Mathematics

Srinivasa Ramanujan

1887 to 1920, Erode and Kumbakonam, India

A self-taught genius who found thousands of deep results by intuition alone, from rapidly converging series for pi to the mock theta functions mathematics is still unravelling.

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Lessons

The Self-Taught Genius and the Notebooks

How a poor clerk in South India, working almost alone from a single crammer’s handbook, filled notebook after notebook with thousands of deep results - stated by intuition, almost never proved - that mathematician…

Hardy, and the Meeting of Rigour and Intuition

The 1913 letter that stunned Cambridge, and the five-year collaboration between G. H. Hardy - apostle of rigorous proof - and Ramanujan - intuition incarnate - that produced results neither could have reached alone, inc…

Infinite Series and the Chase for Pi

Ramanujan’s astonishing rapidly converging series for 1/π, each term adding roughly eight correct digits; his mastery of continued fractions and the Rogers-Ramanujan identities; and his audacious, intuitive handli…

The Taxicab Number and the Structure of the Integers

1729 as the smallest number that is a sum of two cubes in two different ways - the famous hospital story - together with Ramanujan’s deep work on highly composite numbers and the theory of the partition function,…

Mock Theta Functions and the Unfolding Legacy

Ramanujan’s final gift - the mock theta functions of his last letter to Hardy in 1920, understood only in the twenty-first century through Zwegers’s work of 2002 - together with his death at thirty-two and t…

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