Riemann Hypothesis
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 -ssumption 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.
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