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Is mathematics about to enter the conservatory?

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Re: Is mathematics about to enter the conservatory?

#101

Post by stabbles »

chr15m wrote: post #98

> 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 communic…

> 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.

Re: Is mathematics about to enter the conservatory?

#102

Post by whoarewethen »

chr15m wrote: post #98

> 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 communic…

Mathematics is not chess, it is about reality. There is a huge value in P=NP for example, if such result is ever rigorously proved, regardless of the proof. Less so perhaps for P!=NP, but it would be a definite answer to a long standing question.

This is why I think "Leiden program" and similar proposals will eventually fail. It is true that the questions to be solved would have to be interesting to humans, though. But I think that also to find such questions, one would use llms more and more.

Re: Is mathematics about to enter the conservatory?

#103

Post by analog31 »

glimshe wrote: post #84
analog31 wrote: post #49

Earlier quoted context omitted.

Oddly enough I'm one of those parents. Yes, I cringed, but at the same time I would also have cringed at watching them go into something they hate just for the money. I've seen that too. 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 th…

>at a time when you had to be a research superstar to apply for a tenure track job at a third rate college. Is it any less competitive now?

Possibly more competitive. I got my degree in the early 90s. Good point.

Re: Is mathematics about to enter the conservatory?

#104

Post by ThrowawayR2 »

a2ff6eeb0 wrote: post #79
sumanthvepa wrote: post #77

Earlier quoted context omitted.

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.

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…

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?

Re: Is mathematics about to enter the conservatory?

#105

Post by falcor84 »

cc81 wrote: post #93
falcor84 wrote: post #65

Earlier quoted context omitted.

> somebody has an idea to express and they're trying to communicate it to me 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.

In my experience the AI still does a lot of heavy lifting of thinking for the person. 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…

Yes, but that sounds to me exactly the process vs. outcome distinction that the parent made, rather than a difference in the intent to communicate.

Re: Is mathematics about to enter the conservatory?

#106

Post by luxcem »

dofm wrote: post #5

> 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 — teac…

I think you are talking about the US. In Europe (at least France & Germany) most professional classical musicians are doing it exclusively (we might be an outlier but it's the norm here), competition is fierce though but at that level it's a full time job. In France we have prestigious ensembles (Orchestre de Radio France, Opéra de Paris, Orchestre de Paris), roughly 20+ subsidised regional orchestras and opera houses, military and police ensembles. That's for full-time permanent job. Underneath that there's the intermittence regime (roughly 100k people) freelance entertainment professional. Between gigs, the government provides a special unemployment insurance program to maintain a steady income. Germany is the same story, on an even bigger scale (100+ state-funded ensembles) but no intermittence equivalent.

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?

Re: Is mathematics about to enter the conservatory?

#107

Post by a2ff6eeb0 »

ThrowawayR2 wrote: post #104
a2ff6eeb0 wrote: post #79

Earlier quoted context omitted.

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…

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?

Here's the transcript: https://www-cdn.anthropic.com/8a0d1add3c637b858a9a181e98c40e...

Jarred is not a mathematician. He just heard about a problem and asked Claude to try solving it.

Re: Is mathematics about to enter the conservatory?

#108

Post by piltdownman »

VladVladikoff wrote: post #23
pianopatrick wrote: post #14

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…

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.

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

Re: Is mathematics about to enter the conservatory?

#109

Post by losvedir »

dofm wrote: post #21
encomiast wrote: post #20

Earlier quoted context omitted.

> 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 as…

There are about twenty of these people, though. 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 instrume…

This is confidently presented, but seems incorrect based on other commenters.

> 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.

Re: Is mathematics about to enter the conservatory?

#110

Post by LoganDark »

hypersoar wrote: post #60
madrox wrote: post #11

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…

>? Especially in art, the anti-AI hate mostly reduces to arguing that art is the process not the outcome. 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 pe…

It sounds like the problem you have with AI art is that instead of an artist iterating over parts of the image to get what they want, someone iterates over entire images to get what they want. (Or... they still iterate over parts of the image, but with a generative model instead of manual brush strokes.) Somehow that process distinction makes the difference for you.
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