Is mathematics about to enter the conservatory?
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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.)
A principal player (I don't think anyone beyond high school band calls them 'first-chair') in a major symphony orchestra in the United States makes $250k-400k a year. These are extremely competitive jobs and they are paid well. Certainly enough to live on if you wanted to.
These people often teach, but not really because they need a "side-gig." If you ask them, they will likely tell you they feel a certain duty to prepare the next generation, they like teaching, and their rehearsal/performance schedule affords them the time.
I said "approximately nobody".
At a first approximation, no musician who does it for money makes a living out of it. Classical, pop, rock, whatever.
Nobody in music, basically, makes real money. Fifty, maybe a hundred violinists in the entire world do earn a pure living. Perhaps another twenty five of each other instrument. A few international soloists in other instruments. But musicians in those jobs are often burning as much money as they are making. (Even Anouskha Shankar has a portfolio career).
This is essentially nobody. Everyone else in classical music is earning just the same way as popular musicians — and society doesn't "support" popular musicians at all! The perception that rock musicians make money touring, for example, is just that: perception. The vast majority of tours either just break even or lose money. Working in music production and staging makes better money than musicians make.
Everyone else, essentially, has another job.
> (I don't think anyone beyond high school band calls them 'first-chair')
Snark noted, though I have no earthly idea why you felt it necessary
There are at least 20 such orchestras in the US alone, not to mention all the orchestras in Europe and Asia. There’s also a very long tail with compensation down to $50k for players.
The US BLS has 35,000 paid musicians listed, with another 10,000 music directors (a lot of church organists are in this category). Median wage of $40/hour, mean of around $52.
So. Not a living then, for most.
Also note that churches, which are a hub for working-class musicians, are exempt from BLS reporting.
Maybe I’m just off the mark but this doesn’t seem like the kind of job you clock in at 9 and stay till 5.
But just because the numbers are small doesn't mean society does not support them. There just isn't a need for a lot of them. It would be like saying society does not support professional athletes. Clearly it does, but only at the highest level. And at that level, it supports the very well.
> Snark noted, though I have no earthly idea why you felt it necessary
I apologize. I come from this world, have close friends in major orchestras and experience on the world's opera stages. This culture is full of shibboleths: referring to works as "songs", clapping in the wrong place, hell, even pronouncing 'Don Giovanni' the same way you pronounce "Don Draper" lets people know you are not from around here.
An observation I made is that the tournament career system is supported by the entire cadre of players and families, of the kids who won't win one of the prize jobs. One reason is we just don't know which 18 year olds will rise to the level needed to win a symphonic audition a decade later. I've always been ambivalent about this, but don't have a good idea for how to reform it.
I majored in math and physics. My parents didn't cringe, at least quite so much. I became, quite honestly, a mediocre physicist at a time when you had to be a research superstar to apply for a tenure track job at a third rate college. The consolation for me was that a mediocre physicist could still earn a decent living doing something in industry, and I'm now at a late stage of a satisfying career.
I also work on the side as a jazz bassist.
Is it any less competitive now?
Corporate sponsorship pays the bigger amounts: that is a side job with its own commitments. Prize money: by definition not available to most.
Directed pay is a tiny fraction of it (stipend level), even at the highest levels.
Athletes have other jobs.
Again: a bad model for mathematicians. None of them are going to be signing merch deals. Most aren’t winning prizes. I am afraid that mathematicians are just going to have to keep doing all the other jobs they already do.
At least some countries have programs where (candidate) Olympians get professional support and a stipend.
See for example https://www.uksport.gov.uk/our-work/investing-in-sport/how-u..., https://www.dosb.de/en/themen/athletes/services-for-athletes
Coming from Vienna, that can't be right. This city alone breaks that assumption with it's largest 4 orchestras combined.
In Germany every small town has a (state-funded) orchestra. I know someone who plays the violin in such an orchestra, he has a solid salary, big house etc.
He has a side gig, he has a quartet with some friends of his, but it's for fun, not for money.
This has to be off by at least two orders of magnitude.
The Reykjavik symphonic orchestra in Iceland alone employs some 30 full time violinists. The nation's population is less than El Paso, tx - which also employs some 80 musicians in their symphonic orchestra.
