7 ms·

I agree that Quanta can be irritatingly stretchy with the metaphors sometimes, but to be fair, "What's the biggest couch you can fit through this hallway corner

I agree that Quanta can be irritatingly stretchy with the metaphors sometimes, but to be fair, "What's the biggest couch you can fit through this hallway corner" is inherently easier to explain to laypeople than like, the Riemann Hypothesis.

huflungdung 8mo ago
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Y_Y 8mo ago
ζ(z)=0⇒-z/2∈ℕ ∨ Re(z)=1/2 i.e. if you apply the zeta function to a complex number, and you get zero, then that number must have been either a negative even integer or had a half as its real part. What could be simpler than that? Those are all fairly simple concepts, and the definition of the function itself is nothing too exotic. I think any highschooler should be able to understand the statement and compute some values of zeta numerically. I'd like to see a statement about couches written so succinctly with only well-defined terms! (I'm being intentionally a bit silly, but part of the magic of the Riemann Hypothesis is that it's relatively easy to understand its statement, it's the search for a proof that's astonishingly deep.)
- wbl 8mo ago
  You need analytic continuation to define the zeta function at the places you are asking for zeros.
  - Y_Y 8mo ago
    That's a good point. I do remember doing problems related to extending formulae outside the radius of convergence in my final year before university, but I don't think it's fair to ask for proper complex analysis from 17-year-olds. As penance I did go an have a look for suitable numerical techniques for calculating zeta with Re(s)<1 and there are some, e.g. https://people.maths.bris.ac.uk/~fo19175/talks/slides/PGS_talk_2020.pdf https://people.maths.bris.ac.uk/~fo19175/talks/slides/PGS_ta...
- StilesCrisis 8mo ago
  Have you talked to a high schooler recently...?
  - Y_Y 8mo ago
    Fair point, I was basing my comment on what the curriculum expects of students, rather than the bleak reality.
- AlanYx 8mo ago
  >What could be simpler than that? At risk of being tongue-in-cheek, a monad is just a monoid in the category of endofunctors, what's the problem?

huflungdung 8mo ago

[dead]

Y_Y 8mo ago

ζ(z)=0⇒-z/2∈ℕ ∨ Re(z)=1/2 i.e. if you apply the zeta function to a complex number, and you get zero, then that number must have been either a negative even integer or had a half as its real part. What could be simpler than that? Those are all fairly simple concepts, and the definition of the function itself is nothing too exotic. I think any highschooler should be able to understand the statement and compute some values of zeta numerically. I'd like to see a statement about couches written so succinctly with only well-defined terms! (I'm being intentionally a bit silly, but part of the magic of the Riemann Hypothesis is that it's relatively easy to understand its statement, it's the search for a proof that's astonishingly deep.)

wbl 8mo ago
You need analytic continuation to define the zeta function at the places you are asking for zeros.
- Y_Y 8mo ago
  That's a good point. I do remember doing problems related to extending formulae outside the radius of convergence in my final year before university, but I don't think it's fair to ask for proper complex analysis from 17-year-olds. As penance I did go an have a look for suitable numerical techniques for calculating zeta with Re(s)<1 and there are some, e.g. https://people.maths.bris.ac.uk/~fo19175/talks/slides/PGS_talk_2020.pdf https://people.maths.bris.ac.uk/~fo19175/talks/slides/PGS_ta...
StilesCrisis 8mo ago
Have you talked to a high schooler recently...?
- Y_Y 8mo ago
  Fair point, I was basing my comment on what the curriculum expects of students, rather than the bleak reality.
AlanYx 8mo ago
>What could be simpler than that? At risk of being tongue-in-cheek, a monad is just a monoid in the category of endofunctors, what's the problem?