from Hilbert space to Fock space, from von Neumann matrix to reduced density matrix, from Lie algebra and Jordan algebra to Kummer variety, from number field to prime numbers, from random matrix to Riemann zeros, what is the underlying relationship in action? Of course, none of them have been easy to tackle. Is the relationship recognizable in some conventional sense? Definitely, the structure or the geometry of the problem needs to be well understood. Should it wait the coming the QuantumComputer, which finally tames the NP problem? Or at least, we may peek something inside, which is extraordinarily splendid?
A. Connes said something like this: all branches of mathematics are connected, which is quite different from other subjects of science.