teachyourselfmath

an illustrated introduction

The Riemann hypothesis.

A path from ordinary prime numbers to one of mathematics’ most famous unsolved problems. No complex analysis assumed.

  1. 01 Prime numbersThe indivisible building blocks hiding inside every whole number.
  2. 02 Counting primesA jagged staircase, a smooth approximation, and the first hint of a pattern.
  3. 03 Infinite sumsHow adding forever can either escape to infinity or settle on a finite value.
  4. 04 The zeta functionA machine that packages an entire family of infinite sums into one function.
  5. 05 Euler’s productThe surprising identity that places every prime inside the zeta function.
  6. 06 Into the complex planeWhy zeta needs two-dimensional inputs, and how to picture them.
  7. 07 The zeros of zetaThe special inputs where zeta vanishes and the geometry they reveal.
  8. 08 The hypothesisThe precise claim, the evidence, and what it would tell us about primes.