This will soon happen with theoretical physics, computer science, and everything which can be verified cheaply. Then, we will have long running projects augmented by agents for 2-4 years while AI companies are collecting data of human workflows. After that we will see AI being able to do those projects by themselves. This will lead to super fast human progress and cheap products. The price of things will be bound by…
Human mathematicians are being outcounterexampled
191–200 of 265 posts
Re: Human mathematicians are being outcounterexampled
#192When I was in grad school, I had the opportunity to take a course from my adviser in which he discussed his current research and some open questions. It was a relatively accessible subject area and the questions were sometimes easy enough that we could meaningfully contribute. On one particular Friday afternoon, he stated a conjecture that he hoped was true, and invited us to try to help him prove or disprove it. It…
> he had spent the entire weekend trying and failing to prove it. I, on the other hand, had put all my energy into finding a counterexample and had one within an hour. For a more extreme (although somewhat inverted) version of this, see Zeeman. He spent years trying to find a knotted sphere in a 5D space. Then realised this was impossible and got a proof for it in a few hours. [1] [1] https://ima.org.uk/28009/sir-eri…
Re: Human mathematicians are being outcounterexampled
#193Human mathematicians have been being out-counterexampled for at least two decades. The main difference, as I understand, is that (A) we now have a lot more compute to throw at such things, and (B) it is currently trendy to do so. But the sizes of counterexample we're seeing are around about what I'd expect pre-generative-AI counterexample search systems to be able to find. It's not easy to find a counterexample to th…
AI is only as good as a human mathemetician, which we don't have enough of? "just"?
https://en.wikipedia.org/wiki/Jacobian_conjecture
> The conjecture was first stated for two variables by Ludwig Kraus in 1884 [...] an example of a difficult question in algebraic geometry that can be understood using little beyond a knowledge of calculus.
> The Jacobian conjecture is number 16 in Stephen Smale's 1998 list of Mathematical Problems for the Next Century. It was notorious for the large number of published and unpublished false proofs that turned out to contain subtle errors.
Re: Human mathematicians are being outcounterexampled
#194Re: Human mathematicians are being outcounterexampled
#195Re: Human mathematicians are being outcounterexampled
#196Next step: "the AI can't find a counterexample, so the conjecture must be true!"
Re: Human mathematicians are being outcounterexampled
#197The framing in these posts is nonsense. ChatGPT isn't doing shit. Human mathematicians using ChatGPT are breaking boundaries.
so if I tell a model "using your advanced knowledge of physics and chemistry 'make alchemy work' (synthesize gold using any cheaper materials) using safe materials legal for a residential hobby chemist with 1 semester of lab work in college to possess and use (this is obviously the really hard part) using less than $1,000 in lab equipment and input materials that can create $2,000 in value at market rate; then walk m…
Even better:
"so if I tell a *human"..."
then whose achievement is the result?
Re: Human mathematicians are being outcounterexampled
#198> A few days earlier I had got an email from a professor in the maths department here at Imperial, expressing surprise that some of our graduate students were paying $200 per month to access models such as Sol and Fable. He said that he thought that these people were crazy. I did not immediately respond. But after meeting with Andrew I emailed the professor back and told him that in my opinion, any PhD student who wa…
Many graduate students view themselves as ethical beings, not machines that "produce meaningful output," and everybody here knows (useful) LLMs are indefensibly evil because of stolen training data and enormous environmental impact.
What level of copyright violation will send us to hell?
Re: Human mathematicians are being outcounterexampled
#199Earlier quoted context omitted.
Planck's Principle: 'Science advances one funeral at a time.' [1] In his exact words: "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it... An important scientific innovation rarely makes its way by gradually winning over and converting its opponents: it rarely happen…
The more important lesson for those of us are are "old" is to not get stuck in things that were learned in the past when they are found false. If you are not yet old, remember this - it is very likely you will old in a few years.
He simply believed on a fundamental level that the universe must be deterministic. Many don't understand that many of his famous quotes like 'spooky action at a distance' or 'god doesn't play dice' were mocking probabilistic interpretations of quantum mechanics, like the Copenhagen Model - the one we still assume to this very day.
Of course there even remains the possibility that at some point in the future he may even be proven correct. And at this point I'm playing into the very same mindset that essentially explains where Planck's Principle comes from, but perhaps such being a part of humanity is not an entirely bad thing. It's certainly been with us even as mankind has gone through unprecedented leaps of understanding and technological advancement.
Re: Human mathematicians are being outcounterexampled
#200the AI doesn't even gloat. a rival mathematician would at least title their paper 'a remark on the falsity of...'
> ..Even more unexpected is the fact that many expositions of this topic commit serious mathematical and logical errors. Moreover, this happened not once or twice, but many times over the centuries, and continues to this day in many printed and electronic publications; the most recent case is in the second issue for 2008 of this journal. I will justify this harsh statement soon, after setting up the necessary background.