Is mathematics about to enter the conservatory?

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

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.

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.

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.

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.

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 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.

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.

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.

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

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.

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 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".

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.

> 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.