## Friday, December 4, 2009

I posted back in June about my favorite math books. Any of those would make a great gift. But I'm excited about a few books I've read recently, and wanted to share them here for those of you who like to give books as gifts. Both are biographies of mathematicians.

Carry On, Mr. Bowditch, by Jean Lee Latham (1955) is written for younger readers, but will charm many adults too. It's a fictionalized account of the life of Nathaniel Bowditch, who loved math, but had to leave school when his family needed his help. He was indentured to a ship chandlery for 9 years, which dashed his hopes of someday going to Harvard to study math. But he spent his spare time learning everything he could on his own - he learned Latin so he could read Newton's Principia Mathematica, and then learned French so he could read another book recommended to him.

After his indenture ended, he sailed with a merchant ship, and became interested in the mathematics of navigation. He was incensed at the errors in the book of tables used for navigation, and began the laborious work of correcting them.
"You don't 'cast your eye' over navigation tables!" Nat barked. "When I checked that one table of Maskelyne's, I worked every figure three times, just to be sure I was right!"
"Three times? Every figure? But why in ..."
"Why not? Nat roared. "Mathematics is nothing if it isn't correct! Men's lives depend on those figures!" (page 161)

He also taught the crews how to "do a lunar", a startlingly egalitarian action back then. In this passage he's talking to a young woman who later becomes his wife, but this is much like the lessons he gave the crews he sailed with:
Nat said, "That's the North Star. If you think of the North Star as the middle of your clock face, and the line from it through those other stars as the hour hand, you can tell time."
"It says about one o'clock. Is that right?"
"No, this clock runs backwards."
"Is it eleven o'clock?"
"No, there's one other difference. It takes twenty-four hours for the Big Dipper to swing around the North Star. So every hour space on the clock face stands for two hours." (page 85)
Bowditch eventually decided to write his own book, which he hoped would be error-free, and would also include navigation lessons and general information needed by sailors. His book, the American Practical Navigator, published in 1902, is still carried on every U.S. naval vessel (according to Wikipedia).

Bowditch was born in 1773 in Salem, Massachusetts. I enjoyed reading about the early days of the U.S. as an independent nation from his perspective. My only concern with a book like this is that I'll mix up what's fiction and what's true. The astronomy lesson I've quoted is a bit oversimplified, but apparently close.

The Man Who Knew Infinity: A Life of the Genius Ramanujan, by Robert Kanigel, would be unbelievable if it were fiction or even slightly fictionalized. A friend of mine, who works with gifted kids, describes their learning style as sitting in the eye of a hurricane and grabbing at the ideas whirling by. As I read about Ramanujan's mathematical discoveries, I keep coming back to that image. Other mathematicians who worked with him were astounded by his process. Bruce Berndt noted that, although Ramanujan's proofs were often full of holes, his results were almost always correct, and suggested, "We might allow our thoughts to occasionally escape from the chains of rigor, and, in their freedom, to discover new pathways through the forest." (page 183)

Ramanujan grew up in South India and attended school sporadically. (In his younger years, he preferred learning on his own. Later, he couldn't deal with exams in subjects outside mathematics, and was kicked out of university.) It took him years of working as a clerk to support himself before he managed to catch the attention of a famous mathematician in England, G.H. Hardy, whose interest in him suddenly changed his life. He went from just scraping by with a job he had little interest in, to a paid position as a research student in mathematics at Presidency College in Madras, India. A year later he would sail to England to begin with Hardy the work of making his mathematical results comprehensible to others.

I'm only halfway through, but have learned much already about India, mathematics at Cambridge in the late 1800's, and the history of mathematics. Kanigel does a good job of giving us enough background so that we have some chance of understanding different cultures and different times. (At times, his own bias shows, but subtly.) His description of Hardy's writing (readable, clear, cogent, almost suspenseful) makes me want to go to my local math library and borrow his 1908 Course in Pure Mathematics.

One of the delights for me is the sweet trivia I'm picking up. Here are two bits I enjoyed.
• When young, Ramanujan played Goats and Tigers, a traditional game in India in which:
Three "tigers" sought to kill fifteen "goats" by jumping them, as in checkers, while the goats tried to encircle the tigers, immobilizing them. (page 18)

• It is so hot traveling through the Red Sea that cabins on the east side of the boat, which can cool down away from the heat of the afternoon sun, are quite a bit nicer than those on the west side. Hence the acronym POSH for Port Outward, Starboard Homeward (page 199).

I've bought both these books to give to my young friend Artemis. (If you prefer giving games as gifts, I highly recommend Blink (under \$10), Set (under \$15), and Blokus.) I'm always searching for ways to enjoy the holiday spirit and still consume less. Used books are part of my solution to that conundrum. And I like getting them from Better World Books because of their interest in global literacy and taking care that old books don't end up in landfills.