Ramanujan's lost notebook

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. The "notebook" is not a book, but consists of 87 loose and unordered sheets of paper, with more than 600 of Ramanujan's formulas.

George Andrews and Bruce C. Berndt (2005, 2009, 2012, 2013) have published several books in which they give proofs for Ramanujan's formulas included in the notebook. Berndt says of the notebooks' 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." (Peterson 2006)

History

After Ramanujan died on April 26, 1920, at the age of 32, his wife gave his notebooks to the University of Madras. On August 30, 1923, the registrar Francis Drewsbury sent much of this material to G. H. Hardy, probably including the lost notebook. Some time between 1934 and 1947 Hardy probably passed the notebook on to G. N. Watson. 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. George Andrews (1985, section 1.5) found the lost notebook in the spring of 1976 while on a visit to Trinity College. It was published on December 22, 1987, by Narosa publishing house.

Contents of the notebook

Rankin (1989) described the lost notebook in detail. The majority of the formulas are about q-series and mock theta functions, about a third are about modular equations and singular moduli, and the remaining formulas are mainly about integrals, Dirichlet series, congruences, and asymptotics.

References

• Alladi, Krishnaswami (17 February 2005), "Ramanujan's lost notebook: a lecture series in Florida", The Hindu
• Andrews, George E. (1986), q-series: their development and application in analysis, number theory, combinatorics, physics, and computer algebra, CBMS Regional Conference Series in Mathematics 66, Published for the Conference Board of the Mathematical Sciences, Washington, DC, ISBN 978-0-8218-0716-3, MR 858826
• Andrews, George E.; Berndt, Bruce C. (2005), Ramanujan's lost notebook. Part I, Berlin, New York: Springer-Verlag, ISBN 978-0-387-25529-3, MR 2135178, OCLC 228396300
• Andrews, George E.; Berndt, Bruce C. (2009), Ramanujan's lost notebook. Part II, Berlin, New York: Springer-Verlag, ISBN 978-0-387-77765-8, MR 2474043
• Andrews, George E.; Berndt, Bruce C. (2012), Ramanujan's lost notebook. Part III, Berlin, New York: Springer-Verlag, ISBN 978-1-4614-3809-0
• Andrews, George E.; Berndt, Bruce C. (2013), Ramanujan's lost notebook. Part IV, Berlin, New York: Springer-Verlag, ISBN 978-1-4614-4080-2
• Askey, Richard (1988), "Book Review: The lost notebook and other unpublished papers", American Mathematical Society. Bulletin. New Series 19 (2): 558–560, doi:10.1090/S0273-0979-1988-15741-2, ISSN 0002-9904, MR 1567721
• Peterson, Doug (2006), "Raiders of the Lost Notebook", LASNews, retrieved 2009-02-19
• Ramanujan, Srinivasa (1988), The lost notebook and other unpublished papers, New Delhi; Berlin, New York: Narosa Publishing House; Springer-Verlag, ISBN 978-3-540-18726-4, MR 947735 Reprinted 2008 ISBN 978-81-7319-947-9
• Rankin, Robert A. (1989), "Ramanujan's manuscripts and notebooks. II", Bull. London Math. Soc. 21 (4): 351–365, doi:10.1112/blms/21.4.351, ISSN 0024-6093, MR 998632

External links

• Schneider, Robert P. "Uncovering Ramanujan's 'Lost' Notebook: An Oral History".
• Srinivasa Rao, K. "Ramanujan's Notebooks".