Talk about math anxiety. I've got it, bad. So bad, in fact, that when I was at the tender age of fourteen too many years ago and failing algebra, I decided right then and there that I would only marry a man talented in maths and sciences. This desperation led me to hang out in the Engineering lounge at UCLA while an undergrad there, seeking the Nerd of My Dreams, hoping to improve my future gene pool. (And yes, I've been married for nearly 20 years to a techie geek, but it was only after we were married that I found out that he was calculator-dependent. I was mortified, but it was too late.)

Frankly, numbers scare me. And I can't for the life of me understand how they could be interesting. So it was not without some trepidation that I read this book, about the arguably greatest mathematician that ever lived. So intense was Ramanujan's passion for prime numbers, equations, patterns and sequences, that (like so many true single-minded geniuses) he neglected every other aspect of his life. In fact, his self-deprivation and torment ultimately led to his own death at a tragically young age.

Robert Kanigel does an outstanding job of documenting Ramanujan's life, from his years as an impoverished Indian youth who couldn't function in a normal school classroom, to the time he spent under his mentor at Cambridge, the eminent British mathematician G.H. Hardy. The Man Who Knew Infinity is part biography, part adventure story, part thriller. But as a mathematically-challenged person, the greatest thing about this book for me, is Kanigel's ability to transmit the mystical excitement and spiritual quality of numbers as seen through the eyes of Ramanujan's genius - - an accomplishment which is no small feat, indeed. Ramanajun's exercises were the mathematical equivalent of Talmudic pilpul, a form of discourse and argumentative reasoning which takes seemingly unrelated conceptual threads, and neatly and amazingly weaves them together to show a unifying relationship that heretofore may have been unrealized. Here is an example found in Kanigel's book:

Take the number 10. The number of its partitions - - or to invoke a precision that now becomes necessary, the number of its "unrestricted" partitions - - is 42. This number includes, for example:


1+1+1+1+1+1+1+1+1+1= 10

and

1+1+1+1+2+2+2= 10


But what if you excluded partitions such as these by imposing a new requirement, that the smallest difference between numbers making up the partition always be at least 2? For example:


8+2= 10 or 6+3+1= 10


would both qualify, as do four others, making for a total of six. All the other thirty-six partitions of 10 contain at least one pair of numbers separated by less than 2 and are thus ineligible.


That's one class of partitions. Here's another, formed by a second, distinct exclusionary tactic: What if you only allowed partitions satisfying a specific algebraic form? For example, what if you restricted them to those comprising parts taking the form of either 5m + 1 or 5m + 4 (where m is a positive integer)? If you do that, the partition 6+3+1 fails to qualify. Why? Because not all the parts, the individual numbers making up the partition, satisfy the condition. The part 6 does; it can be viewed as 5m + 1 with m = 0. But what about 3? Make m anything you want and you can't get a 3 out of either 5m + 1 or 5m + 4 (which together can generate only numbers whose final digits are 1, 4, 6 or 9).


Two partitions that would qualify are:


6 + 4 = 10 and 4+1+1+1+1+1+1 = 10


Each satisfies the algebraic requirement. In all, qualifying partitions come to six.


Six also happens to be the number of partitions that fit the first category. Except that it doesn't "happen to be." It always turns out that way. Pick any number. Add up all its partitions satisfying the "minimal difference of 2" requirement. Then add up all its partitions satisfying the "5m + 1 or 5m + 4" requirement. Compare the numbers. They're the same, every time.

But even if you want to skip the parts of the book that demonstrate some of Ramanajun's mathematical findings, you will still find The Man Who Knew Infinity to be nothing less than a remarkable read.

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