It didn't come up with a counterexample for the P versus NP problem, I wonder if they just didn't ask about it...
Ten advances in mathematics and theoretical computer science
881–890 of 1001 posts
Re: Ten advances in mathematics and theoretical computer science
#882Earlier quoted context omitted.
I do not think it is so clear. Programming has verifiable and non-verifiable aspects. Competitive programming, passing tests, and performance can all be verified. But translating English requirements into actual software, software architecture, taste, or UI design cannot. And yet over the last couple years we’ve seen huge lifts in all of these areas, not just the verifiable ones. Verifiable areas I think are clearly…
> we’ve seen huge lifts in all of these areas, not just the verifiable ones. most gains are still coming from data. isnt that supposed to 'run out' though?
thats the whole point of turning to formal verification:
Imagine a hypothetical oracle, call her MyladyMath, imagine you can turn to MyladyMath, submit a correctly formed dossier of axioms and definitions, theorems with proofs, and then a newly putatively proven theorem T. MyladyMath will complain if your dossier is malformed, and point out where and why. If the dossier is not malformed it will eventually read in the claimed theorem T, evaluate its proof and then either point out a which step is erroneous and why, or ultimately accept the proof.
Instead of a large corpus of human authored text, this map from dossier/theorem -> accept / reject is a huge implicit array of bits, something fundamental, and this weird gigantic array of bits that effectively describe all accept/reject responses MyladyMath would return exactly. We would never run out of "corpus" when it comes to math, if humans had access to such an oracle.
And we do have access to this oracle, and possess compact algorithms that describe the accept / reject bits. One of them is called MetaMath, a minimalistic verifier, which keeps the concepts of prover and verifier separated, this choice results in concrete proof objects (a sequence of step label references).
The machines are going to comb through all possible paths of the next N steps, for progressively larger N, efficiently compress those results in the weights of an LLM and then use the gained experience as the intuition for guided "not-so-brute"-force proof search, using the prior iterations intuitions to grade the surprisal of the N+1't iteration of results, etc.
The money will not stop flowing in that direction: all power blocs, nation states, militaries, banks, ecommerce, ... depend on cryptography. And the machines will soon do more rigorous proof search grounded in more balanced and objective observations. There is no responsible disclosure mechanism for flawed hardness assumptions in cryptography. It's going to get rocky, and the common man will wonder why the gods have gone crazy, wonder why they don't just pull the plug out of the machines, but nobody will in a staring contest to see who dares keep the plug in the longest (and dominate global cybersecurity).
It's the end of the age of artisanal mathematics, it will now become industrialized mathematics.
Re: Ten advances in mathematics and theoretical computer science
#883Earlier quoted context omitted.
> 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.
This is what most people seem to forget, OpenAI has probably spent more money the last year than all of math research has during human existence.
Re: Ten advances in mathematics and theoretical computer science
#884People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…
we gonna go full Pandora’s Star where the AI discover laws of physics that are impossible for humans to understand and create the wormholes
Re: Ten advances in mathematics and theoretical computer science
#885Earlier quoted context omitted.
> 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.
nothing prevented us from defining cryptocurrencies, auto-rewarding new math in objective manners, grading theorem surprisal objectively, etc. before the advent of LLM's.
being lucky enough to receive the opportunity of hiding in some academic closet, poking your hand out begging for scraps, was a different, perfectly alternative path humans decided to take instead.
It's a bit late to start standing up for your rights when the robot overlords arrive.
Re: Ten advances in mathematics and theoretical computer science
#886Earlier quoted context omitted.
What about them?
Cambridge Analytica gathered data to build targeted profiles and used these profiles for political advertising without informed consent: https://en.wikipedia.org/wiki/Facebook%E2%80%93Cambridge_Ana...
Yes, but there is little evidence this had a meaningful effect on votes.
Re: Ten advances in mathematics and theoretical computer science
#887Earlier quoted context omitted.
How do I directly benefit from this supposed "growth"? Seems like its just making things worse for most people.
Plenty of people are making money from AI? And I am not sure I've seen it "making things worse for most people" yet, do you have a source behind this? If your source is AI layoffs, there were plenty of layoffs with the invention of the horseless carriage, but that doesn't mean it made humans worse off overall. There are reasons to be skeptical about progress and AI and all that but the 'making things worse for most p…
>Plenty of people are making money from AI?
Is the amount of people making money from AI greater than the amount of people who lose money from AI? Is maximizing prosperity across humanity even a goal, at this point? Am I to be expected to believe, without doubting, that the end goal is the benefit of the many?
Re: Ten advances in mathematics and theoretical computer science
#888People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…
>let people express their own values in democracies, or will we just get much better at manipulation?
Both are the same thing. Two sides of the same coin.
Re: Ten advances in mathematics and theoretical computer science
#889It didn't come up with a counterexample for the P versus NP problem, I wonder if they just didn't ask about it...
You can't come up with a counterexample for P != NP because there isn't a formula to disprove. For P = NP you would propose a general algorithm to convert all NP problems into P in P time, and an AI could then find a counterexample which would disprove that particular method. To demonstrate P != NP you need to prove that no possible algorithm can convert any NP into P which is much harder than providing a counterexample.
AI has just gotten to the intelligence that it can make clever counterexamples to mathematical conjectures, but the frontier isn't quite smart enough that it can make novel contributions to mathematics. We are really close though. Only a matter of months away.
Re: Ten advances in mathematics and theoretical computer science
#890Earlier quoted context omitted.
... not overtly, intentionally evil. FTFY
What’s the case that they’re secretly, unintentionally evil?
The margins for groceries are objectively thin. The only way to provide food at lower prices is to provide a worse good or service, eg. less variety, less quality, less availability, etc. You will see all of these outcomes in NYC, if anyone even accepts the bids to begin with.