RamanujanThe 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 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.
-Galia Berry
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