[Y_Y]

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.)

[AlanYx]

>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?

[wbl]

You need analytic continuation to define the zeta function at the places you are asking for zeros.

[Y_Y]

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_ta...

[StilesCrisis]

Have you talked to a high schooler recently...?

[Y_Y]

Fair point, I was basing my comment on what the curriculum expects of students, rather than the bleak reality.