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If you want to see just how few clothes the emperor really has, ask an LLM a nontrivial problem in algebra. I just gave a math olympiad question (on the very easy end of the spectrum) to chatGPT and I cringed at its response. If it was a human being I wouldn't even criticize what they wrote, I'd be too embarrassed. And this is not because the answer's bad (and wrong), but because of the very obvious effort that this hypothetical human is making to *look* like it understands what is so obviously does not understand at all.

It's as if LLMs perfectly encapsulate the superficial and vapid nature of the Silicon Valley-rooted modern culture. There's no there there.

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Discussion

YODL 1y ago

I only recently started playing around with it. Wrt math, I found it good for surfacing high level properties of algebraic structures, but falling way short of going much deeper with the conversation.

Am curious, can you share the question you posed?

waxwing 1y ago

Yep,

prove that x^4 + y^4 + z^2 >= sqrt(8)*x*y*z

YODL 1y ago

Disappointed in myself for not seeing solution yet :/ Gonna give it a bit more thinkin’…

waxwing 1y ago

It's simple but not easy :) I didn't find it, but to be fair I didn't really try, just looked up the answer after 5 minutes 😄

Rand 1y ago

tis the season, Bless the mess

YODL 1y ago

Oh, wasn’t aware of the AM-GM inequality, not that I would have solved it had I known. Looks like it’s frequently used in Olympiad questions as it’s the first item listed in a study guide google found for olympiads. Met a guy who’d excelled in those, was very smart, but nothing extraordinary when it came to more general/abstract math (I’m prob jealous, still)

waxwing 1y ago

If you want a hint, try finding a way to apply AM-GM twice.

YODL 1y ago

I read the solution already, but that’s a solid hint. Kinda glad to have learned of the AM-GM ineq, feels like something I could have used once or twice in the past

waxwing 1y ago

Yeah. Another one that's very useful is the Cauchy-Schwartz inequality, gets used a ton in e.g. mathematical physics

YODL 1y ago

Ha, had to look it up to make sure I remembered that one.

YODL 1y ago

Btw, your write up on CTs is great. Been making some reading stops along the way of going through 02bp’s paper (and related things).

Rand 1y ago

have U tried others/*

Tim Bouma 1y ago

A tool made in the image of its creator…

Johnathan Corgan 1y ago

My own experience has been different. I mostly work with linear algebra, statistics, and differential equations, and it has been pretty good (but not perfect) as an assistant to help work out some some thorny problems in well-established areas.

waxwing 1y ago

I can believe it, seeing what it's done with coding problems, a few times. What's really shocking about what I just saw is how massively it hallucinated simplifications in a short problem (by the way, this one, to give you a sense: prove that x^4 + y^4 + z^2 >= sqrt(8)*x*y*z ). I think Olympiad problems (even easier ones) are designed to require some kind of "craft", creativity, rather than only handle turning. So unsurprisingly it immediately appealed to the AM-GM inequality (bread and butter for this kind of thing), but then made 2 or 3 dreadful mistakes to pretend that the structure was simpler than it was, before confidently asserting in great detail why so and so was true, when it was patently false.

I think it can be very good and giving you hints and strategies appealing to its vast knowledge base. Doing something new or actually *thinking*, it's just absolutely dreadful.

Johnathan Corgan 1y ago

Sure. I think it is still at the point where you need to understand a subject well enough to "fact check" its replies, and it does best at being a savant-like research assistant than an original thinker. I find myself most productive using it for problems that are hard to solve but easy to verify 😆

niftynei() 🇺🇸💸🧡 1y ago

it reminds me of that little book, On Bullshit

waxwing 1y ago

You're good with the obscure book references.

Nowadays I'm stuck with basic Spanish language novels. But I have graduated from Harry Potter type stuff to Agatha Christie so it's not so bad.

niftynei() 🇺🇸💸🧡 1y ago

“Obscure books” comes with the “got a degree in liberal arts” 😂

my high school teacher had us reading parts of Don Quixote in the original ancient Spanish and i do not recommend it 🫠

niftynei() 🇺🇸💸🧡 1y ago

wrt to LLMs i think this is the crucial point

atyh 1y ago

this actually makes alot of sense.

Rand 1y ago

t-y/* makn me rethink

atyh 1y ago

im frequently left with the “why, you little weasel!” sentiment when using llms, and when thinking about SV.

Currency of Distrust 1y ago

Man, working for SV style tech companies has driven me mad with all their AI hype. The vapidness of it is crushing my soul. I’m so sick of it.

spacebear 1y ago

LLMs: a fascinating tool for accomplishing vapid tasks

McCoy 1y ago 💬 1

AI bubble will pop. Even this gets better: LLMs only improve human flourishing if the saved time is used to produce something. Doing your work faster and “going home early” is not going to cut it.

Telluride 1y ago

Its an amazingly primitive & creative tool at this point.

I use it frequently for tasks that would take half my day In moments.

waxwing 1y ago

No question. Hugely useful. But it also regularly shocks me with what it can't do, but thinks it can :)

Telluride 1y ago

Its a bullshitter fosho