The Man Who Knew Infinity: The Life of the Genius Ramanujan
by Robert Kanigel
©1992 Washington Square Press
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
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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