Ramanujan & Hardy
An extraordinary partnership that produced some of the most beautiful mathematics of the 20th century
21.1 Srinivasa Ramanujan
Srinivasa Ramanujan (1887–1920), largely self-taught, produced thousands of original results in number theory, infinite series, and modular forms. In 1913, he wrote to G.H. Hardy at Cambridge, who recognized the work of a genius.
21.2 The Partnership
Together Hardy and Ramanujan proved the asymptotic formula for the partition function. Hardy rated Ramanujan's natural ability at 100, compared to 80 for Hilbert and 30 for himself. The taxicab number 1729 = 1³ + 12³ = 9³ + 10³ became famous from their hospital conversation.
21.3 Legacy
Ramanujan died at 32 but his notebooks continue to inspire research. Hardy's A Mathematician's Apology remains one of the most eloquent defenses of pure mathematics.