Hooray for (Math) History

Photo by Benimoto.

John Napier foiled a thief with the aid of logic and a black rooster. For this and other acts of creative problem solving, his servants and neighbors suspected him of witchcraft.

What does this have to do with mathematics?

Math was Napier’s favorite hobby. He invented logarithms to help people handle large numbers easily, and he even created a calculator out of a chessboard. [See how it works: addition, subtraction, multiplication.]

More Stories from Math History

Isaac Newton caused a UFO scare by flying a kite that carried a lantern. As a boy, Newton was a poor student who became a scholar only to show up the class bully.

Maria Agnesi solved math problems while sleepwalking. When she got stumped, she left the problem on her desk and went to bed. The next morning, she found the correct solution neatly written on her paper.

After teaching calculus to her younger brothers, Agnesi wrote what became Europe’s most popular calculus textbook for the next 50 years. But there was something she loved more than math — she longed to become a nun, and she devoted much of her life to helping the poor and homeless.

Sofia (Sonya) Kovalevskaya became intrigued with math from reading her bedroom wall, papered with old calculus lecture notes. To escape Russia, where women were not allowed to study mathematics, she arranged a marriage of convenience. When her husband died, she struggled on as a single mother. Kovalevskaya won a prestigious prize for original mathematical research — and her paper was so brilliant that the judges increased the prize to nearly double what they usually awarded.

The Key to Understanding

The story of mathematics is the story of interesting people. They faced the normal challenges of daily life as well as the creative challenges of mathematical imagination. For some, calculation and problem solving seemed as natural as breathing. Others worked for years in fits and starts before reaching a solution. Some had long and happy lives. Others died tragically young.

What a shame it is that our children see only the dry remains of these people’s passion. Worksheet exercises are the bare, abstract skeletons of what were once living puzzles.

As Victorian-era math professor James Glaisher said, “I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.”

Math and history — what can they possibly have in common?

After all, history is all about kings and wars, while math is numbers and rules. Isn’t it?

“Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals — the flotsam and jetsam of historical currents,” according to popular math writer Martin Gardner. “The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.”

It does not have to be that way for our children. By teaching math history, we can help our students build a mental picture of the ebb and flow of ideas through the centuries. They will see how men and women wrestled with concepts, made mistakes, argued with each other, and gradually developed the knowledge that today we take for granted.

“I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would be claiming too much,” wrote Alfred North Whitehead, a pioneer of mathematical philosophy. “But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming… and a little mad.”

A “Living Books” Approach

Most homeschool teachers, whatever our curriculum or schooling approach, understand the importance of teaching with “real” books. We read aloud biographies, historical fiction, or the classics of literature. We scour library shelves for the most creative presentations of scientific topics that interest our children. We encourage our high school students to go back to the original documents whenever possible.

And we teach math with a textbook.

One reason for this imbalance is that most of us never learned math history ourselves. We may not even be aware that math has a history. Our teachers made it seem like something handed down from on high, to be accepted and memorized — and never to be challenged.

Fortunately, when we decide to embark on a tour of math history, we won’t have to go it alone. Several talented and knowledgeable guides are available. Some of them may be sitting on the shelf at your local library right now, just waiting to lead you along the way…

Math History in Pictures

You can begin exploring the excitement of mathematics with your children through picture books. What’s Your Angle, Pythagoras? offers a fanciful look at the childhood of that famous mathematician. The Librarian Who Measured the Earth tells how Eratosthenes calculated the circumference of the earth using sunlight and shadows. Dear Benjamin Banneker skips forward in history to examine the life of a self-taught African-American astronomer and mathematician.

For beginning readers: A Fly on the Ceiling will make children laugh while they learn about René Descartes, the father of analytic geometry. Ben Franklin and the Magic Squares tells a lively story about one of old Ben’s favorite pastimes.

Treat your older children (and yourself) to a couple of our family favorites. Archimedes and the Door of Science describes the life and discoveries of one of the greatest mathematicians who ever lived. Carry On, Mr. Bowditch follows the inspiring life of an 18th-century American hero whose mathematical studies saved the lives of countless sailors.

Edited to add: The Wonderful World of Mathematics will give your children a great overview of math in many cultures from Ancient Egypt to the Industrial Revolution. It is out of print, but used copies are available, or you may be able to get it through your library. [Thanks to Brian Foley for reminding me of this book in the comments below.]

Meet the Men (and Women) Who Made Math History

Mathematicians Are People, Too [and Volume 2] features short, fictionalized vignettes for teachers to read aloud to elementary or middle school students. The authors have also written a three-volume reference series called Historical Connections in Mathematics: Resources for Using History of Mathematics in the Classroom [Volumes II and III], which offers basic facts and anecdotes about each mathematician, without fictional elaboration, and includes related worksheets.

Older students (and adults) will enjoy Famous Problems and Their Mathematicians. Another combination of anecdotes and activities, the book touches on many ideas that have challenged mathematicians for centuries.

If you want more complete biographies, start with Of Men and Numbers: The Story of the Great Mathematicians. For junior high or older students, try Men of Mathematics, a classic of math history that has been called over-romanticized, but I have not heard of anyone who didn’t enjoy it.

For balance, you may want to sample Women in Mathematics or Math Equals.

And those are just a few of the books available. Indeed, there is a lot more to the history of mathematics than most people ever suspect.

Edited to add: The World of Mathematics looks like a wonderful resource, and I can’t wait to get it from my library. Editor James Newman has collected four volumes of articles by eminent mathematicians and other thinkers “from A’hmose the Scribe to Albert Einstein, presented with commentaries and notes.” [Thanks to G Johnson for recommending this book in the comments below.]

And Here Are Some of My All-Time Favorites

William Dunham writes for the general adult audience, but high school students will find his books pleasant reading. The Mathematical Universe offers an A-to-Z smorgasbord of math topics and people. Journey Through Genius follows the development of several discoveries by the great masters of mathematics.

Also for older readers, Keith Devlin provides insight into historical and modern math for a general audience in Mathematics: The Science of Patterns. This book covers a wide range of topics and gives readers an idea of what modern mathematicians do for a living.

Coming Soon to “Let’s Play Math!” Blog

The Internet contains such a wealth of math history resources that they require a post of their own. I plan to work on that for next week [Now posted here.] — and will, I think, be adding a math history section to my resources page as well.

Finally, my math newsletter always used to include historical tidbits and quotations. I have been republishing the Alexandria Jones stories, but I’ve fallen behind in the history department. Over the summer, I hope to catch up on my backlog.

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This post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, now available at your favorite online book dealer.