Terence Tao, together with Ben Green, proves in 2004 that the prime numbers contain arbitrarily long arithmetic progressions: for any length k, there exist infinitely many k-term arithmetic progressions formed exclusively of prime numbers. The result, which combines additive-combinatorics techniques with Szemerédi's theorem and methods from ergodic theory, is surprising for demonstrating such regular structure within a set — the primes — intuitively considered "chaotic" or pseudorandom. The official 2006 Fields Medal citation explicitly mentions this theorem among Tao's central contributions, alongside his broader work in partial differential equations, combinatorics, and number theory.