How much do you all think it would cost to "buy" these advances from PhDs, practicing scientists?
https://mathstodon.xyz/@sergiosh/116847266951670037
https://mathstodon.xyz/@sergiosh/116976232522229829
Look at this two threads.
Ten advances in mathematics and theoretical computer science
851–860 of 1000 posts
Re: Ten advances in mathematics and theoretical computer science
#852Re: Ten advances in mathematics and theoretical computer science
#853Any 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
#854Earlier 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
#855What 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
#856Earlier 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
#857Earlier 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
#858This 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
#859Can’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
#860Earlier 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.