But mathematicians have invented some bizarrely twisted geometries that are based on the primes. In the same way, 2-adic geometry pulls together all the even numbers. To put all the primes in the mix, Connes constructed an infinite-dimensional space called the Adeles. Last year Connes proved that his prime-based quantum system has energy levels corresponding to all the Riemann zeros that lie on the critical line. That last step is a formidable one.
Some experts advise caution.
Berry, for his part, doesn't flinch at the mathematical peculiarity of Connes's system. I'm absolutely sure that if he's right, someone will find a clever way to make it in the lab. Then you'll get the Riemann zeros out just by observing its spectrum. Berry and Keating are now turning around this connection with physics, using mathematics based on the Riemann zeta function to predict the behaviour of chaotic systems. Most models of quantum chaos are complicated and difficult to calculate.