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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

#931

Post by camdenreslink »

azan_ wrote: post #837
bamboozled wrote: post #690

Earlier quoted context omitted.

As others have said, it's hard to know how significant these results are without more transparency around the methods used to obtain them.

Not really. Why would that be the case?

If the prompt was crafted by an expert mathematician with pages of context and insights provided to the LLM to put it on the right path, that is a lot less impressive than a prompt that just says "find a counterexample to this conjecture".

Similarly, if they are spending millions of dollars in inference just churning on thousands of problems and these are the 10 solutions they came up with, that would be less impressive than if they chose these 10 problems specifically and were able to come up with solutions.

Re: Ten advances in mathematics and theoretical computer science

#932

Post by andai »

alberto-m wrote: post #903
DiscourseFan wrote: post #841

Earlier quoted context omitted.

Can you expand on this?

Not OP, but my interpretation is this. Quantum waveform collapse has been proposed as explanation for consciousness, allowing to explain how an entity can have free will and yet obey rigid physical laws: https://en.wikipedia.org/wiki/Consciousness_causes_collapse I think OP is suggesting a similar thing happened in the LLM, implying it gained consciousness despite following a well-defined compute process.

No I just meant WFC as an algorithm for solving problems.

https://github.com/mxgmn/WaveFunctionCollapse

It's one of the coolest things I've ever seen.

I guess I've been pronouncing it wrong though. It's wave function collapse, not waveform.

I haven't studied it properly yet but it kind of looks like how sudokus work. You have a bunch of plausible options, and the various possible worlds overlap with each other but not completely and then you eliminate the things that are not possible until the actual possibility remains.

I think thinking works similarly, and I wouldn't be surprised if artificial thinking also worked similarly.

Re: Ten advances in mathematics and theoretical computer science

#933

Post by camdenreslink »

uh_uh wrote: post #343
dgacmu wrote: post #330

Earlier quoted context omitted.

It's disjointed? The post that started this sub-thread asked: > 1. How many total problems were given to the model, and what percent were left unsolved at what cost before giving up? 2. How many attempts did you give the model at solving these problems? 3. How expensive was the harness, e.g. did the model have access to a job cluster? I think it's an extremely relevant question to ask, because it helps us better unde…

It just feels silly to haggle about the price here. It doesn't even matter because it's going to drop by an OOM quickly. If these 10 problems were solved by humans, it would be pretty impressive, even if it took a large number of researchers! Yet when AI does it, HN commenters suddenly feel the urge to play accountant.

The interesting question is "Which problems are LLMs good at solving, and which problems are LLMs bad at solving?", which could also be restated as "Which problems are cheap for an LLM to solve?". So cost is relevant here.

Re: Ten advances in mathematics and theoretical computer science

#934

Post by noslenwerdna »

energy123 wrote: post #50
piker wrote: post #2

I don’t feel the existential dread of mathematicians is correct. It seems to me in fact these results are bringing math mainstream. I now personally look forward to the interpretations and discussions of the significance of such results by human mathematicians. Now I understand that it’s mostly the super stars benefitting from the increased attention. Folks who are less established don’t share in that glory. But on t…

The old way of establishing career credibility is being destroyed, for better or worse. Accomplishments that used to be career-defining are hard to distinguish from AI, and correlate more with access to compute. Think about Bill Gates's math paper he wrote in college. That kind of thing is gone now as a path to credibility. There's still competitions and grades, but the diversity of paths is going away. Maybe new one…

I mean there were problems with the "old way" as well. Not clear if this change is net positive or negative in my opinion.

Re: Ten advances in mathematics and theoretical computer science

#935

Post by joshmarlow »

axus wrote: post #642
joshmarlow wrote: post #437

Earlier quoted context omitted.

I don't understand why this got downvotes - simply extrapolating current trends leads to the need to answer all of these questions. My own $0.02 on the economics piece - every country should have a sovereign wealth fund. Governments should block market access from automated[0] companies until those companies provide equity contributions to the wealth fund for that country. This aligns regulator and corporate interest…

Nationalize the data centers, reserve enough inference to automate power generation, food production, transportation, and housing. Is there any government that has gotten socialism correct for its citizens? I'd point to UAE/Qatar if they didn't depend on human servitude and inequality.

