Book Description
The influence of Ramanujan on number theory is without parallel in mathematics. His papers, problems and letters have spawned a remarkable number of later results by many different mathematicians. Here, his 37 published papers, most of his first two and last letters to Hardy, the famous 58 problems submitted to the Journal of the Indian Mathematical Society, and the commentary of the original editors (Hardy, Seshu Aiyar and Wilson) are reprinted again, after having been unavailable for some time.

In this, the third printing of Ramanujan's collected papers, Bruce Berndt provides an annotated guide to Ramanujan's work and to the mathematics it inspired over the last three-quarters of a century. The historical development of ideas is traced in the commentary and by citations to the copious references. The editor has done the mathematical world a tremendous service that few others would be qualified to do. ... Read more

Customer Reviews (1)

intended semi differential analysis
Srinivasar was an enigma in the latter years of his life,when his work output suddenly quadrupled and his critics began to find their voices.His semiautonomials plowed new ground and his multiequanipseudonomials are said to have come to him late at night after a prolonged episode of religious fasting and penance wherein he shed 14 pounds over a 34 day period and was forced by his wife to consult 3 different doctors.Most think he was lucky to escape with his life.Such was his dedication to pure non-imaginary antinomials. ... Read more

Customer Reviews (52)

LIFE TO INFINITY
MISFORTUNE AND GENIUS ARE TOO OFTEN INTERTWINE.STARTING LIFE IN THE INDIAN CASTE SYSTEM IS CERTAINLY A BURDEN FOR ANY GENIUS (MAHATMA GANDHIDENOUNCED THE CASTE SYSTEM).DOWN IN SOUTHERN INDIA AMONG THE MULTITUDES ONE NEEDS A PRODIGIOUS MIND TO ASCEND FROM SUCH A DIFFICULT ROOTAGE.HOW CAN YOU READ OF THIS MAN AND NOT BE THRILLED WITH THE STARS OF INSPIRATION? HERE IS A SALUTE TO THE BRITS FOR SHOWING THE WORLD THIS NUMERICAL PUNDIT.

Perfect Demonstration Of How A Biography Should Be Written
As some of the other reviewers have pointed out, Kanigel does not dwell much on Ramanujan's mathematics. However, this is a spectacularly outstanding biography (this is not an exaggeration, believe me). Anyone who reads this book cover to cover will 'know' Ramanujan as well as they know their best friend. The many sides of this prodigy's personality - his affinity for mysticism, his need for public approbation, his gentle good nature - are all expertly transmitted. The tragedy of a life cut short at the height of its productivity will be felt keenly even by the 'toughest' of readers. Kanigel deserves high praise indeed for the masterly way he evokes time and place: Southern India and Cambridge (England) during 1900-20. If it were possible to award 6 stars, I would have done that.
A few further points: 1) Kanigel's decision to give G. H. Hardy equal importance (almost) as Ramanujan is a strength of this book, not a drawback. This decision adds much richness to the narrative. 2) Kanigel returns to one question repeatedly: What is 'genius' and where does it come from? He succeeds in getting the reader to wonder along with him. There is probably no (one) good answer, but a life such as Ramanujan's should lead one to ponder this deeply. 3) I wish that in a future edition Kanigel would include an appendix, with some of the more accessible of Ramanujan's mathematical formulae. I am sure that any one of the 'gang of three' Ramanujan specialists (George Andrews, Richard Askey, and Bruce Berndt) would help him with this if he requested. The biography is superb, as already stated, but this would be dessert for those readers who have a mathematical background.

A perfect Indian Student story
A very very good read....... Ramanujans story still has relevance even after almost a 100 years. The images of colonial Madras and England before the war are very desciptive and well researched. In all one of the best books I have ever read.

A thorough account of the man and those around him
Having just finished this, I wanted to jot down a few thoughts. I feel largely positive about the presentation. The mathematically inclined will find very little about the details of Ramanujan's work. This is much more biographical, about the man's upbringing, his life in Madras, his work with Hardy at Cambridge, and his untimely death. Kanigel presents enough of the surroundings and influences of his life (his struggle with the Indian academic establishment, the influency of his mother, his marriage to Janaki, being trapped in England for WW1) to make an epic movie. The story does pull you in, and leads you to admire the man's accomplishments in the face of daunting adversity.

What I didn't like about the book is that it talks almost as much about G.H. Hardy. Fascinating a character as he may have been, and as influential as he was in the nurturing of Ramanujan's genius, this isn't really supposed to be about him. And yet, I'd estimate a third to a half of the book is about him. I'd rather hear more about, um..., Ramanujan.

In the end, I am struck by how it would seem that Ramanujan seemed destined to be unhappy. You get a sense that he loved living in India, thrived on its culture, but felt isolated by his need to do mathematics far beyond what anyone there at the time could appreciate. In England, he could excel at math and dazzle the establishment with his brilliance, and yet the isolation from his homeland left his life incomplete somehow.

A though-provoking work, and good light reading for any mathematician.

