Riemann Hypothesis

What makes this fascinating

• It's really a statement about primes — The zeros of the zeta function control how irregularly the prime numbers are scattered — a proof would pin down that pattern.

• The critical line — Every nontrivial zero is conjectured to lie exactly on the line Re(s) = ½. Over 10 trillion have been checked, all on the line — yet no proof exists.

• A million-dollar problem — It's one of the seven Clay Millennium Prize Problems, with a $1,000,000 reward for a solution.

Frequently asked questions

Has the Riemann Hypothesis been proven?

No. Posed by Bernhard Riemann in 1859, it is still unproven. More than 10 trillion nontrivial zeros of the zeta function have been computed and every one lies on the critical line, but a proof covering all of them has never been found.

Why does the Riemann Hypothesis matter?

Its zeros control how the prime numbers are distributed, so a proof would firm up a large body of number theory that is currently only conditional on it. It is also one of the seven Clay Millennium Prize Problems, with a $1,000,000 reward.

Do I need to be a mathematician to understand it?

No. The statement is reachable with high-school math and patience — what the zeta function is, what its zeros are, and what it means for them to lie on the critical line. Cordelet builds that understanding step by step from wherever you start.

More summits in Mathematics

• P vs NP

  If a solution is easy to check, is it always easy to find? A million-dollar question at the heart of computing.

• Navier–Stokes existence and smoothness

  We use the equations of fluid flow daily — yet can't prove their solutions never blow up.

• Birch and Swinnerton-Dyer conjecture

  A startling claim that a curve's whole-number solutions are encoded in a single function.

• The Collatz conjecture

  A rule a child can follow, an answer no mathematician can prove. Start anywhere — do you always reach 1?