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Ten advances in mathematics and theoretical computer science

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Re: Ten advances in mathematics and theoretical computer science

#851

Post by plaidfuji »

GPerson wrote: post #727
plaidfuji wrote: post #672

Any computable problem will eventually fall to computers. LLMs have made math proofs more computable, in the sense that a computer can both generate potential solutions and check the validity of its solutions on its own, with a reasonable chance of converging on something correct. I assume this was already doable to some extent, but it seems like it’s now exponentially easier. That still doesn’t mean that all math is…

In my opinion, after seein the Jacobian conjecture go, the Riemann hypothesis only has about a year left. I’m not sure if people just aren’t as aware, but the Jacobian conjecture practically was on par with those other great problems.

I would be genuinely very impressed - but still not scared - if the Riemann hypothesis were solved. I suspect that we may require “new math” to make progress on that. If a new operator / symbol is required, is that fundamentally not doable by an LLM because it’s outside of current tokenization space?

Re: Ten advances in mathematics and theoretical computer science

#852

Post by aswegs8 »

watutalkinbout wrote: post #655
fasterik wrote: post #478

Earlier quoted context omitted.

Saying that AI is "matrices" is like saying human cognition is "neurons." Maybe true at some level, but it's a low-level implementation detail. The important part of a language model is the function that maps tokens to contextual embeddings. You could compute this function using analog computing, biological neurons, or any other substrate.

It isn't an implementation for neurons, unless you believe in a designing god. Matrices are an implementation detail in reconstructing the surface of human knowledge. It's a complex surface, but it's a regurgitation.

What's the argument here? It's not about the implementation method, it is about the behavior that emerges from it. You could calculate the next token by hand on paper if you had enough time.

Re: Ten advances in mathematics and theoretical computer science

#853

Post by sergiomiguens »

avaer wrote: post #37

What happens when OpenAI et al stop being open about these things, and just pack it into the training?

https://mathstodon.xyz/@sergiosh/116847266951670037 https://mathstodon.xyz/@sergiosh/116976232522229829

Look at this two threads.

Re: Ten advances in mathematics and theoretical computer science

#854

Post by dnautics »

wombatpm wrote: post #735
tyre wrote: post #546

Earlier quoted context omitted.

We will get much better at manipulation and better at people “writing” things to justify their own feelings. What’s new about LLMs is that you can scalably manipulate people individually. It used to be that you could either have scale (speeches, tweets, interviews, website, etc.) or individual engagement (replying to mail/tweets/town hall questions.) Now you can pull the history and preferences of an individual, then…

Biology would greatly benefit. We barely understand transcription and protein structure. And the straightforward systems that we know like insulin have complex post translational modifications. So while we have a map of the partial proteonome, we have barely scratched the surface on networks regulation and interactions.

> And the straightforward systems that we know like insulin have complex post translational modifications.

insulin is not straightforward, the way the insulin molecule interacts with its receptor is nuts. on the other hand its post translational modifications are simple and dont have anything particularly surprising (no glycoslation, disulfide bonds where you would expect, nothing special kex2 cuts, arent really defective in disease states even)

Re: Ten advances in mathematics and theoretical computer science

#855

Post by dash2 »

MinimalAction wrote: post #583
dash2 wrote: post #348

Earlier quoted context omitted.

It sounds like you think no technological advances will make the world richer in the long run. I politely suggest that the past century of economic growth shows problems with this argument. I also think that, while jobs are important for prosperity, the jobs of mathematicians are a minuscule fraction of a percent of the total.

So, you're arguing that just because mathematicians are a minuscule, it doesn't matter for prosperity? Because, if so, that is an insane take honestly.

Really? "The benefit to all of humanity from advances in mathematics outweighs the lost jobs of research mathematicians". That's an insane take?

Re: Ten advances in mathematics and theoretical computer science

#856

Post by energy123 »

andai wrote: post #812
nnm wrote: post #705

This is impressive. The real game-changer will be when AI creates an entirely new, significant branch of mathematics.

Which only it understands?

I would argue we're crossed that point recently. This is a comment from twitter that I appreciated:

> "Already, there are very few mathematicians qualified to verify OpenAI’s new results. As progress continues, that number will approach zero."