Your main point might still have merit, but this forum is one where missing the numbers by so much will distract many readers. It distracted me, at least. :)
Pop musicians have fewer options and need to chase gigs, but the payoffs are also larger if they make it. One-hit wonders drive Ferraris.
What sort of job would that even be? It's a traveling show so they can't even work a normal job--they're in a new town every week.
> Snark noted, though I have no earthly idea why you felt it necessary
I think it's useful if you are, in fact, talking out your ass. It's hard to tell given your confident phrasing, but saying something which gives away that you don't actually have meaningful experience in the subject is worth calling out. It sounds like your interlocutor has a better sense of the state of the music world, and that was a way for them to indicate it.
But even in the US, are you sure that musicians from the big 5 need side gigs? It seems that the salary in those orchestra are in the $100k-$200k range annually. Enough to live even in the most expensive cities, right?
It already is. Pure math departments are largely service oriented. They exist to teach engineers calculus. They are already spending a great deal of time doing non-research tasks, just like musicians you described. The exceptions would be the very top researchers at R1 schools, and even then they often spend time advising students and teaching occasional courses. It's not super common to have people do nothing but research in a pure math department.
We need to distinguish "professional opera singer" and "professional orchestra player" vs Pavarotti though :). Just like there are hundreds and thousands of "professional singers" and one Jennifer Lopez (though one could argue she's a perfect example of side gigs:).
My musician friends teach, do social networks, do all kinds of gigs, and are usually "multi barely employed". Not a single one of them, and two are fairly successful, are "full time employed" in the same sense a corporate professional is :-/.
Yes, if you're one of the few world famous sopranos you don't need to teach, but most singers are not world-famous. I knew one singer who toured internationally, had sung in front of thousands of people, had sung with world famous people, etc. But who lived in shared accomodation and worked several other part-time jobs to make ends meet.
Yes, they really did. Getting to that level requires training at an intensity that closes off the option of training for an alternative career.
So, even though you try hard to become a pianist, if you don't become famous, you're ok.
A friend of mine did this, he lives in a massive house and just enjoys his music, teaches occasionally.
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.
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.
The same has been true to some extent in the past for popular music. Up through maybe the 70s and even 80s, a lot of the instrumental parts for the "hits" were recorded by trained jazz musicians.
And they have been for a long time:
https://en.wikipedia.org/wiki/Concerto_for_Group_and_Orchest...
No one mistakes a pop artist or afficianado for some great connoisseur of culture.
Classical music was somewhat elitist even at the time, coexisting with popular/folk music traditions. The Romantic period definitely saw music and art break away for traditional forms and conservative mores, but it wasn't a free for all.
The people who enjoy classical music today are largely the same people who enjoyed it at the time. Educated and 'enlightened' upper/middle classes, who sought music celebrating their aspirations. Freedom from political oppression and aristocratic control. A world where people could succeed based on talent, hard work, intelligence, and propriety. Where the middle class would have the power to reshape government and social institutions to advance their interests rather than those of the nobility. A personal experience of the religious rather than state ordained. The music pivots to natural, romantic, mystical themes as these people lost faith that industrialization will deliver for them.
Compare modern popular music which deals with universal themes - love, loss, sex, money, partying. You can enjoy pop music and still feel that these themes are not important to you.
People don't fake enjoying classical music to convince you that they're smart and cultured. They just gravitate to music which represents their idea of smart and cultured. The same is true for a lot of art.
Outside church settings, classical music of the Baroque, Classical and early Romantic eras was for the elites, and the masses had their own musics. This only changed gradually over the 19th century.
It's also weird to still be hung up on atonality in the contemporary classical world, when the pop-music world has for decades now had acts like Merzbow that are often farther out into noise.
>I threw all my past music career in the garbage. There was no longer any need for concepts like 'career' and 'skill'. I stopped playing music and went in search of an alternative. — Masami Akita
Pulse Demon is the only Merzbow album with any cultural importance, and that's mostly because the eye-catching cover art let it replace Lou Reed's Metal Machine Music as the default "check out how extreme this is" meme album. Only a tiny minority of music listeners will enjoy listening to it, and there is no establishment pushing it as the future of music.