The Stuff of Fable
The story of Ramanujan is the stuff of fable.As Hardy put it "a poor and a solitary Hindu pitting his brains against the accumulated wisdom of Europe".A man for whom paper was precious, with access only to a second rate library, with very little material resources, who rose to become one of the greatest mathematical geniuses of all time by the bodacious gifts bestowed on him by nature and that he further increased by his devotion to mathematics. A life that Michiko Kaku has described as "a bursting super nova".This enthralling book is a must read for any one who has an interest in mathematics or in the psychology of genius. When I first ran into Ramanujan in the World of Mathematics I was exalted and inspired to bring out the best in me intellectually. His life made me pursue a life of the mind and hold the truth of passion before me. ... Read more

Book Description
Srinvisa Ramanujan(1887-1920) hailed as the greatest Mathematician of India and compared to all time greats,Euler,Gauss and Jacobi,for natural genius, is an eternal source of inspiration,especially for the student of mathematics.This Book presents a brief biographical account of his life and glimpses into his work on highly composite numbers.elliptic functions,partitions,hypergeometric series,continued fractions,mock theta functions and other topics. A unique feature of this Book is that it provides complete lists of all the papers pertaining to Ramanujan in the Wren Library of Trinity college,Cambridge and the letters and other material about Ramanujan with the National Archives,New Delhi and the Tamilnadu Archives,Chennai.In the words of Prof.Bruce C.Berndt,who is the world expert on the note books of Ramanujan,this Book significantly adds to our Knowledge about Ramanujan and his work. ... Read more

Book Description
Among his thirty-three published papers, Ramanujan had only onecontinued fraction, the Rogers-Ramanujan continued fraction.However, his notebooks contain over 100 results on continuedfractions. At the end of his second notebook are 100 pages ofunorganized material, and the third notebook comprisesthirty-three pages of disorganized results. In these 133 pagesof material are approximately sixty theorems on continuedfractions, most of them new results. In this monograph, theauthors discuss and prove each of these theorems. Aimed at thoseinterested in Ramanujan and his work, this monograph will be ofspecial interest to those who work in continued fractions,$q$-series, special functions, theta-functions, andcombinatorics. The work is likely to be of interest to those innumber theory as well. The only required background is someknowledge of continued fractions and a course in complexanalysis. ... Read more

Book Description
Ramanujan occupies a unique place in analytic number theory. His formulas, identities, and calculations are still amazing three-quarters of a century after his death. Many of his discoveries seem to have appeared as if from the ether. His mentor and primary collaborator was the famous G. H. Hardy. Here, Hardy collects twelve of his own lectures on topics stemming from Ramanujan's life and work. The topics include partitions, hypergeometric series, Ramanujan's $\tau$-function and round numbers.

Hardy was the first to recognize the brilliance of Ramanujan's ideas. As one of the great mathematicians of the time, it is fascinating to read Hardy's accounts of their importance and influence. The book concludes with a chapter by chapter overview written by Bruce C. Berndt. In this overview, Berndt gives references to current literature, developments since Hardy's original lectures, and background information on Ramanujan's research, including his unpublished papers. ... Read more

Customer Reviews (1)

A nice reprint of a valuable book
This is a great book for those of you who want to learn the works of the great Indian Mathematician Srinivasa Ramanujan. It was written by G.H.Hardy, who intorduced Ramanujan to the western world of Mathematics. 12subjects are discussed, as written by Ramanujan, with comments. The layoutand printing of the book are excellent. This edition corrected a number oferrors of the previous editions. I expected a little more comments by theeditors for people less proficient in Number theory. You will need a copyof "An Introduction to Theory of Numbers" by Hardy and Wright, tofollow this book. If you want to know more about Ramanujan, some greatbooks are: "The Man who knew infinity: A Life of the GeniusRamanujan" byRobert Kanigel (the best biography of Ramanujan) and"A Mathematician's apology" by GH Hardy et al. ... Read more

Book Description

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.

Book Description
The letters that Ramanujan wrote to G. H. Hardy on January 16 and February 27, 1913, are two of the most famous letters in the history of mathematics. These and other letters introduced Ramanujan and his remarkable theorems to the world and stimulated much research, especially in the 1920s and 1930s. This book brings together many letters to, from, and about Ramanujan. The letters came from the National Archives in Delhi, the Archives in the State of Tamil Nadu, and a variety of other sources. Helping to orient the reader is the extensive commentary, both mathematical and cultural, by Berndt and Rankin; in particular, they discuss in detail the history, up to the present day, of each mathematical result in the letters. Containing many letters that have never been published before, this book will appeal to those interested in Ramanujan's mathematics as well as those wanting to learn more about the personal side of his life.

Ramanujan: Letters and Commentary was selected for the CHOICE list of Outstanding Academic Books for 1996. ... Read more

Customer Reviews (1)

Get personal with Ramanujan through letters
Ramanujan was most certainly the most talented mathematician of this century. With essentially no formal training, he managed to discover an enormous number of formulas, many of which were quite different from those previously known. The story of how he came to the attention of the mathematical community and was brought into "formal" mathematical circles is an interesting one. Given the colonial nature of the relationship between England and India, it would have been "natural" for the English mathematicians to consider an untrained colonial native to be beneath them. However, to their credit, there is no evidence that the English mathematicians ever felt or acted this way.
This book is the story of Ramanujan told through the letters that were written by and about him. While many are very formal, you still see the personalities emerging. G.H. Hardy is at times in awe of Ramanujan's ability, proving to be a person of high quality as he tries as best he can to aid him in adapting to British society and to doing mathematics in a formal way. Many others are also involved, and it is clear that they do have a genuine interest in his welfare as a person and as a mathematician. The commentary included among the letters is very helpful in establishing a context for the text. The authors do a very good job in explaining the circumstances of the letters. Some deal with social conditions and others are as simple as a description of what a word means.
What is most impressive about the book is that there is no undercurrent of colonial class consciousness running through the material in the letters. Given the situation in the early part of the twentieth century, that would have been typical of most English men of the times and it is a tribute to the mathematicians that they avoided it. Not many others would have been so noble.

Published in Journal of Recreational Mathematics, reprinted with permission. ... Read more

Book Description
This book contains essays on Ramanujan and his work , as well as 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 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.

Copublished with the London Mathematical Society. ... Read more