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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

#891

Post by samuelknight »

MichaelMoser123 wrote: post #883

It 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

#892

Post by naasking »

tyre wrote: post #750
0xWTF wrote: post #747

Earlier 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.

Re: Ten advances in mathematics and theoretical computer science

#894

Post by fg137 »

w4yai wrote: post #341
fg137 wrote: post #107

Earlier quoted context omitted.

Didn't know I was part of an elite.

You're were for 4 months. That's what we're talking about. It used to be.

I've been on this site for much longer than that.

When's the cutoff date?

Re: Ten advances in mathematics and theoretical computer science

#895

Post by datsci_est_2015 »

deviation wrote: post #893

Genuine question, from someone with a non-math background - at what point does the constraint become the number of unsolved conjectures remaining, instead of the ability for LLMs to actually solve for one?

Not entirely following the question, but there are an infinite number of conjectures, the blinding majority of which serve nearly no purpose to humanity. Consider that for every executable program one could create a conjecture, and therefore a mapping exists from executable programs to conjectures. Now, consider the infinite possibility space of executable programs…

Anyway, unless you mean conjectures that humans have already posited, or ones that are particularly famous, that list is much shorter, but also contains conjectures that I’m not convinced can be solved before the heat death of the universe using all available compute power. P != NP is a conjecture, for example. Also a lot of prime number conjectures that are extremely computationally expensive.

Re: Ten advances in mathematics and theoretical computer science

#896

Post by chrisjj »

oblio wrote: post #874
chrisjj wrote: post #863

Earlier quoted context omitted.

> 8. Do they reduce the workweek Sure. Often to zero.

I'm talking statistically, not what happens for a lucky few. Keynes was hoping that our workweek would be 20h/week by now, through technological advancement. Instead places like the US are thinking about adopting 9/9/6 and some US states are legalizing child labor again.

> what happens for a lucky few.

I'm talking about the unlucky.

Re: Ten advances in mathematics and theoretical computer science

#897

Post by desterothx »

Legend2440 wrote: post #515
alightsoul wrote: post #513

Earlier quoted context omitted.

you are working on coding. they are working on things like "creative writing" remember that gpt 4o was popular among those who had ai as a romantic partnet?

Well that's on purpose lol. OpenAI does not want you falling in love with their chatbot and have been deliberately training it to be less romantic.

sure they do if it makes them money, probably just not worth the controversy right now

Re: Ten advances in mathematics and theoretical computer science

#898

Post by desterothx »

nightsd01 wrote: post #798
fckgw wrote: post #671

Earlier 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…

most devs i talk to say that they would love to go back to coding without ai, if everyone had to do it, so there's that. Oh also scammers have gotten so much better with llms, so a significant amount of peoples lives are worse due to that

Re: Ten advances in mathematics and theoretical computer science

#899

Post by JohnHammersley »

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…

Yes, the rate and nature of the results being produced is impressive, and Anthropic have recently invested in building out more in-house capability to do life sciences research (see e.g. [1]).

Overall I'm excited for this acceleration in discovery, even if it's causing disruption to existing research workflows. I wrote a bit about it recently [2], after seeing Levent Alpöge's counterexample to the Jacobean conjecture.

[1] https://www.cnbc.com/2026/06/30/anthropic-launches-ai-drug-d...

[2] https://scholarlyfutures.substack.com/p/frontier-models-tran...

Re: Ten advances in mathematics and theoretical computer science

#900

Post by nylonstrung »

JohnHammersley wrote: post #899
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…

Yes, the rate and nature of the results being produced is impressive, and Anthropic have recently invested in building out more in-house capability to do life sciences research (see e.g. [1]). Overall I'm excited for this acceleration in discovery, even if it's causing disruption to existing research workflows. I wrote a bit about it recently [2], after seeing Levent Alpöge's counterexample to the Jacobean conjecture…

Life sciences will get way more interesting once Demis Hassabis completes his simulated cell and we have more genomic foundation models
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