1. Sep 13, 2006

### lokofer

If you could..what kind of "Millenium problems" (not only in abstract math but in any aspect of life, subject dealing with math... )..

*The "Meassure" Problem:= give a mathematic consistent, and useful definition of "Infinite dimensional meassure" for a Function space, so integrals (of functionals) in the form:

$$\int D[f]G[f]$$ can be evaluated, the problem is to find a justification for the "Functional meassure" D[f] :grumpy: :grumpy:

The problem is very important to "Physics and Quantum Field Theory" since it could provide a way to define the propagator in Quantum Gravity.

*The "Riemann Gas":= Euler product can be interpreted in the form of the "partition function" of a certain gas in the sense:

$$\zeta(s)= \prod_{k}(1-e^{-slog(p_{k})$$ which describes a "solid state gas" interacting under an Harmonic potential..the "problem2 is to define a way to obtain "theoretically" the dispersion relations $$\omega (k)$$ from the Partition function..what would allow us to know all the primes...(and hence the prime number counting function).