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Is mathematics about to enter the conservatory?

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Re: Is mathematics about to enter the conservatory?

#111

Post by johnnyanmac »

OroPla wrote: post #74
johnnyanmac wrote: post #24

Earlier quoted context omitted.

>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.

AI seems to be the new CGI. If it's invisible nobody cares and you only notice when it's awful.

Yeah, that's my impression from games. Even being told that a game was vibe coded doesn't matter much unless the game runs like crap. GenAI is a OR disaster, though, and very few Indies can really "hide" the usage as of now. How AAA navigates it will be interesting to see, but this isn't exactly a booming time in industry to begin with.

Re: Is mathematics about to enter the conservatory?

#112

Post by piltdownman »

a2ff6eeb0 wrote: post #83
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 progr…

What did the Medicis or Guggengheim's do other than be rich and idle at the right time and place in history?

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.

Re: Is mathematics about to enter the conservatory?

#113

Post by lioeters »

istjohn wrote: post #46
sankhao wrote: post #38

>Mathematics, especially pure mathematics, has always been about communicating stories that help us understand reality more deeply. I'm pretty sure pure mathematics is the part of math which is not about reality.

Reality encompasses more than the physical universe. Abstract mathematics describe an aspect of reality, too.

One might argue that mathematics is more fundamental to reality than space and time, which emerge from it.

Re: Is mathematics about to enter the conservatory?

#114

Post by QuesnayJr »

kdavis wrote: post #89
QuesnayJr wrote: post #58

Earlier quoted context omitted.

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 origina…

I don't see how you came to that conclusion, since I'm telling you the actual state of play. There's a big literature on what results require the Axiom of Choice, for example. (The book Handbook of Analysis and Its Foundations covers this thoroughly.) There are many results on what follows from the Continuum Hypothesis or other cardinal arithmetic axioms. There is a big literature on what follows from assuming the existence of large cardinals. There's a separate literature on adding "forcing axioms", like Martin's maximum. There are hundreds of papers on open questions that are settled by adding additional axioms to ZFC, and to identifying the weakest axioms to add to settle various open questions.

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.

Re: Is mathematics about to enter the conservatory?

#115

Post by QuesnayJr »

kdavis wrote: post #68
QuesnayJr wrote: post #58

Earlier quoted context omitted.

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…

What name does this "well-developed field of mathematics" go by? (I just want to get a taste of what the field is like.) 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".

"Descriptive set theory" is a good starting point, though it's the bulk of what set theorists in general do.

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).

Re: Is mathematics about to enter the conservatory?

#116

Post by adgjlsfhk1 »

rowanG077 wrote: post #85
frikskit wrote: post #50

Earlier quoted context omitted.

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.

it's nowhere close. Most orchestras are playing 1-2 nights a week (max) and each performance has 0 or 1 rehearsal (1 if it's a new program, 0 otherwise). Average when performing is maybe 20hr a week

Re: Is mathematics about to enter the conservatory?

#117

Post by djeastm »

whateverboat wrote: post #95

> Could this model work for mathematicians? It’s easy to imagine: in Euclid’s time, mathematics largely existed as an intellectual pursuit worthy of a few inclined people. 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.

Do we know much at all about Pythagoras or his motivations outside of legendary accounts from many years later?

Re: Is mathematics about to enter the conservatory?

#118

Post by saberience »

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.

As someone who's been close to several opera singers (long story), I would say that the amount of opera singers who don't have side gigs in teaching or otherwise is very, very small.

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.

Re: Is mathematics about to enter the conservatory?

#119

Post by bananaflag »

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?

First of all, because mathematicians themselves are now asking the right questions to the public models to solve problems.

Re: Is mathematics about to enter the conservatory?

#120

Post by kazinator »

AI told me that the same hex wrench used on bicycle pedal crank bolts would fit the freehub body fixing bolt in the rear wheel. (Spoiler: nope!)

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.

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