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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

#391

Post by 8note »

c7b wrote: post #211
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…

I believe we're seeing a new kind of mathematics that will require completely new formats for publication, a bit similar to those used in experimental sciences. AI-powered mathematics should be fully reproducible, so it's the authors' responsibility to disclose the exact model type, inference settings/seeds and the full prompt history leading to the result. Of course that would ideally require open weights models. It…

why is reproduceability the thing?

shouldnt the paper be the math of the argument? the reproduction is reading the following the proof

Re: Ten advances in mathematics and theoretical computer science

#394

Post by armchairhacker »

lkey wrote: post #388
kypro wrote: post #381

Earlier quoted context omitted.

[flagged]

Your 'serious' proposal is unlimited global military bombing campaign on civilian infrastructure by the United States (which is currently losing a war using the same strategy) to 'solve safety' preemptively against a 20% number you just made up? And you accuse the 'other side' of 'suicidal apathy'?? You should put down the AI and do some self-reflection on how you came to hold these views.

GP said cooperation, never implied the US would do it alone.

Re: Ten advances in mathematics and theoretical computer science

#395

Post by [deleted] »

mag7269 wrote: post #375
NitpickLawyer wrote: post #198

Earlier quoted context omitted.

> We improve, we learn, we recalibrate our expectations based on what we've learned. That's not what people mean when they say "moving the goalposts". It means that people are adamant that something wasn't important/hard/impressive once the "AI" solves it. And then they come up with another thing that needs to be solved in order to prove it is important/hard/impressive. And once that happens, they do it again. And ag…

“AGI will only, truly, be achieved when the machine can destroy an industrial-type toilet after downing a Supreme Burrito and a large Baja Blast.” -Alan Turing (allegedly)

[deleted]

Re: Ten advances in mathematics and theoretical computer science

#396

Post by jvanderbot »

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.

Or, that the mathematical formalisms that model the limits of software performance are firm enough that barring P==NP, nothing much will change despite proofs of beautiful math.

Re: Ten advances in mathematics and theoretical computer science

#397

Post by bigyabai »

kypro wrote: post #381
c7b wrote: post #374

Earlier quoted context omitted.

And what does taking it seriously entail?

[flagged]

> We are now at the point where RSI is feasible

  What can be asserted without evidence can also be dismissed without evidence.
- Hitchen's Razor

Re: Ten advances in mathematics and theoretical computer science

#398

Post by seanhunter »

monktastic1 wrote: post #354
danparsonson wrote: post #284

Earlier quoted context omitted.

It's almost like I disagree with your use of the phrase in this context, rather than that I don't know the meaning of it.

So you defined your own idiosyncratic version of "moving the goalposts" and used it to rebut his argument, with a condescending "you understand that's how science works, right?"--instead of being honest that it is you who are changing the definition, and not his failure to understand anything. I don't see how that's any better.

He rebutted the argument about moving the goalposts by moving the goalposts. It’s better by dint of sheer bravado.

Re: Ten advances in mathematics and theoretical computer science

#399

Post by pama »

DrBazza wrote: post #96

Replace philosophers for mathematicians and Douglas Adams was spot on again. Whilst current models can't 'intuit' and come up with conjectures, they can certainly disprove some of them very quickly through the kind of grind that humans can't do. I suppose there really are some mathematicians out there today, whose last few years of study, have just been up-ended by this. -- "Yes we are," insisted Majikthise. "We are…

> Whilst current models can't 'intuit' and come up with conjectures

I disagree. I routinely let LLMs speculate or generate hypotheses along the way of helping with technical research. Sometimes they can prove the correctness of a concrete math idea but other times even an unproven conjecture helps with the numerical algorithm implementation and the result is then simply supported by additional data. I guess that any autoresearch-adjacent application has LLMs intuiting and coming up with hypotheses/conjectures—as do the steps/lemmas along a complex proof. In my opinion the modern LLMs are powerful intuitive thinkers that generate lots of conjectures of varying quality or importance.

Re: Ten advances in mathematics and theoretical computer science

#400

Post by cubefox »

addaon wrote: post #392
kypro wrote: post #381

Earlier quoted context omitted.

[flagged]

> "probably only 20% chance we all die" Bad news for you -- there's a 100% chance we all die. Sorry to be the one to tell you.

Logical mistake. There is a difference between every human dying eventually and humanity going extinct. The former doesn't imply the latter. The previous commenter clearly meant the latter.
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