Here is a view of the Riemann Zeta function graphed from x=1.2 to 10. You will notice a sharp spike as x goes toward 1, where it shoots off to infinity. The Riemann Zeta function at x=1 is the harmonic series. Since *everybody* knows the harmonic series diverges, so does the Riemann Zeta function at x=1. As x gets larger, the function approaches 1 quickly. This function directly determines the statistical properties of the distribution of prime numbers, so mathematician go wild studying everything about it.

If you can prove that the only solutions to the equation Zeta(z) = 0 occur on the line Re(z) = 1/2 (aka The Riemann Hypothesis), then you get a million bucks!

## Leave a comment