101–110 of 607 posts
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Remember when people thought multiplying numbers, remembering a large number of facts, and being good at rote calculations was intelligence? Some people think that multiplying numbers, remembering a large number of facts, and being good at calculations is intelligence. Most intelligent people do not think that. Eventually, we will arrive at the same conclusion for what LLMs are doing now.
Remember when people thought solving Erdos problems required intelligence? Is there anything an LLM could ever do that would cound as intelligence? Surely the trend has to break at some point, if so what would be the thing that crosses the line to into real intelligence?
Doing formalized mathematics is as intelligent as multiplying numbers together.
The only reason why it's so hard now is that the standard notation is the equivalent of Roman numerals.
When you start using a sane metalanguage, and not just augmrnted English, to do proofs you gain the same increase in capabilities as going from word equations to algebra.
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... shit that solved an apparently significant Erdős problem. That is not nothing , no matter how much you hate AI.
It shows that AI is apparently very good at brute-forcing.
I wonder if the rationalizations people come up with for why this isn't real intelligence will be as creative as ChatGPTs solution.
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Solving open math problems is strong evidence of intelligence so there's not really any need for rationalization? I don't understand why intelligence would require intent or motive? Isn't intent just the behaviour of making a specific thing happen rather than other things?
I'm curious, do you think that this also applies to stable diffusion? Are these models "creative" too?
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GPT 5.5 Pro is not available to any plan outside of ChatGPT Pro ($100 or $200) tier or the API as far as consumer access.
Yes, but don't we expect GPT 5.5 Pro will eventually be a free tier? Maybe I'm missing something because I only use the free tier. But the free tier has gotten way better over the last few years. I'm pretty sure, based on descriptions on this site from paid subscribers, that the free tier now is better than the paid tier of say 2 years ago. That's the lag I'm wondering about.
Earlier quoted context omitted.
Solving open math problems is strong evidence of intelligence so there's not really any need for rationalization? I don't understand why intelligence would require intent or motive? Isn't intent just the behaviour of making a specific thing happen rather than other things?
I'm curious, do you think that this also applies to stable diffusion? Are these models "creative" too?
The LLM took an entirely different route, using a formula that was well known in related parts of math, but which no one had thought to apply to this type of question. Of course LLMs are still absolutely useless at actual maths computation, but I think this is one area where AI can excel --- the ability to combine many sources of knowledge and synthesise, may sometimes yield very useful results. Also reminds me of th…
> Every Mathematician Has Only a Few Tricks > > A long time ago an older and well-known number theorist made some disparaging remarks about Paul Erdös’s work. > You admire Erdös’s contributions to mathematics as much as I do, > and I felt annoyed when the older mathematician flatly and definitively stated > that all of Erdös’s work could be “reduced” to a few tricks which Erdös repeatedly relied on in his proofs. > W…
We may have collectively filled libraries full of books, and created yottabytes of digital data, but in the end to create something novel somebody has to read and understand all of this stuff. Obviously this is not possible. Read one book per day from birth to death and you still only get to consume like 80*365=29200 books in the best case, from the millions upon millions of books that have been written.
So these "few tricks" are the accumulation of a lifetime of mathematical training, the culmination of the slice of knowledge that the respective mathematician immersed themselves into. To discover new math and become famous you need both the talent and skill to apply your knowledge in novel ways, but also be lucky that you picked a field of math that has novel things with interesting applications to discover plus you picked up the right tools and right mental model that allows you to discover these things.
This does not go for math only, but also for pretty much all other non-trivial fields. There is a reason why history repeats.
And it's actually a compelling argument why AI is still a big deal even though it's at its core a parrot. It's a parrot yes, but compared to a human, it actually was able to ingest the entirety of human knowledge.