Ramanujan: Letters and Commentary by Bruce C. Berndt and Robert A. Rankin [XI] is a classic work containing the first letter from Ramanujan to Hardy, ``one of the most famous letters in the history of mathematics'', and Ramanujan's last letter - containing until the discovery of the `lost' Notebook, ``the only information available about Ramanujan's work in 1919 - 1920''. The authors have left no stone unturned to acquire as many letters as possible, since most of these letters, especially those exchanged by Hardy and Ramanujan (when the latter was for about two years in different sanatoria in England) contain interesting mathematical results. In fact, the two Memorial Numbers Ramanujan: Letters and Reminiscences [I] and Ramanujan: an Inspiration edited by P.K. Srinivasan and published by Muthialpet High School, Madras, in 1968, are the precursors to this book by Berndt and Rankin.

After a brief Biography of Ramanujan, transcripts of 172 letters are reproduced with Commentaries at the end of each of them, by Berndt and Rankin, in eight chapters, in this book whose Special Indian edition (1997) has 363 + xviii pages and is prices at Rs. 295/-. In Chapter 1, the letters regarding Ramanujan's first position at the Madras Port Trust and the correspondence with Prof. M.J.M. Hill (referred to in Chapter 1 of this book) are reproduced. In Chapter 2, the first two historic letters of Ramanujan to Hardy are reproduced in full and the commentary is on each one of the formulae contained in them. This is the first time that the second letter of Ramanujan to Hardy appears in full. In the Collected Papers [III] there is missing material marked by ... at certain places. There are brief biographical sketches (of a few lines or a few paragraphs) of almost all the characters who wrote to Ramanujan or who are mentioned in his letters in this book. Hardy's list of six New Year wishes, contained in a post card to a friend of his in the 1920's is an example of a delightful snippet in one of the Commentaries [XI, p.33] :

 

(1) prove the Riemann hypothesis; (2) make 211 not out in the fourth innings of the last test match at the Oval; (3) find an argument for the nonexistence of God which shall convince the general public; (4) be the first man at the top of Mt. Everest; (5) be proclaimed the first president of the U.S.S.R., Great Britain, and Germany; (6) murder Mussolini.

 

The next four chapters are devoted to the letters pertaining to Ramanujan's Preparing to go to England, Ramanujan at Cambridge, Ramanujan's illness and those written after Ramanujan returned to India. Berndt and Rankin have brought out in this volume, for the first time, Ramanujan's letters from sanatoria (Matlock House, Hill Grove, Fitzroy House). Ramanujan who was confined to sanatoria off and on for nearly half the time of his five-year sojourn in England, wrote several notes/letters to Hardy and received notes/replies from Hardy. These contain mathematical insights into the problems of interest to the two of them. These letters and commentaries on them, therefore, make this book significant to the mathematicians. The letters of Ramanujan to his kith and kin and friends reflect the human angle of Ramanujan. The incisive commentaries by the editors provides a proper perspective of the persons with whom Ramanujan corresponded. The last letter written by Ramanujan to Hardy, on Jan. 12, 1920 is reproduced and a portion of the letter following the first paragraph of the letter has been missing [XI, p.223-224]:

 

For almost 60 years, the only information available about Ramanujan's work in 1919 - 1920 was contained in his last letter to Hardy. Now we know that the results Ramanujan described in this letter are part of a much longer collection, called the ``lost notebook'' [XI].

 

In this letter, Ramanujan (as pointed out earlier) did not even hint to Hardy that he had not only not recovered from his suspected tuberculosis but that his health was on the decline. However, it contained the heart-warming news to Hardy that he had found new results on `mock' theta functions.

The minor role I had in providing the editors with letters written by Ramanujan to his boyhood friend, Mr. E. Vinayaka Row, is explicitly stated in Chapter 4 of the book [XI, p.113] :

 

The three letters below that Ramanujan wrote to Mr. E. Vinayaka Row on 11 June 1914, 24 march 1915 and 10 September 1915 have been made available through the courtesy of Professor K. Srinivasa Rao of the Institute of Mathematical Sciences, Madras. They were given to him by Mr. V. Madhava Rao, the son of E. Vinayaka Row. The latter was a lawyer and resident in Mylapore and a friend of K. Srinivasa Rao's father. The letters, parts of which have become somewhat moth-eaten, were discovered in a suitcase in Mr. Madhava Rao's attic. ... Hardy first reported Ramanujan's illness in the spring of 1917. In this letter [dated 24 March 1915], we learn that already during Ramanujan's first winter in England he was not feeling well.

 

The originals of these letters have since been handed-over by Mrs. Saraswathi Dole (daughter of Mr. E. Vinayaka Row) to the Ramanujan Museum in Royapuram, Madras.

In Chapter 7, the letters announcing the death of Ramanujan to Hardy, settling of the balance amount in the account of Ramanujan with the Barclays Bank Ltd. in Cambridge, correspondence between the relatives of Ramanujan (his mother and his wife) wrangling for the pension with the Government of Madras and its resolution, and letters by Hardy to the University of Madras and the Port Trust are reproduced. In Chapter 8, the letters pertaining to the publication of the Collected Papers and manuscripts of Ramanujan, and some correspondence between Hardy and G.N. Watson and from G.N. Watson to B.M. Wilson are dealt with. In Chapter 9, a very brief account of the Family history and the Family Record of Ramanujan with the National Archives in Delhi are presented.

Berndt and Rankin were interested in getting an Indian Edition of this book originally published by the American Mathematical Society and the London Mathematical Society, in 1995, and they graciously permitted me to write a Preface to the Indian edition and include a few Additions to the Indian Edition, published by the Affiliated East West Press Ltd. (1997) [XI]:

 

In this Indian edition, which coincides with the second printing of this book published by the American Mathematical Society (AMS) and London Mathematical Society (LMS), an Errata to the first edition is appended at the end of this volume, in a section entitled Additions to the Indian Edition. The letter of Mr. E.S. Montagu, referred to as No.22 - Financial dated February 24, 1921, in the AMS-LMS edition, and a xerox copy of Ramanujan's letter to Mr. E. Vinayaka Row (one of three reproduced, on p. 113 - 117) now deposited with the Ramanujan Museum in Royapuram, are included. ...

To the excellent collection of photographs in the AMS-LMS edition, are added three photographs of the busts of Ramanujan: that made by Paul Granlund, that by N. Masilamani and that on the beautiful white marble Saraswathi temple tower (`gopuram') of the Birla Institute of Technology (BITS).