The Riemann Hypothesis

In 1859, Bernhard Riemann studied a single function — ζ(s) = 1 + 1/2ˢ + 1/3ˢ + 1/4ˢ + … — and noticed its zeros held the secret of the primes. He conjectured that all the non-trivial zeros lie on one vertical line, Re(s) = ½. A proof has eluded the world for 165 years. It is the first of the Clay Mathematics Institute's Millennium Prize problems — worth $1,000,000 — and widely considered the most important open question in math.