Reddit reviews The Man Who Knew Infinity: A Life of the Genius Ramanujan

I highly recommend reading The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel. The first 1/3rd or so is slow, it's about Hardy & Littlewood and the Tripos-test era in Europe, but it really picks up when Ramanujan is introduced.

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If you'd like to browse through the textbook which inspired Ramanujan, it's available here.

• The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel
  
• Mathematics: Its Content, Methods and Meaning by A. D. Aleksandrov et al.
  
• Visual Complex Analysis by Tristan Needham
  
• Geometry and the Imagination by David Hilbert and Stephan Cohn-Vossen
  

God Created the Integers, edited by Stephen Hawking. Includes selected works of various big names in mathematics with a brief biography of each preceding the math. The wiki article on the book has a list of all mathematicians included.

Prime Obsession, about Riemann and his famous hypothesis.

The Man Who Knew Infinity, about Ramanujan.

A very accurate account of Ramanujan's life

There's Ramanujan's biography that looks very interesting. And of course, the one about Nash (the one the movie A Beautiful Mind was inspired by): A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash.
I own a copy of both and I haven't read them cover to cover yet, but I found they have exactly what I'm looking for in this kind of biography: 1. they attempt as far as possible to describe the inner workings of these people's minds, not just the final output; 2. they devote some time to explain some of the trickiest concepts developed by them (and thus these are also good popular science/math books); 3. they have a good narrative/historical element, too, with interesting anecdotes and vignettes.

http://www.amazon.com/The-Man-Who-Knew-Infinity/dp/0671750615

Excellent biography of S.Ramanujan