I would not advocate nationalization of any operations - I think the free market will run the data centers better in general.

I'm only suggesting (eventual) negotiations between countries and automated corporations - to operate here, you contribute equity.

Re: Ten advances in mathematics and theoretical computer science

#936

Post by killerstorm »

sothatsit wrote: post #535

People 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…

The reason writing is hard might be that post-training pulls style into a particular direction.

In other words, big labs are much more interested in making "AGI" than in making a good writer, especially as what qualifies as "good writing" is rather subjective. E.g. before AI use of metaphors and rhetorical devices were generally a sign of a good writing. Of course, not if you keep spamming the same rhetorical device - but a stateless AI can't know which one it is over-using.

Re: Ten advances in mathematics and theoretical computer science

#937

Post by flaburgan »

alasano wrote: post #691
J_Shelby_J wrote: post #651

Earlier quoted context omitted.

I've noticed that out of all LLMs I've ever used that Fable is the MOST LLM; the text it produces is abomination. It's impressive how much I hate it. It is such an awful writer - it assumes the reader has zero context and therefore gives every single bit of context and detail - which is nice if you're writing a legal document I suppose. But it uses, niche, $10 words to describe every facet of everything it's discussi…

Just praised Fable in another comment but what you're saying is also insanely true. I literally roll my eyes and cringe quite often at its output pretty much daily. I don't like to overload my sessions with skills but I've been using a "write-normal" skill I made just to have it rewrite outputs that particularly piss me off. https://gist.github.com/alasano/1c734fa055231a5defcfd213217e... I'm sure there's a million of…

"the test is whether the sentence would work as a pull quote or a LinkedIn post. If it would, rewrite it until it would not." LinkedIn really became the default garbage example

Re: Ten advances in mathematics and theoretical computer science

#938

Post by CamperBob2 »

sdenton4 wrote: post #702
pama wrote: post #514

Earlier quoted context omitted.

It is unfair to dismiss contributions to decades old open problems as equivalent to calculating more digits of pi. It missed the mark by a lot—as does the two bucket simplifaction.

Five (maybe six?) of the results are improvements on bounds. These kinds of problems tend to have some initial advances, and then stall out as the complexity of the bound skyrockets... until some grad student is bored enough to push the boundary. The big-O complexity of matrix multiplication is a good example of how this works: yeah, it's a useful problem, but the solutions are galactic algorithms, and increasingly c…

As someone with a PhD in combinatorics, you're aware that it takes only one counterexample to invalidate a conjecture.

There's nowhere else to move the goalposts. You've already stashed them in the far corner of the parking garage down the street from the stadium. If you go any farther you'll leave the school grounds entirely.

Re: Ten advances in mathematics and theoretical computer science

#939

Post by pama »

sdenton4 wrote: post #926
pama wrote: post #818

Earlier quoted context omitted.

Your inverted logic does not hold. The fact that such useless problems for bounds exist does not mean that improving bounds is useless. 9 fields medals in the last twenty years, including the one to Terrence Tao, were for improvements on bounds. 3 of the 4 medals in 2022 were for bounds; 2 of these medals were in combinatorics.

I stated that boring bounds improvement problems exist, not that all bounds problems are boring... Sigh.

I agree boring problems exist; bounds may have a fare share of them. None of the bounds problems in this set are even close to this category; many of them are closer to the type of contributions that in the past got recognized by special awards. Your initial replies were misleading.

Re: Ten advances in mathematics and theoretical computer science

#940

Post by amelius »

arenaninja wrote: post #435
Chance-Device wrote: post #105

Pretty cool. The impact of AI is getting undeniable, there aren’t many positions left to move the goalposts to at this stage, next they’ll have to be outside the stadium entirely. The sooner people can be broken out of their denial about all this the better, and we can start actually taking it seriously.

It's indeed very exciting. I'm looking forward to new advancements/predictions in physics. Preferably as beautifully explained as E = M*c^2

A formula like e^(i*pi)+1=0 is probably closer.

But it's not clear if LLMs will produce abstractions that humans would find elegant.

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