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Publisher:

American Mathematical Society

Publication Date:

2002

Number of Pages:

254

Format:

Hardcover

Series:

AMS Chelsea Publishing

Price:

41.00

ISBN:

0-8218-2023-0

Category:

General

[Reviewed by , on ]

Allen Stenger

06/18/2015

The Indian mathematician Ramanujan (1887–1920) had a brief but spectacular mathematical career, ended by his death at the age of 32. Much of his work was done in collaboration with the English mathematician G. H. Hardy (1877–1947), the author of this work. In this book Hardy gives a brief scientific biography of Ramanujan and then covers his work. The present volume is a 2002 corrected reprint by AMS Chelsea of the 1940 Cambridge edition. This edition includes an eighteen-page supplement by Bruce C. Berndt, with additional notes, commentary, updates, and references to more recent work,.

The biography here is brief (21 pages) and deals mostly with his scientific work rather than his personal life or education. There is an excellent book-length biography by Kanigel, *The Man Who Knew Infinity* (that book also has a lot about Hardy). Ramanujan is also the subject of a 2014 film, that appears to have been released only in India.

Each following chapter covers one technical area that Ramanujan worked in. The narrative weaves together two stories: Hardy’s view of how Ramanujan thought about mathematics and how he came up with his ideas, and a description of how contemporary (i.e., 1940s) mathematicians viewed those same areas. One of the most interesting aspects is that the book covers a number of Ramanujan’s errors and how he went astray.

There is a whole Ramanujan industry today, nearly a century after his death, devoted to mining his notebooks. The present book deals mostly with his published work, although Chapter VII on hypergeometric series and Chapter XII on elliptic functions instead deal with chapters out of his notebooks.

Bottom line: an interesting historical document, which was much more valuable when it came out, but most of the mathematical content has now been surpassed by more recent accounts.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis.

- The Indian mathematician Ramanujan
- Ramanujan and the theory of prime numbers
- Round numbers
- Some more problems of the analytic theory of numbers
- A lattice-point problem
- Ramanujan's work on partitions
- Hypergeometric series
- Asymptotic theory of partitions
- The representation of numbers as sums of squares
- Ramanujan's function $\tau(n)$
- Definite integrals
- Elliptic and modular functions
- Bibliography

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