Riemann Hypothesis

The Riemann Hypothesis is one of the most difficult unsolved problems in pure mathematics. It concerns the locations of the "zeros" of a specific function called the Riemann zeta function. The significance of the Riemann Hypothesis lies in its deep and unexpected connection to the distribution of prime numbers. The zeros of the zeta function control the subtle oscillations and irregularities in the way prime numbers are distributed among the integers. If the hypothesis is true, it provides the best possible estimate for the error in the Prime Number Theorem, guaranteeing that the primes are distributed as smoothly as possible. A proof would unlock many other dependent theorems in number theory.