Ramanujan’s 1/π series is a masterpiece of mathematical intuition.
Published in 1914, it converges extraordinarily fast, adding roughly eight decimal digits of accuracy with each successive term. Ramanujan had limited formal university-level mathematical training, yet produced results whose deeper mathematical foundations involve modular equations and related number theory.
He did not provide a proof of this famous series in his original work; rigorous proofs came much later. Ramanujan also described some of his mathematical insights in terms of divine inspiration, particularly his devotion to the goddess Namagiri. His 1/π formulas remain important examples of the remarkable mathematical structures he discovered.