I don't care for the genre myself, but having been to events and seen pleasurable crowd reactions and met people who traveled some distance for it, I can't deny it has at least some real following. Who cares if it isn't discussed as the future of music? There are punk, metal, and hardcore subgenres that draw the same narrow audiences and don't aim to shake the world, but claiming that disqualifies them as part of the popular-music world would be silly.
What an incredibly cynical take. I’ve done several chamber music collaborations with a violist who also plays pop music gigs on keyboards.
There are arrogant pricks in classical music. And in software engineering and every other discipline. Personality is orthogonal to field of interest.
Anyway you complain that classical musicians look down on pop music while you yourself do the same about modern composers.
I literally gave several examples of modern genres in which classical composers still produce good work. I just said they're unlikely to be found in academia
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.
That is not my objection to AI art at all. The value of art for me is that somebody has an idea to express and they're trying to communicate it to me. That's totally absent from AI-generated material. I'm not categorically opposed to AI, but my interest in automatically generated content tailored to indulge my personal taste is absolutely zero.
I don't see why that would exclude GenAI - you have an idea, you write a prompt, you get something that's sort of but not quite what you were going for, so you iterate a bit until it's good enough to communicate what you wanted.
Just like if I tell an artist can you draw a painting of a deer in the forest, but make it ominous and tense. I could have a vague idea of what that would mean for me but the professional artist will make correct decision in composition, light etc. to create that.
Just my sentence is nothing but the image can evoke feelings if done right.
Even engaging with the nuance is beyond the pale.
I express myself with AI all the time, I just can't share it with anyone because it's banned from all the platforms where I'd care to do so. I don't really write stories without AI anymore, so probably people won't see expressions like that from me again. Maybe you could call that "AI hurts artists", dunno.
The outcome is also bad though, once you scale past static images. That's why consumers, who otherwise are apathetic at scale, are extremely negative against generative AI. at least where they (perceive to) notice it.
Besides, I don't think you can be driven by thousands of outcomes, by definition, as you can't be in love with thousands of people. Your main motivation must be the thing that unites them. Perhaps you are driven by the process of imagining solutions to problems and/or realizing your ideas.
Put another way, “draw me something sad” is too vague; a million people can issue the same prompt, and what comes out does not correlate to any specifics of their own experience of sadness.
It's both. The outcome is bad (boy is it ever bad), and even if it were good I still would rather enjoy art produced by humans.
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.
That's great. A lot is lost when art has to cater to audiences.
You could pump a large part of those resources into supporting other kinds of music and arguably the outcome would be more interesting.
Of course, some poor people do enjoy these kinds of things! But if you gave them a choice between the subsidised ticket or the embedded subsidy as cash in hand, I'm sure most poor people would take the cash.
> You could pump a large part of those resources into supporting other kinds of music and arguably the outcome would be more interesting.
Or give the money to poor people, or leave the money with tax payers, etc.
God I miss those days.
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.
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.
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.
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.
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".
Certainly more effort has been put into exploring the relationship between... Bach and Godel than your surmise suggests; SHRDLU, Toy of Man's Designing!
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.
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?
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.
I'm not a mathematician so I can't judge the results (which is kinda my point).
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.
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
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.
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.
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.
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.
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:
“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.
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".
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".
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).
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.
In another direction, there's even a literature on what happens when you allow sets to contain themselves as members, like Aczel's Anti-Foundation Axiom. There's literatures on purely constructive versions of set theory, where everything has to be computable. Like I mentioned before (reverse mathematics), there's work on what happens when you adopt much weaker axiom sets, like second-order arithmetic but weak choice principles such as taking Kruskal's tree theorem as an axiom.
So while AI would accelerate this work, the existing body of work on alternate axioms is tremendous. A surprisingly large amount of it translates between systems, and there are precise tools to measure how weak or strong a system is, relative to its competitors.
I'm pretty sure pure mathematics is the part of math which is not about reality.
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.
> 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.
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.
> 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.
Jarred is not a mathematician. He just heard about a problem and asked Claude to try solving it.