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Ten advances in mathematics and theoretical computer science

openai.com

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Re: Ten advances in mathematics and theoretical computer science

#171

Post by artninja1988 »

traes wrote: post #10
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…

Every time someone makes a comparison to chess I die inside. Chess is a spectator sport primarily funded by a few eccentric billionaires. Players artificially constrain themselves in timed environments knowing that they will never be able to produce better moves than a smartphone because a select few people find it interesting. Only ~30 top professionals actually make enough money to have a full career playing chess,…

>Only ~30 top professionals actually make enough money to have a full career playing chess, maybe a few hundred more can sustain a meager lifestyle with coaching gigs.

Was this different before chess computers were invented?

Re: Ten advances in mathematics and theoretical computer science

#172

Post by asdfologist »

woeirua wrote: post #150
ultimatefan1 wrote: post #118

one of the early premises of how ai takeoff would go was that a system that could solve open problems in advanced mathematics would also discover novel advances in math and computer science that directly unlock drastically better software performance. we are seeing frontier level math breakthroughs (ie performance that would put it in the top 100 or 1000 mathematicians in the world if it were a human, meaning top .00…

This makes no sense. To believe this you have to think that the models are somehow being overfit explicitly on academic mathematics and it doesn’t carry over at all to more practical software engineering. I wouldn’t make that bet.

Unlike math, software is constrained by the physical world.

Re: Ten advances in mathematics and theoretical computer science

#173

Post by whattheheckheck »

aabhay wrote: post #6

My main gripe here is the lack of transparency around the total experiment and construction. I doubt that they simply pointed their model at these ten specific problems alone and gave the model one shot; therefore the $2000 number could be completely misleading, similar to P-value hacking by not disclosing the total experimental setup. I want to know: 1. How many total problems were given to the model, and what perce…

Yeah I remember reading about something along the lines of Mathematics is now about the scaffolding around you find the problems/solutions not just the problems and solutions. For teaching purposes. This was before this ai craze

Re: Ten advances in mathematics and theoretical computer science

#174

Post by whattheheckheck »

mungaihaha wrote: post #110
dist-epoch wrote: post #95

Earlier quoted context omitted.

I don't think you want to bring cost into this argument. Even if the cost was $1 mil for these 10 problems, that's maybe 10-20 math researchers for a year. Do you really think that if you paid that to humans, they will deliver the same results?

Grad students on zero pay solve problems like this everyday. What exactly is your point here?

Give the grad students these resources and they can do even more!!!

Re: Ten advances in mathematics and theoretical computer science

#175

Post by sashank_1509 »

energy123 wrote: post #89
traes wrote: post #10

Earlier quoted context omitted.

Every time someone makes a comparison to chess I die inside. Chess is a spectator sport primarily funded by a few eccentric billionaires. Players artificially constrain themselves in timed environments knowing that they will never be able to produce better moves than a smartphone because a select few people find it interesting. Only ~30 top professionals actually make enough money to have a full career playing chess,…

The distinction is mathematician vs mathematics. Mathematics is going to reach new heights beyond the wildest dreams of contemporary mathematicians. But perhaps without the participation of many paid mathematicians.

Just sounds dystopian,

Re: Ten advances in mathematics and theoretical computer science

#176

Post by Ar-Curunir »

threatofrain wrote: post #166
woeirua wrote: post #150

Earlier quoted context omitted.

This makes no sense. To believe this you have to think that the models are somehow being overfit explicitly on academic mathematics and it doesn’t carry over at all to more practical software engineering. I wouldn’t make that bet.

This also makes the assumption that frontier math has all the long hanging fruits already taken... also very dubious.

Some of the problems solved here, at least in CS, have been open for decades, and have been worked on by very smart leading researchers in the field, including Turing Award winners.

Like, these would be best-paper awards at many top CS conferences.

Re: Ten advances in mathematics and theoretical computer science

#177

Post by Ar-Curunir »

kcexn wrote: post #158

Not being an expert in any of the fields OpenAI has "advanced" I don't want to prematurely downplay the significance of this contribution. However, I am worried that the language they are using in this blog post is exaggerating for the sake of marketing. It is true there hasn't been a reliable computational approach to solving these problems before. But do these proofs contribute new ideas to the mathematical corpus,…

The problems from CS (CVP and circuit complexity) are very important problems that have been worked on by top researchers for 30-40 years. Some of these researchers include Turing Award winners. A solution to them would be a best-paper award at many top CS conferences.

Re: Ten advances in mathematics and theoretical computer science

#178

Post by kittoes »

einpoklum wrote: post #14
aabhay wrote: post #6

My main gripe here is the lack of transparency around the total experiment and construction. I doubt that they simply pointed their model at these ten specific problems alone and gave the model one shot; therefore the $2000 number could be completely misleading, similar to P-value hacking by not disclosing the total experimental setup. I want to know: 1. How many total problems were given to the model, and what perce…

Also, have there been examples of researchers not affiliated with OpenAI (or another LLM creator), who have done something similar? Another question I have is whether or not OpenAI 'simply' hired capable combinatorics researchers to work on problems, and they have, and the use of the model is incidental / secondary to their work.

https://blob.byteterrace.com/public/bds-theorem.html

I have no affiliation whatsoever with any AI company, nor any formal education outside high school, for what it's worth. Simply being curious and persistent can get you quite far in my anecdotal experience.

Re: Ten advances in mathematics and theoretical computer science

#179

Post by vector_spaces »

uh_uh wrote: post #119
dist-epoch wrote: post #95

Earlier quoted context omitted.

I don't think you want to bring cost into this argument. Even if the cost was $1 mil for these 10 problems, that's maybe 10-20 math researchers for a year. Do you really think that if you paid that to humans, they will deliver the same results?

It is comical at this point. Some people just can not stand the thought of AI actually delivering and are trying to find whatever ways to discredit it.

Sure, but I don't really understand what the argument is to _not_ be transparent about methodology, since if the models are so powerful, then doing so would easily support the claims and put these concerns to rest. People are right to be skeptical given what is being implied and the orientation of the narrative

I know it's more exciting to say "AI disproved a longstanding conjecture" vs to say "it did so AND it took several PhD specialists in the field this many attempts to even produce a prompt that got the model spitting out something useful under some configurations, and many iterations to optimize the configurations, and the prompt itself, and many trials with that configuration to solve the problem. All told we spent more than a typical math academic can hope make in their career."

By not being transparent, they invite skepticism and cynical takes, like maybe it's just that tempered and qualified claims are an existential threat to companies that are fully subsidized by the hype train?

I don't know. Either way, it seems like it would be easy to address these, so why should they not do it?

To be clear, even if that tempered version is close to reality, it doesn't make the models not useful! It just forces a certain calibration of expectations

I say this btw as someone who uses these things extensively, including to disprove an old conjecture my advisor and I were stuck on recently. I know they are powerful and that everything is different now because of them. Let's be sober when discussing them though

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