Riemann Hypothesis

What is Riemann Hypothesis?


1.

Without question, THE most important unsolved problem in all of mathematics. The hypothesis, put forth by Bernhard Riemann in 1859, states that ALL non-trivial zeros of the Zeta function have a real part of one-half. Another way to put this is that the distribution of numbers with an odd number of prime factors vs. those with and even number of prime factors is roughly 50/50. Anyone who can prove the Riemann Hypothesis without the aid of a computer will win a $1,000,000 prize. A great deal of mathematical theorems rest on the assumption that this hypothesis is true. If anyone can find a non-trivial zero of Zeta with a real part not equal to 1/2 will destroy a lot of mathematical work, and become very famous.

The Zeta function = 1 + 1/2^S + 1/3^S + 1/4^S .... to infinity. The Riemann Hypothesis states that Zeta = 0 only when the real part of S = 1/2 (non-trivial zeros on the critical line). Has eluded a proof for almost 150 years.

See math, geometry, numbers, physics, arithmetic


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