441–450 of 681 posts
This is the second ChatGPT shared conversation I've seen today that is truly fascinating. The first one was someone proving another conjecture false by just repeatedly saying "keep going" to ChatGPT: https://x.com/DmitryRybin1/status/2079904005652893709 What a world we live in.
> Construct a counterexample to the Collatz conjecture. You should do a breakthrough and find a structured counterexample.
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But... what is a ring? What is a formal variable? What is a vector space? What does "algebra over the ring" mean? His point is the terms are dense too
Absolutely agree. All formal statements (like mathematical ones) are going to have some level of assumed background. And as the assumed background expands, the language naturally becomes more information dense. As for your specific questions, I believe Wikipedia does a great job of answering two of them for a layperson: https://en.wikipedia.org/wiki/Ring_(mathematics) https://en.wikipedia.org/wiki/Vector_space For th…
Not like a drink with jam and bread.
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they're still bounded by training data and how it relates to the real world. Yes and no. They can extrapolate and build upon the training data, as was the case with the last dozens of math proofs
Yes, but the point being for the LLM to be useful to us it has to do something relevant for us and we have to define what is relevant. Even if you view them as fully human level or beyond (in terms of agency) there's still some purpose that we have to help provide them with. To put it differently, if you have some idealized model in front of you that can do anything a team of humans can do, what do you say to it? It'…
Someone will still need to ask for something (or maybe it will just run autonomously making things it thinks we'll like) but it won't require any expertise in the field.
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> I don't think chatgpt could have come to this on its own without the amount of steering he did, which just validates the idea that AI is not a replacement for human expertise but an amplifier. The problem is that, what happens to human expertise as people start to use AI earlier and earlier in their careers, so that in 50 years? The problem is that Terry Tao spent decades as a mathematician before ever encoutering…
I don't know if I agree with the premise that having access to AI results in dulling human intellect. I feel like to get to Terry's level you need a combination of passion and aptitude for the subject. People that don't want to learn about a topic will always look for shortcuts, which I think represents the vast majority of people. Terry Tao is quite exceptional, and I think exceptional people will still exist even w…
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"OpenAI's internal team solves famous maths problem" is technically impressive but dispiriting. Non-experts solving a problem by just throwing resources at it is kind of the worst possible optics for knowledge workers. It's just disempowering. "Famous mathematician uses ChatGPT to solve famous math problem" is equally technically impressive, but now you're telling those very same knowledge workers "that famous mathem…
Then they should give grants of tokens to famous mathematicians. EDIT: oh, they do offer grants of $1000 of API credits to researchers https://help.openai.com/en/articles/10139500-researcher-acce...
Depends. The headline 'some rando solved a famous problem with a consumer grade subscription' might be a really good way to sell these subscriptions.
"Some already famous guy with special access solved a problem" might not be as inspiring.
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"OpenAI's internal team solves famous maths problem" is technically impressive but dispiriting. Non-experts solving a problem by just throwing resources at it is kind of the worst possible optics for knowledge workers. It's just disempowering. "Famous mathematician uses ChatGPT to solve famous math problem" is equally technically impressive, but now you're telling those very same knowledge workers "that famous mathem…
I don't think they care if it's disempowering. They'd gain more in market share by indicating that this is God than missing out on a few subscriptions from math theory people. My guess is they don't do this because they don't have time. They're all trying to build a company that makes them generationally wealthy before the music stops.
It’s endlessly fascinating to read the AI transcript of an expert who _really_ knows how to cut to the chase. It just shows how much you can potentially squeeze out of these models. I’m also surprised to see that even Terrence Tao seems to use it in a way that resembles, in progression, how I use llms in my area of expertise (emphasis on progression and usage patterns, not absolute skill, obv I don’t match that): sho…
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I’m a bit surprised OpenAI isn’t finding these big results far faster than the product’s user base. With no limits on runtime, access to dev models, custom tuning, and top talent, you’d think there’d be a constantly running internal project with the goal of solving famous math problems. And who knows, perhaps there is, but it would be interesting to compare the rate of success per unit “effort” of the internal mathem…
How could they? That's why the free market works, millions of agents in parallel beats any planned economy (by humans)
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"OpenAI's internal team solves famous maths problem" is technically impressive but dispiriting. Non-experts solving a problem by just throwing resources at it is kind of the worst possible optics for knowledge workers. It's just disempowering. "Famous mathematician uses ChatGPT to solve famous math problem" is equally technically impressive, but now you're telling those very same knowledge workers "that famous mathem…
Then they should give grants of tokens to famous mathematicians. EDIT: oh, they do offer grants of $1000 of API credits to researchers https://help.openai.com/en/articles/10139500-researcher-acce...
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I have a pi extension that just runs the same prompt in a loop 25 times. I tried giving it a loop breaker but I found that it'd give up too readily. When the task is actually complete each iteration didn't do a lot of work so it was efficient enough. I suppose another way is to call out to a separate context to check if the task is complete?
Commands like /goal and similar are the more complex version of this; you write a prompt like it was a singular iteration, it runs one iteration, then runs an "evaluator" to determine if the goal has been reached, then runs the prompt again with a little extra to make it go again - and so on. The evaluator is just an LLM with most of the result or context looking at the original goal and the state and answering the q…