This article appeared in the Fall 2016-Spring 2017 Bryn Mawr Math Alumnae Newsletter.
Tell us a little bit about yourself. How did you get connected to Bryn Mawr?
My permanent job was at Muhlenberg College in Allentown, Pa. I taught my last class there three years ago. My wife, Penny, and I moved to Bryn Mawr when we retired. I should note that Penny was also a mathematics professor at Muhlenberg. The Bryn Mawr Math Department made us “research associates," so we have had an affiliation with the College for a while.
Since retiring, I have had opportunities to teach courses on the history of mathematics at some great schools: Harvard, Princeton, Cornell, and Penn. Next on the docket is Bryn Mawr. In the spring semester of 2017, I'll be teaching a history of math class here. Penny will be teaching here as well, offering a course called “Codes and Ciphers." We are looking forward to meeting the students and becoming a more significant part of the Bryn Mawr family.
Tell me more about the course you'll be teaching next semester.
It is a mathematics class, but my math is the “old stuff." For instance, we will examine Euclid's Elements to see how he started with a few definitions and postulates, built a tower of ever more sophisticated propositions, and finished Book I with brilliant proofs of the Pythagorean theorem and its converse. It's quite an amazing logical development. And remember, this was done in 300 B.C.E. Besides Euclid, we'll look at results from Archimedes, Newton, Euler, Cantor, and others. The course will thus sample some of the great landmarks of mathematics.
How did you get interested in math history?
When I was your age as an undergrad at the University of Pittsburgh, I was torn between mathematics and history. I chose the former as my major and then went on to Ohio State and got a Ph.D. in mathematics. But I never abandoned my love of history. In particular, I wanted to know how mathematics got started, where it came from, and what it looked like two hundred—or two thousand—years ago.
What was the first article you wrote?
It was called “The Bernoullis and the Harmonic Series." In 1689, the brothers Jacob and Johann Bernoulli each devised a proof that the harmonic series diverges. Their arguments are not what people see in modern textbooks. I went back to look at their wonderful old results (written in Latin!) and then wrote an account of how they did it. Both of these proofs, by the way, will be in my course when we get to the Bernoullis.
What is the process like when you are writing a math history book?
Well, first you must have an idea. After the idea has brewed in your mind, you pitch it to the publisher. If the publisher likes it, you are given a contract, and then away you go. For the four books I've done, the writing took the better part of a year, from first word to finished manuscript. At that point, there is a sense of being done. The surprise is that, with the manuscript submitted, you are really only half done. There is so much more to do: get editorial feedback, make revisions, prepare an index, get permissions for photographs, choose a title, consider cover designs, check and recheck the galleys, etc. I'd describe this ordeal as the closest I've ever come to having a baby—except instead of being “with child" I was “with book." A very large part of one's life is consumed by the process. It's a very rewarding experience, though.
The first book I wrote was Journey Through Genius: The Great Theorems of Mathematics (Wiley, 1990). My course at Bryn Mawr will be largely based on that. It covers landmarks from thousands of years of math history, going from Hippocrates of Chios in 440 B.C.E. all the way to Georg Cantor at the end of the 19th century.
Who is the most interesting mathematician you've studied?
I would definitely say Leonhard Euler. He's my favorite. For one thing, Euler was off the charts in terms of the quantity of work; he was history's most prolific mathematician. But he was also off the charts in terms of the quality of his work. He made significant contributions to number theory, analysis, discrete math, geometry, applied math, and the list goes on. Euler was the dominant mathematician in the 18th century. Whereas nowadays mathematicians are specialists, it's been said that Euler's specialty seemed to be omniscience.
One other thing: for much of his life he was half-blind, and for some of his life he was totally blind. Yet this never slowed him down. As a result, Euler is, for me, the most inspirational figure in the history of mathematics.
If you could interview anyone, dead or alive, who would it be?
Euler! He was brilliant and by all reports a nice person. Some of the characters from math history would have been tougher dinner companions, though. For example, Newton was not the sweetest guy in the room. He was mean-spirited, jealous of Euler's reputation, slow to praise, and easily offended. Of course, Newton might well have been the smartest person who ever lived, but talent can come in strange packages.
Any other interesting facts about the personalities of some of the mathematicians you've studied?
Well, Archimedes was famously absent-minded. There's the “Eureka" story, where he jumped out of his bath in the thrill of discovery and ran through the streets shouting joyously...but forgot to put on his clothes. Likewise, Archimedes was famous for forgetting to eat or bathe or do other routine tasks. I'm sure you're shocked that a mathematician could be absentminded.
Have you heard the story of his death? Archimedes was in his hometown, Syracuse in Sicily, at work on a theorem as the invading Romans broke through the fortifications and rampaged across the city. A Roman soldier came upon Archimedes and tried to take him prisoner, but Archimedes refused to go until he had completed the proof he was working on. The soldier, furious, killed him on the spot. Ever since, it has been regarded as the ultimate mathematical death!
What are some interesting things you can tell me about Bryn Mawr mathematicians?
Charlotte Angas Scott was the first math professor at Bryn Mawr when the College opened in 1885. Scott was the first woman to get a Ph.D. in mathematics in Great Britain. She was recruited to come to the New World and spent her career here, and she certainly set the bar high. Anna Pell Wheeler, who was hired by Scott, was another distinguished mathematician at Bryn Mawr. Wheeler was a charter member of the American Mathematical Society (AMS), which was largely a male bastion at the time. She was the first woman to give an invited address to the AMS.
I should mention another: Emmy Noether, one of the great mathematicians of the 20th century. She mainly spent her career in Germany, where she came to be called the “Mother of Modern Algebra." But, because she was Jewish, she had to flee when Hitler came to power, and she ended up at Bryn Mawr. Unfortunately, Noether was here less than two years before her unexpected death. Her ashes are buried in the Cloisters of Old Library. The Mother of Modern Algebra thus lies forever on this campus. So there is plenty of math history at Bryn Mawr, and I'd like to think that that history is still being made.