Im in the middle of something but that doesn’t look that hard
The seventh most popular easily understood unsolved problem on MathOverflow
11–20 of 108 posts
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#12One of the comments was "the Collatz conjecture feels like we're missing a branch of mathematics", or something to that effect. I followed that rabbit hole a bit and found the Plya conjecture[0], which was disproven when a counter example was found at approximately 10^361. Here I was naively thinking that if no counter examples were found in the first, say, 10^10 numbers, no counter examples should exist. If only it…
That reminds me of a parody song from 3Blue1Brown[0] about how certain numerical patterns don't quite hold and can fool you if you don't look far enough out.
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#13Gourevitch's conjecture is based on a transformed Ramanujan pi formula via Dougall's identity .
more info
https://www.ams.org/journals/mcom/2014-83-285/S0025-5718-201...
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#14I love how these raw mathematicians consider something proved when they can understand, meanwhile the computer can prove it easily just by counting a finite number of bits. What exactly would be considered proof in this case? Any explanation only mathematicians can understand?
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#15One of the comments was "the Collatz conjecture feels like we're missing a branch of mathematics", or something to that effect. I followed that rabbit hole a bit and found the Plya conjecture[0], which was disproven when a counter example was found at approximately 10^361. Here I was naively thinking that if no counter examples were found in the first, say, 10^10 numbers, no counter examples should exist. If only it…
Okay but the Collatz conjecture is a little different in that there can't just be a one-off counterexample: it's a statement about a sequence. The counterexample would have to be either a cycle (that excludes 4/2/1), or a sequence of numbers that keep spiraling up indefinitely. And they've proven that any cycle would have to be very long[1]. Either way, it would mean trivially unlocking a sequence of numbers that happens to satisfy a very specific criterion.
[1] https://en.wikipedia.org/wiki/Collatz_conjecture?useskin=vec...
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#16> fairly simple That's your definition of a fairly simple identity?!
it fits in a line. it's simple
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#17One of the comments was "the Collatz conjecture feels like we're missing a branch of mathematics", or something to that effect. I followed that rabbit hole a bit and found the Plya conjecture[0], which was disproven when a counter example was found at approximately 10^361. Here I was naively thinking that if no counter examples were found in the first, say, 10^10 numbers, no counter examples should exist. If only it…
That's just the first counterexample that was proven to exist. The smallest counter example is less than 10^10 (in fact smaller than 10^9). > The Pólya conjecture was disproved by C. Brian Haselgrove in 1958. He showed that the conjecture has a counterexample, which he estimated to be around 1.845 × 10^361.[3] > An explicit counterexample, of n = 906,180,359 was given by R. Sherman Lehman in 1960;[4] the smallest cou…
I believe inability to do arithmetic correctly is more common in folks with maths and other STEM degrees
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#18This may be a question that misses the point - respectfully, what are some practical applications in physics or engineering for such proofs and/or the search for a conjecture counterexample?
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#19I love how these raw mathematicians consider something proved when they can understand, meanwhile the computer can prove it easily just by counting a finite number of bits. What exactly would be considered proof in this case? Any explanation only mathematicians can understand?
The computer can only check a finite number of cases computationally, a proof can prove the results for all N.
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#20One of the comments was "the Collatz conjecture feels like we're missing a branch of mathematics", or something to that effect. I followed that rabbit hole a bit and found the Plya conjecture[0], which was disproven when a counter example was found at approximately 10^361. Here I was naively thinking that if no counter examples were found in the first, say, 10^10 numbers, no counter examples should exist. If only it…
John Conway showed that if you generalise the coefficients of the Collatz conjecture then some instances are undecidable. So maybe there is no proof.