The seventh most popular easily understood unsolved problem on MathOverflow
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Re: The seventh most popular easily understood unsolved problem on MathOverflow
#2It still boggling we haven't proved the sum of pi + e is irrational. Who cares anyway?
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#3> fairly simple
That's your definition of a fairly simple identity?!
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#4It still boggling we haven't proved the sum of pi + e is irrational. Who cares anyway?
> Who cares anyway?
I can’t tell if you’re just joking. Proofs of facts that seem obvious or irrelevant are very important not for the yes-no question they answer but for the development of the deep mathematical theory they necessitate.
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#5It still boggling we haven't proved the sum of pi + e is irrational. Who cares anyway?
It's not that mind-boggling. In general we need to use specific properties of numbers to prove whether they are irrational, and pi+e has very few useful properties to work from. Even proving pi is irrational is not trivial and it is one of the transcendental numbers we know the most about.
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#6It still boggling we haven't proved the sum of pi + e is irrational. Who cares anyway?
> Who cares anyway? I can’t tell if you’re just joking. Proofs of facts that seem obvious or irrelevant are very important not for the yes-no question they answer but for the development of the deep mathematical theory they necessitate.
It was a joke, I know there are lots of people who care about that.
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#7> fairly simple That's your definition of a fairly simple identity?!
In his defense lots of unsolved questions are inscrutable for the majority of people. So this one looks decent.
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#8One 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 were so easy.
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#9One 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 counterexample is n = 906,150,257, found by Minoru Tanaka in 1980.[5]
EDIT: rephrased because despite having a maths degree I can't count.
Re: The seventh most popular easily understood unsolved problem on MathOverflow
#10One 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…