**History of Mathematics**

Volume: 22;
2001;
347 pp;
Hardcover

MSC: Primary 01;
Secondary 11; 33

Print ISBN: 978-0-8218-2624-9

Product Code: HMATH/22

List Price: $96.00

Individual Member Price: $76.80

**Electronic ISBN: 978-1-4704-3890-6
Product Code: HMATH/22.E**

List Price: $96.00

Individual Member Price: $76.80

# Ramanujan: Essays and Surveys

Share this page *Edited by *
*Bruce C. Berndt; Robert A. Rankin*

A co-publication of the AMS and the London Mathematical Society

This book contains essays on Ramanujan and his work that were written
especially for this volume. It also includes important survey articles in
areas influenced by Ramanujan's mathematics. Most of the articles in the book are
nontechnical, but even those that are more technical contain substantial
sections that will engage the general reader.

The book opens with the only four existing photographs of Ramanujan,
presenting historical accounts of them and information about other people in
the photos. This section includes an account of a
cryptic family history written by his younger brother, S. Lakshmi
Narasimhan. Following are articles on Ramanujan's illness by R. A. Rankin, the
British physician D. A. B. Young, and Nobel laureate S. Chandrasekhar. They
present a study of his symptoms, a convincing diagnosis of the cause of his
death, and a thorough exposition of Ramanujan's life as a patient in English
sanitariums and nursing homes.

Following this are biographies of S. Janaki (Mrs. Ramanujan) and S.
Narayana Iyer, Chief Accountant of the Madras Port Trust Office, who first
communicated Ramanujan's work to the Journal of the Indian Mathematical
Society. The last half of the book begins with a section on
“Ramanujan's Manuscripts and Notebooks”. Included is an important
article by G. E. Andrews on Ramanujan's lost notebook.

The final two sections feature both nontechnical articles, such as Jonathan
and Peter Borwein's “Ramanujan and pi”, and more technical
articles by Freeman Dyson, Atle Selberg, Richard Askey, and G. N. Watson.

This volume complements the book Ramanujan: Letters and Commentary,
Volume 9, in the AMS series, History of Mathematics. For more on Ramanujan, see
these AMS publications, Ramanujan: Twelve Lectures on Subjects Suggested
by His Life and Work, Volume 136.H, and Collected Papers of Srinivasa
Ramanujan, Volume 159.H, in the AMS Chelsea Publishing series.

#### Table of Contents

# Table of Contents

## Ramanujan: Essays and Surveys

- Cover Cover11
- Title page iii4
- Copyright iv5
- Dedication v6
- Contents vii8
- Preface ix10
- Photograph credits xiii14
- Citations for previously published papers xv16
- The life of Ramanujan 118
- Photos (Ramanujan) PH-i20
- The four photographs of Ramanujan 324
- The books studied by Ramanujan in India 930
- The influence of Carr’s synopsis on Ramanujan 1738
- The notebooks of Srinivasa Ramanujan 2142
- A recently discovered letter giving Ramanujan’s examination scores 2344
- On Ramanujan 2546
- Indian Mathematical Society PH-v50
- The Ramanujan family record 2952
- Ramanujan’s illness 3962
- Ramanujan as a patient 4164
- Photo PH-vii88
- Ramanujan’s illness 6590
- An incident in the life of S. Ramanujan, F.R.S.: Conversations with G. H. Hardy, F.R.S. and J. E. Littlewood, F.R.S. and their sequel 77102
- S. Janaki 81106
- Photo PH-ix108
- S. Janaki Ammal (Mrs. Ramanujan) 83110
- Conversation “I didn’t understand his work, but I knew his worth” 89116
- Photo PH-xi122
- S. Narayana Iyer 95124
- Photo PH-xiii126
- A short biography of S. Narayana Iyer 97128
- Photo PH-xv130
- The distribution of primes 99132
- Some theorems in summation 101134
- E. H. Neville 105138
- Photo PH-xvii140
- Srinivasa Ramanujan [redacted] 107142
- University lectures in Madras 113144
- Ramanujan’s manuscripts and notebooks 115146
- Ramanujan’s manuscripts and notebooks 117148
- Ramanujan’s manuscripts and notebooks, II 129160
- An overview of Ramanujan’s notebooks [redacted] 143174
- An introduction to Ramanujan’s “lost” notebook 165176
- Nontechnical articles on Ramanujan’s work 185196
- Ramanujan and pi [redacted] 187198
- 𝜋 related developments since 1988 201200
- Reflections around the Ramanujan centenary 203202
- The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society 215214
- Somewhat more technical articles on Ramanujan’s work 259258
- A walk through Ramanujan’s garden 261260
- Ramanujan and hypergeometric and basic hypergeometric series 277276
- The final problem: An account of the mock theta functions 325324
- Back Cover Back Cover1347

#### Readership

General mathematical audience.

#### Reviews

A valuable source of initiation into Ramanujan's mathematics for some time to come.

-- B. Sury, Resonance

The book under review assembles a fine collection of essays by several
distinguished authors on a variety of topics that range over Ramanujan's
remarkable life and contributions … This book is a worthy sequel to *Ramanujan: Letters and
Commentary*. It also nicely complements Hardy's classic *Ramanujan: Twelve Lectures on
Subjects Suggested by His Life and Work* and Ramanujan's *Collected Papers*
… Selberg's … article provides many insights and is a magnificent
tribute to Ramanujan … This book, with its delightful collection of
essays and surveys relating to Ramanujan's life and mathematics, is accessible
to, and an inspiration for, laymen, students, and professional mathematicians
alike.

-- MAA Monthly