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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

#831

Earlier quoted context omitted.

> Whilst current models can't 'intuit' and come up with conjectures People keep saying this. Why? Surely the AI can complete the prompt “Generate new research questions based on these observations”? When I read the reasoning traces of coding models they are constantly asking themselves questions and attempting to answer them.

I like the illustration that the models are working on a convex hull of known information. Filling gaps with linear combinations of known facts and results. They can't exit the hull until the "intuition" starts spawning points outside the convex hull.

I have news for you. All humans do is also filling gaps with combinations of known facts and results - in new ways. "Everything is a Remix" is a good watch on youtube that explains this. Picasso might look like he has an invented personal style, but his style is a combination of different little details he took from others and mixed in a new way. Mozart the same. No music artist could ever create music in a vacuum. Everyone, for every art and science, the same. I know many are trying to cling to the last hope of human specialness, that "thing" that AI can never get to.

It's a convex hull of information that is reflective and spans outside of itself and combines in a new way, when you shine two known rays of light together from the inside.

Now it gets better. AI can be orders of magnitude more creative than any human could ever hope for, because his convex hull of information is orders of magnitude larger, and the possibilities for new combinations are equally larger.

Re: Ten advances in mathematics and theoretical computer science

#832

Earlier quoted context omitted.

Sigmoidal, not exponential. It would be insane to assume an exponential curve

in the absence of a stalling signal. it's better to assume exponential and work backwards than hope the next bottleneck is impossible.

Since when does realism become hope? (It's the other way around)

Re: Ten advances in mathematics and theoretical computer science

#833

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.

Those that claim their opponents are in denial are most likely in denial themselves

Re: Ten advances in mathematics and theoretical computer science

#834

Earlier quoted context omitted.

In fact I don't think that rich people are cartoon villains who enjoy watching the poors starve. If AI leads to greatly increased productivity, then at existing tax rates there will be more than enough to provide good living conditions for people who can't find jobs.

so why do we have the poverty and inequality today? why do they spend the money they do on the things they do? they are not altruists and they never will be. they could change millions of lives today, but most do not. pure naivete.

Poverty and inequality keeps declining all the time thanks to economic growth.

Re: Ten advances in mathematics and theoretical computer science

#836

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…

Sigmoidal, not exponential. It would be insane to assume an exponential curve

That's a false binary. The right binary is whether it's a convergent function or a divergent function. A sigmoid is convergent, which is not well substantiated and more farfetched than a divergent function, even if it's true that 2^x is too optimistic.

Re: Ten advances in mathematics and theoretical computer science

#837
post #672

Earlier quoted context omitted.

It is marketing, they are a shady company, and yet, if someone had access to these results before today's modern AI tools, they could get tenure at any university in the world.

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?

Re: Ten advances in mathematics and theoretical computer science

#838
post #548

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…

We will get much better at manipulation and better at people “writing” things to justify their own feelings. What’s new about LLMs is that you can scalably manipulate people individually. It used to be that you could either have scale (speeches, tweets, interviews, website, etc.) or individual engagement (replying to mail/tweets/town hall questions.) Now you can pull the history and preferences of an individual, then…

> Part of this can be good (you talk about what they care about, where 90% of broadcast messaging might not apply) and part of it can be bad (manipulation.)

Side note: it's manipulation either ways because you chose what to talk about, with a goal in mind.

Re: Ten advances in mathematics and theoretical computer science

#839

Earlier quoted context omitted.

That's a good test for a robot, not for AGI. AGI should test only intelligence and should not require limbs.

Okay we can make a completely digital environment for it to make coffee in then. It would still fail unless you let it randomly try every combination potentially thousands of times until it stumbles upon the right path. It doesn't take intelligence to read off a recipe, it does take intelligence to read a recipe, understand it, adapt it to your specific tools and materials on hand which may differ from the recipe, an…

Why do you think it would fail? I think it’d be zero shot.

Re: Ten advances in mathematics and theoretical computer science

#840

Earlier quoted context omitted.

Dude it's not a system prompt, it's the training.

The API lets you adjust the temperature. Lower values introduce more deterministic outputs, which likely helps with the hallucination rates. If you want creative writings, use the API and play with the sliders.

They actually removed the temperature parameter starting with GPT-5.
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