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OK, I'm starting this topic for people to post any unsolved mathematical problem which they think is very important. I'll start with the Riemann Zeta function (if you solve this, $1,000,000 is the prize money!).

zeta(s) = sum(n^(-s)) from n = 1 to infinity

s can be any complex number except s = 1

The Riemann Hypothesis states that the only non-trivial zeroes of this function have a real part equal to 1/2.

Any negative even integer is a trivial zero. Any other zero is nontrivial.

Nobody has yet been able to prove the hypothesis true or false.

What unsolved problem do you consider very important?

zeta(s) = sum(n^(-s)) from n = 1 to infinity

s can be any complex number except s = 1

The Riemann Hypothesis states that the only non-trivial zeroes of this function have a real part equal to 1/2.

Any negative even integer is a trivial zero. Any other zero is nontrivial.

Nobody has yet been able to prove the hypothesis true or false.

What unsolved problem do you consider very important?