Not that I'm good enough at math to have any uniquely formed opinion, but after reading commentary from people who are, my impression is that these new results are bamboozling the humans due to using tools from so many disparate areas.

At least, we can say that there isn't a single human who is smart enough to understand all ten proofs, even if there is a collective sense in which all proofs are understood.

Re: Ten advances in mathematics and theoretical computer science

#857

Post by chrisjj »

evenhash wrote: post #429
amazingamazing wrote: post #137

Can’t wait for this stuff to have quality of life increases for the average person. So far all I see is that AI has made owning a computer more expensive, made some jobs redundant, increased spam and distrust with questionable authenticity of content and of course made some Americans very rich.

Not everyone works for Evil Corp. I work in the public sector and my work supports public health and safety initiatives. AI has allowed my team to get much more done than we would have otherwise which improves the quality of life of the people in my community. So I would like to counter your cynicism with a “YMMV” depending on who you work for.

> AI has allowed my team to get much more done

We often hear this. Likewise to get things done faster. And to get things done cheaper.

Almost never to get things done beteer.

Re: Ten advances in mathematics and theoretical computer science

#858

Post by simianwords »

AngryData wrote: post #586
simianwords wrote: post #234

Earlier quoted context omitted.

It’s not obvious at all. If it were obvious to you, it would’ve been to OpenAI. It’s in their interest to accurately predict demand. The assumption that OpenAI/Sam is both really powerful but simultaneously ignorant to know what others know as obvious is well.. just strange. Especially strange when OpenAI has more information on models, breakthrough and usage patterns and we don’t. I’m not participating in the slingi…

You say that like the tech world isn't littered in a field of dead and failed companies and billions of dollars burned on failed ventures and ideas. Sure LLMs have proven they have value, but where is the trillion dollars of current investment going to be paid back from? So far it is still entirely speculation that they have such a high value, and they can't just play the long game of "well after a few decades of pro…

I agree with you but from your own comment, it seems to indicate that an obvious bubble doesn't exist. The possibility does.

Re: Ten advances in mathematics and theoretical computer science

#859

Post by chrisjj »

roncesvalles wrote: post #680
amazingamazing wrote: post #137

Can’t wait for this stuff to have quality of life increases for the average person. So far all I see is that AI has made owning a computer more expensive, made some jobs redundant, increased spam and distrust with questionable authenticity of content and of course made some Americans very rich.

It has had significant quality of life increases for me. I use LLMs for everything from: - travel and restaurant recommendations. my last few outings have been entirely LLM-advised and they turned out excellent. LLMs seem to have ingested every single Google review, photo, and menu of every business on Earth and can answer very nuanced questions like "is the garlic chicken at garnished with coriander?" - fitness, nut…

> perfect two-way communication

That's a surprise. E.g. I've found these bots pretty poor at body language.

> "There are 12 chapters in the book . Can you give me a 2 sentence synopsis of each chapter?"

Really? You tell the bot the chapter quantity?

Re: Ten advances in mathematics and theoretical computer science

#860

Post by koe123 »

akoboldfrying wrote: post #764
casey2 wrote: post #707

Earlier quoted context omitted.

We definitely are not on an exponential. Don't say we are because this isn't up for debate. AI progress is logarithmic the million dollar question is 2x or 10x for linear improvement. The nearest qualitative shift would be very fast inference so people could start writing real software on top of LLMs. A 0.001% optimization on a packing problem just isn't interesting for the amount of investment.

> A 0.001% optimization on a packing problem just isn't interesting for the amount of investment. I think you have completely misunderstood what OpenAI have accomplished here. Almost certainly no one cares about the specific concrete results achieved; they only care about (a) how difficult it would be for an intelligent human to achieve the same feat (ETA: the feat is the proof), which can be estimated by the amount…

On the other hand, if provided the financial incentive would mathematicians have solved these problems? Its not hard to imagine a world where some hard problems were not selected by the sparse experts for whatever reason (lack of interest, whatever), which could have been solved if someone was throwing down millions for solutions.
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