71–80 of 467 posts
Good post, it perfectly captures the problem with AI. Here we have a claim that the double cover conjecture has a proof. Verified by… no one per the link. Now imagine this proof is wrong. How would you know? Ok, think about the process in which you determine the correctness - why not do that initially? And there it is. The problem laid bare. Ironically it reduces to the P and NP one.
This is not a remark about AI, but there's something funny about mathematics in that every novel result is broadly perceived as a big deal. We attach basically zero value to writing a new program that hasn't existed before, or a piece of text that hasn't existed before. It's boring, or even a net negative, unless you can show that the result benefits the world in some way. We'd find it weird if OpenAI put out a relea…
there is no "software" that a lot of people want, yet nobody managed to create yet because they failed too due to it was being hard to implement (excluding AGI/ASI which is not really software)
It might be a better mathematician than most humans at this point. Kind of like when chess software started beating everyone except grandmasters.
What’s left? Proposing and building out entirely new theories and frameworks? Then better than any human? Then alien math results we struggle to comprehend?
Earlier quoted context omitted.
> Spend at least 8 hours on this before even thinking of returning or giving up. Do current model harnesses have concepts of amount of time spent? Sometimes the model notices if a subprocess takes too long/hangs and kills it, but I've never seen it time itself.
Many harnesses include a current date and time in their system prompt, and if there is a way for the model to call for an updated time (either a dedicated time tool or calling the OS' `date` tool) they can track time they spent doing something. If not told up-front, they can try to infer it from timestamps in their logs. Sort of like a human - if you ask them to time something and give them a stopwatch, they do it. I…
Is there anyone more knowledgeable than me about proof checking software who could tell me how off the mark I am here? Assuming you have decent proof checking software, is it possible that this solution was achieved by throwing GPT at the problem a couple hundred thousand times until it passed the proof checker?
This is not a remark about AI, but there's something funny about mathematics in that every novel result is broadly perceived as a big deal. We attach basically zero value to writing a new program that hasn't existed before, or a piece of text that hasn't existed before. It's boring, or even a net negative, unless you can show that the result benefits the world in some way. We'd find it weird if OpenAI put out a relea…
Wow, you couldn't be more wrong here. Math is something humans invented and is a model, nothing else. There is no logic per se, but a model that works quite well for us. I studied Math and CS as a very highly gifted and quickly found out, there is no beauty of Mathematical Logic, only humans approval of what they deem most accurate. A good example is set theory. Cantor was not openly welcomed after he introduced his…
It's almost like a twisted mirror of Conway's law.
This is not a remark about AI, but there's something funny about mathematics in that every novel result is broadly perceived as a big deal. We attach basically zero value to writing a new program that hasn't existed before, or a piece of text that hasn't existed before. It's boring, or even a net negative, unless you can show that the result benefits the world in some way. We'd find it weird if OpenAI put out a relea…
>mathematics is basically the only scientific discipline that rejected any notion of utility I think this might depend on the department, but I was at a pure math department last year, and struggling with my Linear Algebra textbook (written by the professor, incidentally, who was not a great communicator). I consulted the machines, and learned, to my great delight, that linear algebra is used in like 20 different fie…
This is not a remark about AI, but there's something funny about mathematics in that every novel result is broadly perceived as a big deal. We attach basically zero value to writing a new program that hasn't existed before, or a piece of text that hasn't existed before. It's boring, or even a net negative, unless you can show that the result benefits the world in some way. We'd find it weird if OpenAI put out a relea…
Wow, you couldn't be more wrong here. Math is something humans invented and is a model, nothing else. There is no logic per se, but a model that works quite well for us. I studied Math and CS as a very highly gifted and quickly found out, there is no beauty of Mathematical Logic, only humans approval of what they deem most accurate. A good example is set theory. Cantor was not openly welcomed after he introduced his…
"Math is something humans invented"
Majority of mathematicians are platonists and believe arithmetic was existed and was discovered and was not "invented".
"There is no logic per se"
There is logic to it! Most logicians are mathematicians at heart. See Russel, Godel, Hilbert, etc
"no beauty of Mathematical Logic"
Mathematicians do focus on beauty. Entire books have been written on this. G.H. Hardy in A Mathematician's Apology even said math MUST be beautfiul
"Proofs are religious things"
What are you going on about...