Self-taught mathematical prodigy Srinivasa Ramanujan had a brilliant but brief life. In 1920, at the age of 32, he died from a combination of illness and malnutrition. Before he passed, he filled various notebooks and manuscripts with nearly 4,000 results and conjectures. These documents have inspired mathematicians ever since, helping solve various conundrums and inspiring new fields of math (See “The Oracle” by Ariel Bleicher in the May issue of *Scientific American*). Here is a timeline tracing Ramanujan’s intellectual legacy.

12/22/1887 Ramanujan (R) born in what is now Tamil Nadu, India. He shows an immense talent for math from a very young age

1/16/1913 Isolated from the greater mathematical community, R sends letters to several prominent English mathematicians. On this date he mails his first fateful letter to G.H. Hardy, who invites him to the University of Cambridge

4/14/1914 R arrives at the University of Cambridge. He has a fruitful five years of collaboration with Hardy

1/12/1920 R's last letter to Hardy

4/26/1920 R dies in Madras, India, weak and malnourished

11/14/1935 English mathematician G. N. Watson, at his retirement, describes his findings on R's "mock theta functions”

1943 German mathematician Hans Rademacher perfects R's asymptotic formula and arrives at a formula that's accurate enough to compute individual values of the partition function p(n)

7/1/1952 M. Rushforth publishes some of Ramanujan's previously unpublished manuscripts

1957 M. Newman proves some of R's claims for the function lambda(n)

1959 O. Kolberg proves that p(n) takes infinitely many even and odd values

1976 American mathematician G.E. Andrews rediscovers R's "lost notebook" in a box of his belongings at the University of Cambridge

1979 J. H. Conway and S. P. Norton use Ramanujan’s work to formulate the so-called Monstrous Moonshine Conjectures

1988 Frank Garvan of the University of Florida proves one of R's formulas and uses it to give a new proof of R's congruence for the partition function p(n)

2002 Dutch mathematician Sanders Zwegers formally defines the mock theta functions originally described by Ramanujan

2004 Inspired by Ramanujan, Jan Hendrik Bruinier and Jens Funke introduce harmonic Maass forms

2005 Andrews and Pedro Freitas establish an infinite family of extensions of Abel's Lemma and apply their results to obtain q-series identities

2007 W.Y.C. Chen and K Q. Ji provide combinatorial proofs of sums of tails of Euler's partition products

2007 Ken Ono and his colleagues use their development of the mock theta functions as the holomorphic parts of Maass wave forms to obtain a general theorem that has corollaries to the mock theta conjectures

1/2011 Ono and collaborators find solution linking the partition function p(n)to higher prime numbers

1/2011 Ono and collaborator describe first formula that directly calculates p(n) for any n

12/2011 Indian government declares R’s birthday National Mathematics Day

# Ramanujan’s Long Legacy

Although he died young, the mathematical prodigy’s genius lives on

This article was originally published with the title "The Oracle" in Scientific American 310, 5, (May 2014)