Unknown Quantity
John Derbyshire
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Buy *Unknown Quantity: A Real and Imaginary History of Algebra* by John Derbyshire online

Unknown Quantity: A Real and Imaginary History of Algebra
John Derbyshire
384 pages
May 2007
rated 4 of 5 possible stars

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What do Florence Nightingale, Victor Hugo, Socrates, Sir Isaac Newton Newton, William Shakespeare, Omar Khayyam, and Immanuel Kant have in common? They make up a part of the set of illustrious historical personages mentioned in Unknown Quantity: A Real and Imaginary History of Algebra by John Derbyshire. Even a person (such as myself) who has difficulty telling the difference between irreducible and resolvent equations will find Derbyshire’s book a fascinating look at the history of algebra and the often colorful people involved in its development.

Before there were numbers - at least, the Arabic numerals (really thought up by the Indians) we use today, there was algebra. Words were used instead of numbers and symbols to convey problems and equations. Derbyshire relates how, through time, people went from thinking “this plus this equals this” to “this plus what equals this?” I will admit that though I took Algebra I and II in high school, and one course in college called College Algebra, that I am far from being an algebra whiz. I got good enough grades, and thought I understood it fairly well, but much of the algebra in Unknown Quantity is way beyond me.

What did I do when this realization struck me? I skipped several parts of the book, because I didn’t understand them at first glance and didn’t especially care to, to be honest. But I still liked the book quite a bit, despite my algebraic incompetence, and I’m sure that anyone who gets into math would enjoy Unknown Quantity.

The reason I liked it, and that I believe many other people would like it who may have little interest in algebraic concepts, is that John Derbyshire, besides knowing his subject and having done a lot of research on the history of algebra, can actually make it interesting. It’s always seemed to me somewhat dull and impersonal, but I have wondered before about the origins of various algebraic ideas and who came up with them. Derbyshire’s book is an excellent resource for the layman and expert alike to learn more about algebra’s history.

Florence Nightingale is only mentioned in passing, in the chapter with the intriguing title “An Oblong Arrangement of Terms.” Besides being known as “the lady with the lamp,” she also had been a student of the English mathematician J.I. Sylvester, who defined a matrix as “an oblong relationship of terms.” Nightingale was, according to Derbyshire, herself “a very capable mathematician and statistician.”

I was reminded during the course of reading Unknown Quantity of the game “Six Degrees of Kevin Bacon,” where every celebrity can conceivably have something to do with Kevin Bacon. Besides Nightingale, for instance, there’s Omar Khayyam - I had known about him before reading Derbyshire’s highly enlightening book as the famous poet who wrote the Rubaiyat, not realizing that he also played a role in the history of algebra. He wrote a book on it, the translated title being “On the Demonstration of Problems in Completion and Reduction.” His main importance to algebra’s development is that “he opened the first serious assault on the cubic equation.”

The lives of many mathematicians are enthusiastically and vividly portrayed by Derbyshire, and we get a glimpse of the faces behind many of the concepts of algebra we’ve read about in school.. For example, there’s George Boole, whose “great achievement was the algebraization of logic into a branch of mathematics by the use of algebraic symbols.” He met an untimely death after having served for fifteen years as a professor of mathematics at Queen’s College, Cork, England, after he walked two miles home from the college in pouring rain “and caught a chill”:

His wife believed that a disease should be treated by methods resembling the cause. so she put George in bed and threw buckets of icy water over him. The result, as mathematicians say, followed.
If you have even a passing interest in mathematics in general or algebra in particular, or are a person who just enjoys reading about ideas, concepts, theories, events, and people who have made a major impact on history and the way we think about the world, you should, to paraphrase John Lennon, “Give Algebra a Chance” and read Unknown Quantity. Also, Derbyshire’s previous book on math, Prime Obsession, is one you’d likely enjoy. He is one of this era’s greatest popularizers of math, and his enthusiasm for the subject is infectious. Algebra, actually interesting? In the hands of John Derbyshire, the answer is a resounding “Yes!”

Originally published on Curled Up With A Good Book at www.curledup.com. © Douglas R. Cobb, 2007

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