You have to be very careful with these "plausibility arguments" that physicists like to make. It may well happen, for example, that there are counterexamples to the Riemann hypothesis, but that they are so rare that they have probability zero (similar to, for example, the zero probability that a random real number in some interval is a rational number). So, a plausibility argument saying how unlikely counterexamples are would prove nothing. Or, it could happen, like the famous disproved Riemannian conjecture on the crossing of pi(x) and Li(x) (see: Skewe's number) that the counterexample exists but it is ridiculously large. The usual kind of ethos in physics is to be a bit too loose with approximations or to disregard very extreme cases.<p>I don't understand the particulars of the spectrum of this operator that they have constructed, but I have heard others describe this approach as a simple reformulation of one hard problem in terms of another equally hard problem.
I don't understand why Quanta magazine keeps getting promoted on HN. Guys, it's sensational writing. Not scientific. Please understand this. Quanta is like Wired. Poor academic quality and sensational writing. Neither are based in scientific rigor.<p>I'm majoring in Pure Maths and this is annoying to see yet another poor scientific article on Math.
Now and since decades ago also, see <a href="https://en.wikipedia.org/wiki/Hilbert%E2%80%93P%C3%B3lya_conjecture" rel="nofollow">https://en.wikipedia.org/wiki/Hilbert%E2%80%93P%C3%B3lya_con...</a>
> As mathematicians have attacked the hypothesis from every angle, the problem has also migrated to physics.<p>eyeroll.. loose use of 'every' is the kind of overreaching probability mathematical rigor eschews<p>quantum mechanics still relies heavily on probability theory and reimann has been probably correct since its inception<p>it is my intended inference that a mathematical model that maps qm will be mappable to reimann, and without any forgiveness of strict symmetries
The article is very interesting and serve one purpose very well - trigger my curisoity of what is that. Both heard of. Not understand much. But somehow it is linked. And strangely talked in a way not totally out of reach.<p>If someone like me with only some basic maths/stats/QM background and interest to know more, any pointer to understand this.
This reminds me of story I heard about a pure math PhD student who wrote a deep proof for their dissertation. Unfortunately, they relied on certain math shortcuts that only work in a physics context. Their advisor didn't catch it, and I recall it ended badly for both the student and the advisor.
These physicists observations won't achieve anything other than to corroborate the existing hypothesis. Proof requires a lot more than just observation.