Reading a diary is such a verboten act! But reading Sophie's Diary should not be. Dora Musielak has given us a delightful book of imaginings of mathematician Sophie Germain’s mind during the late 18th century. As we’re told in the author’s note, she was inspired to write this book because there is no record of how Germain managed to learn enough mathematics to make the substantial contribution to Fermat's Last Theorem that she did.
Learning mathematics is, for most of us, hard work. But learning mathematics is not something we have to do alone. Nor is it something that society views as improper. (Perhaps odd, but not improper!). For Germain, a young girl during the French Revolution, however, education of any academic sort was considered inappropriate. Young ladies of her wealthy social class learned to sew and play piano, and those less well-off learned to clean houses. Women certainly didn't learn mathematics!
Musielak’s book is written entirely in diary form, beginning when Sophie is thirteen. This coincides with the French Revolution, and the author takes great effort to intertwine historical events. The inclusion of history enhances the book substantially. The author does a nice job of interspersing the history with the mathematics, and the interplay makes the novel more believable as a diary and helps keep the reader’s attention.
Mathematically, the book begins with definitions of rational, irrational and prime, and musings on how to solve linear and quadratic equations. Included along the way are proofs of the irrationality of the square root of 2 and the infinitude of primes, common enough topics in more popular books. Musielak goes beyond this, however, and discusses topics such as transcendental numbers, Mersenne primes, and infinite series. By the end of the novel, she is writing of differential and integral calculus. She does a nice job of spiraling the topic of prime numbers, returning throughout the book at more and more depth as Sophie’s mathematical maturity increases.
The ideal reader for this book is a young girl looking to be enticed by mathematics (or whom one is looking to entice). The book is written with many easy stopping points. It’s a perfect format for introducing an idea or stating a question and letting the reader stop to ponder it for herself. But be advised: the author does intentionally include some inaccurate statements. This will keep readers on their toes, and either help the budding mathematician develop some skepticism or promote a bit of frustration. It certainly reflects a small piece of learning mathematics with little guidance, as Sophie did.
And as to the broader question of how a woman in this historical time period could have learned mathematics without any formal teacher, Musielak does present enough figures sympathetic to Sophie’s passion and indeed enough zeal on Sophie’s part to be realistic. The author also manages to instill a measure of gratitude for Germain’s contributions to the landscape of mathematics today.
See also our review of the first edition.
Michele Intermont is an associate professor of mathematics at Kalamazoo College in Kalamazoo, MI.