The Man Who Knew Infinity: A Life of the Genius Ramanujan Paperback – Illustrated, April 26, 2016

For Rulers: Priming Political Leaders for Saving Humanity from ItselfThis is a fascinating book, as recognized by the many reviews. But I suggest a different perspective, namely the challenge posed by the mind of Srinivasa RAMANUJAN to the idea of “super-intelligent robots” which is at the core of what is appropriately called by Ray Kurzweil “Spiritual Machines” and “Singularity.”Ramanujan was more that one of the few persons recognized as “geniuses.” He was a super-genius, “a man who grew up praying to stone deities; who for most of his life took counsel from a family goddess, declaring it was she to whom his mathematical insights were owed; whose theorems would, at intellectually backbreaking cost, be proved true—yet leave mathematicians baffled that anyone could divine them in the first place” (p. 4).All mathematical creativity depends on inspiration and imagination, followed by strict proof. However the mental processes resulting in the radical breakthroughs of Ramanujan, despite his social circumstances and lack of minimal education, are on an unequalled level. This outstanding biography does not even try to explain them, nor do the top mathematicians with whom Ramanujan worked at Cambridge and who continue to draw radically novel ideas from his handwritten notebooks.This brings me to current efforts to spawn robots with artificial general intelligence and, beyond them, robots with super-intelligence. But the phenomenon of Ramanujan (and a few other geniuses) is not only beyond the scales of intelligence, but above the concept of “intelligence” itself. No enhancement of human intelligence opens a door to becoming a Ramanujan; and no algorithm is likely to produce robots with the abilities of Ramanujan. This would require more than super-intelligence namely a quantum leap into what we do not understand and cannot even conceptualize.Artificial intelligence experts will probably respond that progress will be in steps: a somewhat super-intelligence entity will develop a more super-intelligent entity and so on, till “minds” of the quality of Ramanujan are understood, achieved and surpassed. But this is a weak hypothesis as long as the mind of Ramanujan remains totally a black box.Thus Ramanujan posed a critical riddle to the idea of super-intelligent robots, whether with biological or mechanical substrata. Therefore, studying this book and pondering the challenge its subject presents is strongly recommended to philosophers, scientists and technologists working on advanced artificial intelligence and the Singularity hypothesis as a whole.Professor Yehezkel DrorThe Hebrew University of Jerusalem

I had read Kanigel's book on Ramanujan way back in college and therefore, to refresh my memory after watching the recent movie and to get a more mature understanding of the story, I read it again. The book achieves the rare distinction of being an evocative picture of both early 20th century southern India and Cambridge, as well as a marvelous exposition of the pursuit of pure mathematics at its highest level by two of its most exalted practitioners. I found it remarkable that Kanigel manages to explain concepts like partitions, modular forms and generating functions in a book that assumes literally no knowledge of math.Ramanujan's cultural, religious and family background is described with empathy and in detail. So much of his success was due to sheer chance; he was recognized by the right people at the right time even after many others had ignored him, and his caste made up for his poverty and lack of connections. Slide the needle of destiny a little to the right or left, and he might have languished in obscurity forever. G. H. Hardy's background and the the culture of Tripos examinations, public school and Cambridge elites is similarly described in vivid terms. Hardy was a singular thinker who enjoyed pure math precisely because of his uselessness (his book "A Mathematician's Apology" is eminently readable for the pride it takes in the pursuit of useless but beautiful ideas). The contrast between the two worlds and the two men could not be more stark, and yet somehow mathematics bridged the very unlikely gap between them; the book is thus even more of a human story than a mathematical one. Even today it's impossible to understand how Ramanujan could derive and prove everything that he did, but it's clear that obsessive hard work combined with a fearless creative streak played an important role in his discoveries.Kanigel also talks about how these discoveries have kept entire schools of mathematicians busy for decades. Ultimately Ramanujan's story is that of a blazing comet which burned bright and quick, guided by the gravitational pull exerted by his own intellect and Hardy's kinship. More than anything else, the story makes the expedience of making sure that other Ramanujans in remote places don't fall through the cracks woefully clear.

I bought this book after seeing the film, although I have always been fascinated by the Ramanujan story.The problems of adapting to postgraduate study, the culture shocks and the complex personality of Ramanujan are well portraited. However I would have wanted to read more on his work - the book is written very much for non-mathematicians.The character of Hardy is beautifully developed. Indeed, the book is almost as much about Hardy as about Ramanujan. I am not sure if Hardy tamed Ramanujan or if he just canalized his inmense genius and energy to problems and fields where work could be jointly developed and published. To his great credit, Hardy also gave him critical support at difficult times. In any case it is hard to see what else could have been done. Without Hardy we would never have learned of Ramanujan, which speaks volumes about the Indian educational system and society at the time.I hope that many elementary and secondary school teachers get to read this book. While most of the world is struggling to get children to learn the basics of mathematics, we cannot forget how important it is to detect and develop early talent. How many Ramanujans are today sitting in a classroom, thoroughly bored with elementary arithmetic taught by an unmotivated teacher?I recommend anybody interested in this book to pick Hardy's "A Mathematician's Apology" as well.