The Mathematician Who Closed the Gaps Between Primes

James Maynard reshaped the study of prime numbers by inventing a flexible sieve method that detects several primes within bounded intervals. After studying at Cambridge, he completed his Oxford doctorate under Roger Heath-Brown in 2013. That same year, his independent breakthrough dramatically improved understanding of small gaps between primes and opened a new route toward prime constellations. This documentary follows his later work in Diophantine approximation and the discoveries recognized by the 2022 Fields Medal.

Prime numbers appear irregular, yet mathematicians suspect they obey subtle patterns, including infinitely many pairs separated by only two. Maynard's method did not prove the twin-prime conjecture, but it showed that bounded intervals can contain arbitrarily large clusters of primes and gave researchers a powerful new toolkit. His work combines ingenious combinatorial design with classical analytic ideas. This documentary explains the breakthrough and why it changed the modern study of primes.