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 hid 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
> 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.)
> Even the first-chair musicians and conductors have side gigs.
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.
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
Most of the major orchestras have a union and they negotiate salaries in the $100-200k range for everyone. It’s a lot more people than you might think (70-150 people on payroll in each orchestra). There are also a lot of touring soloists in the world compared to what you expect. It’s a very stressful life, but it yields somewhere between $100k and $1M per year, and many of your living expenses are fully paid for on top of that.
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.
> 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.
I understand your point. Music is one of those careers, like professional athlete, that make parents cringe when optimistic children announce an intention to pursue it. Your numbers are off (the base pay of the Chicago Symphony Orchestra last time I checked was around $200k) and there ~30 violinists in that orchestra alone. But it's not an order of magnitude.
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.
But society in general does not really support professional athletes in any directed “conservatory” sense, beyond the weird obsession with college sports in the USA.
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.
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.
> 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.
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?
The idea that classical composers (before about Liszt) were the "pop music" of their day is uninformed. Consider 1) the size of the venues that Mozart or Haydn's secular music was performed in, and 2) the fact that the bulk of the population was peasantry who wouldn't be admitted to such venues in a time of strict class distinctions.
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.
> 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.
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.
Europe is actually worse, or at least Germany, because the government pays for opera, so it doesn't have to stand on its own two feet. So they don't (have to) care about listeners as much.
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...
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.
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.
>the anti-AI hate mostly reduces to arguing that art is the process not the outcome.
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.
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.
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".
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.
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.
> 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.
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?
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.
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.
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.
I'm pretty sure pure mathematics is the part of math which is not about reality.
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 hid 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
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.
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.
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.
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.
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?
And they have been for a long time:
https://en.wikipedia.org/wiki/Concerto_for_Group_and_Orchest...
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 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.
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.
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.
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.
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".
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.
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.
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?
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.