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Is mathematics about to enter the conservatory?

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Re: Is mathematics about to enter the conservatory?

#81

Post by busyant »

nxpnsv wrote: post #51

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?

> 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.

Re: Is mathematics about to enter the conservatory?

#82

Post by Xmd5a »

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…

He did a frog's job, not a bird's.

Re: Is mathematics about to enter the conservatory?

#83

Post by a2ff6eeb0 »

marcus_holmes wrote: post #8

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…

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.

Re: Is mathematics about to enter the conservatory?

#84

Post by glimshe »

analog31 wrote: post #49
encomiast wrote: post #32

Earlier quoted context omitted.

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 societ…

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?

Re: Is mathematics about to enter the conservatory?

#85

Post by rowanG077 »

frikskit wrote: post #50
rowanG077 wrote: post #43

Earlier quoted context omitted.

$40/hour is $83,000 per year, that is more then livable in the US, and by definition of the median half make more. So I can't agree that it's not a living wage for most.

Assuming they work 40 hours a week. Do they? 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.

I would expect much more hours when performing and less when not. I would expect it indeed would be approximately a fulltime job.

Re: Is mathematics about to enter the conservatory?

#86

Post by lukeh »

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.

Re: Is mathematics about to enter the conservatory?

#87

Post by vintermann »

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 don't think fully employed opera singers, and professional orchestra musicians, tend to have side gigs. But it's also extremely difficult to get full employment in such jobs, and I think they're pretty intense: of the few people from my school days who succeeded in getting that, at least two of them quit/downshifted into teaching jobs after a decade or so.

Re: Is mathematics about to enter the conservatory?

#88

Post by vintermann »

analog31 wrote: post #49
encomiast wrote: post #32

Earlier quoted context omitted.

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 societ…

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…

Conservatory kid parent reporting here too. At least I live in a country where there is likely a job for him, even if he shouldn't win out against all the other extremely determined classical piano students.

Re: Is mathematics about to enter the conservatory?

#89

Post by kdavis »

QuesnayJr wrote: post #58
kdavis wrote: post #55

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?

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…

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.

Re: Is mathematics about to enter the conservatory?

#90

Post by NikolaNovak »

vintermann wrote: post #87
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 don't think fully employed opera singers, and professional orchestra musicians, tend to have side gigs. But it's also extremely difficult to get full employment in such jobs, and I think they're pretty intense: of the few people from my school days who succeeded in getting that, at least two of them quit/downshifted into teaching jobs after a decade or so.

My experience is different ; Somehow I befriended a bunch of professional opera and orchestra singers in my mid 20s. It is now 20 years later and they absolutely all have side gigs.

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 :-/.

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