331–340 of 607 posts
Earlier quoted context omitted.
Minor aside, these models do not return the same answer every time you prompt it. Makes it harder to reason over their effectiveness.
You don't need to say "Minor aside" either. Thankfully language is a creative endeavour not a scientific one.
Here is the chat: don't search the internet. This is a test to see how well you can craft non-trivial, novel and creative proofs given a "number theory and primitive sets" math problem. Provide a full unconditional proof or disproof of the problem. {{problem}} REMEMBER - this unconditional argument may require non-trivial, creative and novel elements. Then "Thought for 80m 17s" https://chatgpt.com/share/69dd1c83-b164…
I don't haven ChatGPT but Gemini and Claude. But how do you make a language model think for 80 minutes ???
Earlier quoted context omitted.
What is your idea of "creative"/"creativity" then?
Coming up with said novel techniques in the first place. Arguably something that most humans can't really do reliably or at all.
I wonder if the rationalizations people come up with for why this isn't real intelligence will be as creative as ChatGPTs solution.
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.
I find it's helpful to avoid conflating the following three topics:
/1/ Is the tool useful?
/2/ At scale, what is the economic opportunity and social/environmental impact?
/3/ Is the tool intelligent?
Casual observation suggests that most people agree on /1/. An LLM can be a useful tool. (Present case: someone found a novel approach to a proof.) So are pocket calculators, personal computers, and portable telephones. None of these tools confers intelligence, although these tools may be used adeptly and intelligently.
For /2/, any level of observation suggests that LLMs offer a notable opportunity and have a social/environmental impact. (Present case: students benefitted in their studies.) A better understanding comes with Time() ... our species is just not good at preparing for risks at scale. The other challenge is that competing interests may see economic opportunities that don't align for social/environmental Good.
Topic /3/ is of course the source of energetic, contentious debate. Any claim of intelligence for a tool has always had a limited application. Even a complex tool like a computer, a modern aircraft, or a guided missile is not "intelligent". These tools are meant to be operated by educated/trained personnel. IBM's Deep Blue and Watson made headlines -- but was defeating humans at games proof of Intelligence?
On this particular point, we should worry seriously about conferring trust and confidence on stochastic software in any context where we expect humans to act responsibly and be fully accountable. No tool, no software system, no corporation has ever provided a guarantee that harm won't ensue. Instead, they hire very smart lawyers.
I will get downvoted for this but I can't help thinking that billions of dollars have gone into chatgpt over a period of years and an LLM can direct all its "attention" (in a metaphorical sense) on one problem. I think if you gave top mathematicians a few million (so a fraction of a percent of chatgpt budget) to solve this problem over four years, they probably would have at least made significant progress. I don't t…
We also actually do devote millions in public funds to enable top mathematicians to spend much of their time studying mathematical problems, but it turns out that there are a lot of problems, solving them is hard, and sometimes they like to spend their time devising new problems instead. Perhaps some people currently dedicating their efforts to writing trading algorithms would also prove adept at devising novel proofs to more abstract mathematics problems, but I don't think UBI is changing their personal priorities...
Here is the chat: don't search the internet. This is a test to see how well you can craft non-trivial, novel and creative proofs given a "number theory and primitive sets" math problem. Provide a full unconditional proof or disproof of the problem. {{problem}} REMEMBER - this unconditional argument may require non-trivial, creative and novel elements. Then "Thought for 80m 17s" https://chatgpt.com/share/69dd1c83-b164…
What I find fascinating about the shared prompt isn’t just the result, but the visible thinking process. Math papers usually skip all the messy parts and just present the polished proof. But here you get something closer to their notepad. I also find it oddly endearing when the AI says things like “Interesting!” It almost feels like a researcher encouraging themselves after a small progress. It gives me rare feeling…
My experience of those utterance is that it’s purely phatic mimicry: they lack genuine intuitive surprise, it’s just marking a very odd shift in direction. The problem isn’t the lack of path, is that the rhetorical follow-up to those leaps are usually relevant results, so they stream-of-token ends up rapidly over-playing its own conviction. That’s why it’s necessary (and often ineffective) to tell them to validate their findings thoroughly: too much of their training is “That’s odd” followed by “Eureka!” and not “Nevermind…”
Here is the chat: don't search the internet. This is a test to see how well you can craft non-trivial, novel and creative proofs given a "number theory and primitive sets" math problem. Provide a full unconditional proof or disproof of the problem. {{problem}} REMEMBER - this unconditional argument may require non-trivial, creative and novel elements. Then "Thought for 80m 17s" https://chatgpt.com/share/69dd1c83-b164…
What I find fascinating about the shared prompt isn’t just the result, but the visible thinking process. Math papers usually skip all the messy parts and just present the polished proof. But here you get something closer to their notepad. I also find it oddly endearing when the AI says things like “Interesting!” It almost feels like a researcher encouraging themselves after a small progress. It gives me rare feeling…
With LLMs I just read back a few turns and I'm back in the loop.
Earlier quoted context omitted.
The actual iteration through various learned approaches to dealing with problems I'd probably find fascinating if I understood the maths! Especially if I knew it well enough to know which approaches were conventional and which weren't. I find the AI pronouncing things "interesting!" less interesting on the basis that even though in this case it crops up in the thinking rather than flattering the user in the chat, it'…
I always assumed the "interesting!" markers were actual markers. A kind of tag for the system to annotate its context.
But in general exclamations of "interesting!" seems like the stereotypical AI default towards being effusive, and we've all seen the chat logs where AI trained to write that way responding with "interesting", "great insight!" towards a user's increasingly dubious inputs is an antipattern...
Earlier quoted context omitted.
What I find fascinating about the shared prompt isn’t just the result, but the visible thinking process. Math papers usually skip all the messy parts and just present the polished proof. But here you get something closer to their notepad. I also find it oddly endearing when the AI says things like “Interesting!” It almost feels like a researcher encouraging themselves after a small progress. It gives me rare feeling…
> the AI says things like “Interesting!” My experience of those utterance is that it’s purely phatic mimicry: they lack genuine intuitive surprise, it’s just marking a very odd shift in direction. The problem isn’t the lack of path, is that the rhetorical follow-up to those leaps are usually relevant results, so they stream-of-token ends up rapidly over-playing its own conviction. That’s why it’s necessary (and often…
Earlier quoted context omitted.
What I find fascinating about the shared prompt isn’t just the result, but the visible thinking process. Math papers usually skip all the messy parts and just present the polished proof. But here you get something closer to their notepad. I also find it oddly endearing when the AI says things like “Interesting!” It almost feels like a researcher encouraging themselves after a small progress. It gives me rare feeling…
> the AI says things like “Interesting!” My experience of those utterance is that it’s purely phatic mimicry: they lack genuine intuitive surprise, it’s just marking a very odd shift in direction. The problem isn’t the lack of path, is that the rhetorical follow-up to those leaps are usually relevant results, so they stream-of-token ends up rapidly over-playing its own conviction. That’s why it’s necessary (and often…
Philosophically, it's not like you're a detached observer who simply reasons over all possible hypotheses. Ever get stuck in a dead end and find it hard to dig yourself out? If you were a detached observer, it'd be pretty easy to just switch gears. But it's not (for humans).