Thread

1. hatthew · 1790903353 · focus · HN ↗

   My comment about humanity's last exam being a misnomer is included, and I proposed better ideas about what a last exam could look like. One of the things I said was "solve an open math problem" which has conclusively been done with Navier-Stokes (regardless of the controversy surrounding that). However, in the spirit of clarifying the goalposts, AI has only passed 1/6 of the tests I proposed. 17% is not a passing grade, so I'd say no, my challenge has not been met.

   Another thing to note is that the (presumably AI-generated) summary of my challenge does not accurately represent what I wrote, listing only half the things I said and saying "or" rather than "and".

   1. an0malous · 1790942234 · focus · HN ↗

      How can you say it’s conclusively been done if it might have been stolen from a math researcher and was aided in unknown ways by a whole team of math researchers? I find it mind boggling that HN just accepts these shenanigans with no transparency. At the very least, they could share the conversation / thinking trace easily and if their claims are true there shouldn’t be anything controversial or negative for their company in the trace.

      1. olmo23 · 1790948160 · focus · HN ↗

         navier stokes is not the only example of an open problem in maths that was solved by AI (eg the counterexample to the jacobian)

         1. tsunamifury · 1790950409 · focus · HN ↗

            In the other hand why does anyone find it surprising at all that a computer solved a math problem.

            1. ben_w · 1791039456 · focus · HN ↗

               To ask that question suggests you are unfamiliar with the difference between arithmetic (which computers are good at) and pure mathematics (which is like metaprogramming combined with formal methods, and Gödel's incompleteness theorem is worse than the Halting problem)?

               Simply put: For the same reason computers have not already solved all problems in mathematics.

               More concretely:

               Consider the Collatz conjecture. It's a very simple rule to write down:

                 Take some positive integer: If the number is even, divide it by two; otherwise triple it and add one. With enough repetition, do all positive integers converge to 1?
               

               Trivial to write a program to test numbers starting at 1 and going up. We know it holds up to at least 2.36e21 (according to Wikipedia), but to prove it is true with such a program requires testing all of the infinite set of positive integers.

               But you may notice some things about the rules, that they suggest a subset of numbers will trivially always converge to 1, so that you don't need to even test them: any integer 2^n where n is also a positive integer.

               You may find other easy wins, or ways to simplify the test, e.g. once you know the numbers up to m will converge to 1, you can terminate your loop early if you test m+1 and it ever has an intermediate value less than or equal to m. You can combine that with applying one of the rules in reverse, and know that all even numbers between m and 2m will on their first move be halved, making them smaller than m, which means you know they'll eventually converge.

               But actually proving this is fully general? Nobody knows. You can't just throw arithmetic at the problem directly, you have to figure out patterns that would let you prove that it always holds, no matter what.

               Or, you may find many such patterns and directly calculate some number not in any of them, to find one which doesn't converge to 1.

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