55-2019 How a chance discovery saved a precious mathematical legacy.


Ramanujan’s last major contribution “mock theta functions” were almost lost forever, but for a fortunate discovery made years later. The story of the lost note book goes like this ::

Ramanujan’s lost notebook is the manuscript in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year (1919 — 1920) of his life. Its whereabouts were unknown to all but a few mathematicians until it was rediscovered by George Andrews in 1976, in a box of effects of G. N. Watson stored at the Wren Library at Trinity College, Cambridge and were due to be incinerated in a few days. The “notebook” is not a book, but consists of loose and unordered sheets of paper — “more than one hundred pages written on 138 sides in Ramanujan’s distinctive handwriting. The sheets contained over six hundred mathematical formulas listed consecutively without proofs.The manuscript contains no introduction or covering letter. In fact, there are hardly any words in the manuscript. There are a few marks evidently made by a cataloguer, and there are a few remarks in the handwriting of G. H. Hardy.

After Ramanujan died on April 26, 1920, at the age of 32, his wife Janaki had given his notebooks to the University of Madras. On August 30, 1923, the registrar Francis Drewsbury sent much of this material to G. H. Hardy, Ramanujan’s mentor at Trinity College, where he probably received the manuscripts of the lost notebook.

Almost surely, this manuscript, or at least most of it, was written during the last year of Ramanujan’s life, after his return to India from England. Undoubtedly, the most famous objects examined in the lost notebook are the mock theta functions.

Some time between 1934 and 1947 Hardy probably passed the notebook on to G. N. Watson, who with B. M. Wilson started on the project of editing Ramanujan’s notebooks. However, Wilson died in 1935 and Watson seems to have lost interest in the project in the late 1930s. After Watson’s death in 1965, J. M. Whittaker examined Watson’s papers (which were a complete mess, due to be incinerated in a few days) and found Ramanujan’s notebook, which he and R. A. Rankin sent to Trinity College Wren library on December 26, 1968. The lost notebook George Andrews, following a suggestion by Lucy Slater, found the lost notebook in the spring of 1976 while on a visit to Trinity College. George Andrews and Bruce C. Berndt have published several books in which they give proofs for Ramanujan’s formulas included in the notebook. Bruce C Berndt says of the notebook’s discovery: “The discovery of this ‘Lost Notebook’ caused roughly as much stir in the mathematical world as the discovery of Beethoven’s tenth symphony would cause in the musical world.”

The “lost notebook” was published on December 22, 1987, by Narosa publishing house, India, 67 years after Ramanujan died !

Also see :: Remembering Ramanujan