Mathematics
The Riemann Zeta Function and Its Connection to Primes
Quick fact
The Riemann zeta function, ζ(s), is defined for s 1 by summing 1/n^s, but through analytic continuation it extends to the whole complex plane. Its zeros (the Riemann Hypothesis) are so important that solving the hypothesis is worth $1 million and would give a perfect formula for prime distribution.
Why this is interesting
You know that adding 1 + 1/2 + 1/3 + 1/4 + ... diverges, but what happens if you raise each term to a power? A simple tweak creates a function that holds the secrets of prime numbers—and a million-dollar mystery.