Landau levels and Riemann zeros
German Sierra and Paul K. Townsend have recently presented an idea that may lead to the solution of the Riemann hypothesis. The Riemann hypothesis is a co-recursively enumerable problem (roughly, there is an algorithm that, when given an input number, eventually halts if and only if the input satisfies the problem, but no algorithm can decide if an arbitrary input satisfies the problem or not). The solution of this and other similar problems would falsify Church's Thesis. Interestingly, Fermat's last theorem and Poincaré's conjecture are co-recursively enumerable problems, nonetheless, these problems have been decided! A proof that Church's thesis is false...?