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Mathematicians issue warning as AI rapidly gains ground

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Re: Mathematicians issue warning as AI rapidly gains ground

#221

Post by redox99 »

rad_val wrote: post #207
par1970 wrote: post #195

Earlier quoted context omitted.

> AI (in this form) will never be able to solve things we truly cannot solve yet. Argument?

The strongest argument for this is structural: what LLMs are. In a brutal simplistic way: each token is represented in a high dimensional vector. LLMs operate on them. They are the true, underlying meaning of the token for the LLM. Think of it as 1000+ ways to think of that word/token. Those meanings are baked in at training time. So, LLMs might be able to cross-reference them and solve a class of problems that flew…

Instead of going into a long technical argument of why your description of LLMs is flawed, I'll go straight to the point, because people keep moving the goal posts.

What exact problem would need to be solved by LLMs to convince you that they DO discover novel solutions?

Re: Mathematicians issue warning as AI rapidly gains ground

#222

Post by andrei_says_ »

nyxtom wrote: post #192

For every interesting problem AI solves there are a long tail of really dumb things that AI performs that humans would never do. Some days I am in awe of one-shot magic eight-ball output and other days I'm so frustrated by the sheer stupidity of what it produces. It remains to be seen whether that long tail of stupidity can ever be resolved in the current form of LLMs.

It’s like a constant game of two truths and a lie.

Re: Mathematicians issue warning as AI rapidly gains ground

#223

Post by fc417fc802 »

plastic-enjoyer wrote: post #180
Huntsecker wrote: post #163

Anyone else draw similarities with this and the artists and authors who complained when gen ai first came out. I think a lot of people don't realise the disruption ai will cause to many industries, until its directly impacting them, basically personal fable at scale ( https://en.wikipedia.org/wiki/Personal_fable ).

The artists will be fine and AI will liberate them. It's the engineers and mathematicians who are walking into the blade. They built their entire sense of self on being the best optimizers in the room and optimization is the first thing the machines take. Their whole identity was a number going up. Now watch it go to zero.

Depends entirely on whether "the market" ends up valuing what humans add to various artistic processes. Same for human engineers, who are still very much needed at least for the time being.

Certainly the scenario where a human touch isn't valued by the market raises lots of very difficult philosophical and economic questions but that's a separate issue.

Re: Mathematicians issue warning as AI rapidly gains ground

#224

Post by redox99 »

jltsiren wrote: post #184
silveraxe93 wrote: post #15

Earlier quoted context omitted.

Assume someone solves P=NP Do you think Stephen Cook and Leonid Levin deserve more credit than whoever solved it?

Depends on the solution. If the solution is that P≠NP, the concept of NP-completeness remains the bigger contribution, unless the proof techniques are particularly interesting and lead to other major results. The same applies if P=NP but the proof does not ultimately lead to a practical algorithm. If we get a practical algorithm, the answer is more valuable than the question.

Do questions like goldbach conjecture, fermats last theorem, etc deserve more credit than whoever answers them?

Re: Mathematicians issue warning as AI rapidly gains ground

#225

Post by cousinbryce »

cout wrote: post #210
nyxtom wrote: post #192

For every interesting problem AI solves there are a long tail of really dumb things that AI performs that humans would never do. Some days I am in awe of one-shot magic eight-ball output and other days I'm so frustrated by the sheer stupidity of what it produces. It remains to be seen whether that long tail of stupidity can ever be resolved in the current form of LLMs.

Are you sure you aren't underestimating human capacity for stupidity?

It’s in the training data!

Re: Mathematicians issue warning as AI rapidly gains ground

#226

Post by glaslong »

cout wrote: post #210
nyxtom wrote: post #192

For every interesting problem AI solves there are a long tail of really dumb things that AI performs that humans would never do. Some days I am in awe of one-shot magic eight-ball output and other days I'm so frustrated by the sheer stupidity of what it produces. It remains to be seen whether that long tail of stupidity can ever be resolved in the current form of LLMs.

Are you sure you aren't underestimating human capacity for stupidity?

We might be undervaluing consistency. You can plan for reliably stupid. Harder to rely on Often Smart, but Unpredictably Stupid.

Re: Mathematicians issue warning as AI rapidly gains ground

#227

Post by rad_val »

redox99 wrote: post #221
rad_val wrote: post #207

Earlier quoted context omitted.

The strongest argument for this is structural: what LLMs are. In a brutal simplistic way: each token is represented in a high dimensional vector. LLMs operate on them. They are the true, underlying meaning of the token for the LLM. Think of it as 1000+ ways to think of that word/token. Those meanings are baked in at training time. So, LLMs might be able to cross-reference them and solve a class of problems that flew…

Instead of going into a long technical argument of why your description of LLMs is flawed, I'll go straight to the point, because people keep moving the goal posts. What exact problem would need to be solved by LLMs to convince you that they DO discover novel solutions?

I'm more interested why you think my understanding is flawed honestly. I thought I distilled it decently well in two sentences. The bottom line is, in this hyperdimensional space you can find relationships that are not easily distinguished by human minds, but the corpus is still fixed, a llm can't truly know anything beyond its training data.

Re: Mathematicians issue warning as AI rapidly gains ground

#228

Post by nick__m »

Jtarii wrote: post #215
tz18 wrote: post #182

Earlier quoted context omitted.

>AI makes the math world more accessible than before. If you have a question about a proof in the lecture, you can just ask it. I think that is great, really! but does anyone remember asking a TA or teacher or prof or parent and getting told you can work it out for yourself, or maybe just given a hint? What if that is an essential part of learning, having to work through things you don't understand, but that you have…

You can ask the LLM for a hint as well.

You can but sadly most people ask for awnsers.

Re: Mathematicians issue warning as AI rapidly gains ground

#229

Post by modriano »

joelthelion wrote: post #117
modriano wrote: post #68

> “The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics,” declaration co-author Michael Harris of Columbia University As a former physicist and current data scientist/engineer, I know for a fact that commercial utility drives math research and researchers. Math is a tool to solve problems. Some mathematicians might only love the process of using the tool,…

It's also a way to model the world and produce new useful abstractions. It's not just about solving problems.

Is there a useful abstraction that doesn't help solve a problem someone has?

Re: Mathematicians issue warning as AI rapidly gains ground

#230

Post by Joel_Mckay »

martin1975 wrote: post #194
Joel_Mckay wrote: post #165

Earlier quoted context omitted.

The Ouroboros in western mythology is a cautionary tale about the uselessness of the first perfect immortal being, and why humans should suffer our imperfections with insightful grace. The concept also made a great Red Dwarf episode. LLM are more like the Mechanical Turk trick, but the persons inside the machine running the con is unaware of how their actions affect the confounded observers. Have a wonderful day =3

Thank you, human being! Have you looked at the price of a RTX 5090? I can get a used car for that.

Indeed, just paid $3k more for the same workstation we purchased last year at this time. Just the DDR5 sticks and NVMe drive cost more than most parts right now including a rtx 5070 Ti 16G card. For h265 hardware encoding, the performance differences on higher-end cards benchmarks was negligible.

Building systems based on application specific benchmarks rather than general what-if use-case scenarios will sometimes show you something interesting. ymmv. =3

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