wikipedia.org/wiki/TCEC https://en.wikipedia.org/wiki/TCEC
whoarewethen 27d ago

rayiner 27d ago

> Consider classical music. Our society does not support classical musicians in the same way that we support ‘popular’ musicians “Society” is a leaky abstraction here. If you reify society as a thing that is capable of “supporting” or “not supporting” something you mean essentially the government. In that case, “society” probably provides more support to classical music than pop music, through grant programs, public funding of symphonies, etc.

deleted 27d ago
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kazinator 27d ago

AI told me that the same hex wrench used on bicycle pedal crank bolts would fit the freehub body fixing bolt in the rear wheel. (Spoiler: nope!) Guess it's too busy pushing math off to the conservatory to know the difference between 8mm and 10mm? You can't trust the shit with first order, ground level facts about the world.

oliviayii 27d ago

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