Ramanujan's lost notebook
Encyclopedia
Srinivasa Ramanujan
's lost notebook is the manuscript in which Ramanujan, the great Indian mathematician from Cambridge University, recorded the mathematical discoveries of the last year of his life. 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.
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."
. 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 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 library on December 26, 1968. found the lost notebook in the spring of 1976 while on a visit to Trinity College, and it was published on December 22, 1987 by Narosa publishing house.
The majority of the formulas are about q-series and mock theta functions, about a third are about modular equation
s and singular moduli, and the remaining formulas are mainly about integrals, Dirichlet series, congruences, and asymptotics.
Srinivasa Ramanujan
Srīnivāsa Aiyangār Rāmānujan FRS, better known as Srinivasa Iyengar Ramanujan was a Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions...
's lost notebook is the manuscript in which Ramanujan, the great Indian mathematician from Cambridge University, recorded the mathematical discoveries of the last year of his life. It was rediscovered by George Andrews in 1976, in a box of effects of G. N. Watson
G. N. Watson
Neville Watson was an English mathematician, a noted master in the application of complex analysis to the theory of special functions. His collaboration on the 1915 second edition of E. T. Whittaker's A Course of Modern Analysis produced the classic “Whittaker & Watson” text...
stored at the Wren Library
Wren Library, Cambridge
The Wren Library is the library of Trinity College in Cambridge. It was designed by Christopher Wren in 1676 and completed in 1695.The library is a single large room built over an open colonnade on the ground floor of Nevile's Court...
at Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
. The "notebook" is not a book, but consists of 87 loose and unordered sheets of paper, with more than 600 of Ramanujan's formulas.
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."
History
After Ramanujan died on April 26, 1920, at the age of 32, his wife gave his notebooks to the University of MadrasUniversity of Madras
The University of Madras is a public research university in Chennai, Tamil Nadu, India. It is one of the three oldest universities in India...
. On August 30, 1923, the registrar Francis Drewsbury sent much of this material to G. H. Hardy
G. H. Hardy
Godfrey Harold “G. H.” Hardy FRS was a prominent English mathematician, known for his achievements in number theory and mathematical analysis....
, probably including the lost notebook. Some time between 1934 and 1947 Hardy passed the notebook on to G. N. Watson
G. N. Watson
Neville Watson was an English mathematician, a noted master in the application of complex analysis to the theory of special functions. His collaboration on the 1915 second edition of E. T. Whittaker's A Course of Modern Analysis produced the classic “Whittaker & Watson” text...
. 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 library on December 26, 1968. found the lost notebook in the spring of 1976 while on a visit to Trinity College, and it was published on December 22, 1987 by Narosa publishing house.
Contents of the notebook
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 equation
Modular equation
In mathematics, a modular equation is an algebraic equation satisfied by moduli, in the sense of moduli problem. That is, given a number of functions on a moduli space, a modular equation is an equation holding between them, or in other words an identity for moduli.The most frequent use of the term...
s and singular moduli, and the remaining formulas are mainly about integrals, Dirichlet series, congruences, and asymptotics.