For many publications you could be critisizing, I'd agree with you, but Quanta usually reaches a higher standard that I feel they deserve credit for. Here's the Quanta article on the same thing [1]. It goes into much more detail, it shows a picture of the perfect sofa, and links to the actual research paper. They're aimed at a level above "finished high school", and I appreciate that; it gives me a chance to learn from the solution to a problem, and encourages me to think about it independently.
I agree with you that Quanta doesn't always "allow specialists to understand exactly what's being claimed", which is a problem; but linking to the research papers greatly mitigates that sin.
[1] https://www.quantamagazine.org/the-largest-sofa-you-can-move...
And here's how they clearly explain the proof strategy.
> First, he showed that for any sofa in his space, the output of Q would be at least as big as the sofa’s area. It essentially measured the area of a shape that contained the sofa. That meant that if Baek could find the maximum value of Q, it would give him a good upper bound on the area of the optimal sofa.
> This alone wasn’t enough to resolve the moving sofa problem. But Baek also defined Q so that for Gerver’s sofa, the function didn’t just give an upper bound. Its output was exactly equal to the sofa’s area. Baek therefore just had to prove that Q hit its maximum value when its input was Gerver’s sofa. That would mean that Gerver’s sofa had the biggest area of all the potential sofas, making it the solution to the moving sofa problem.
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.
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.)
>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?
You need analytic continuation to define the zeta function at the places you are asking for zeros.
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...
Have you talked to a high schooler recently...?
Fair point, I was basing my comment on what the curriculum expects of students, rather than the bleak reality.
It’s a simple problem that you can explain to kids, hence the no jello. And they don’t even begin to describe how the solution even looks like!
So I don’t think this article can even qualify as a good example for explaining math problems to laymen.
