From an early age I’ve been fascinated with mathematics. Unfortunately, my biggest desire, which was to understand the subject of calculus, never translated into a grade above C-. I would spend the entire semester waiting for the limit to reach 0 or infinity or whatever it was approaching. It didn’t when I took calculus in High School. It didn’t in college either.
I’m thinking about this again, because yesterday I took a walk with a friend who, after teaching a college course for 5 years as an adjunct, was about to give it up. She said she didn’t feel qualified to teach and most of the students didn’t like the syllabus anyway. We agreed that though men and women may share the same insecurities, women are more likely to express them.
My mother studied math in college, which she couldn’t complete because she supported my dad getting a college degree. Growing up, (I’m 56 as I write this) almost all of my math teachers were male. All the big names in math were men, Euclid, Euler, Newton, etc.
Unfortunately, I formed the impression that real mathematicians were men and that the women who taught math had an odd facility with the subject, but no real insight. I say that partly because my mom couldn’t explain it to me either (sorry Mom!).
Before I go on, I’m pointing out this perception of women as second-class citizens of the mathematics world, to make a point about the different contributions of insiders (men) and outsiders (women). You may believe this is a gender issue, but not all of it. Like all good mathematicians, male or female, I want to reduce the problem down to its simplest form.
After college, in the late 80s, I took a job on Wall Street and began reading economics, much of it written in the mathematical language of statistics. Statistics, like calculus, was another obscure world in which I longed to unlock its secrets. Rummaging through a used bookstore I came upon Mathematics Essential for Elementary Statistics, written in 1934. It was $1.50. I noticed that it was written by a woman, Helen M. Walker. The new books, written by men, were much more expensive, so I figured I’d get the best value for that dollar and fifty cents, even if it was written by a woman.
My expectations were as low as can be. Not only was she a nobody to me, the book was old, written long before people had electronic calculators. I probably figured I’d skim the book in the bathroom. I was also curious about how poorly mathematics was understood in the 1930s. Did I point out that my C-minuses didn’t seem to affect my overall arrogance? Now that might be a “male” thing !
Like most math books, it begins with a few tests to determine just how stupid you are. “If you have made the computations quickly and without error, go on at once to Chapter 2.” That wouldn’t be me. I went on skimming. I would read the text of each chapter, usually a few paragraphs long, then as much of the formulas as I could, until I got lost.
I knew I should have spent more time on the problems, but that wasn’t my personality. I need to understand why. Anyway, none of the men who taught math in my junior high school, high school, or college could ever cure me of my dullness. I went up to them all, and interrogated them with as many questions as I could think up. In that I was never shy.
Thirty years ago, in my mid 20s, I pretty much gave up on getting it.
Then on page 87, Ms. Walker, whose book was “written primarily for the adult who once had understood but through disuse had forgotten elementary algebra”, a book that was one step from the garbage truck (no recycling in those days), a woman who I later learned had died at the age of 91 in 1983, a few years before reading a paragraph, in Chapter 7: Algebraic Symbolism, blew my mind.
The change of subject from “The dog bit the boy” to “the boy was bitten by the dog” is similar to the change of subject in a formula, as for example … In each case, the two sentences state the same relationship, but with different emphasis.
In all my years I never got all that moving of symbols around. All the “multiply this side with that, divide that side with this” type of instruction. Of course, I had a general idea that it had to be done. But I just didn’t get why mathematicians didn’t just start with the formula they wanted. Why did they want to torture those of us bad at math?
Dr. Walker, let me call her Dr. Walker, did what no other mathematician could do, even though I asked them many times and read the famous books.
As I write this essay I am constantly moving words around, trying to get the sentence that best expresses my thought. In writing, I’m not expecting my final sentence to prove anything on its own. There is no way for one to test the truth of any statement. Therefore, there is no reason to learn complicated rules for moving words around. Good is good enough.
In math, as we all know, one has to prove a big truth through the connection of small truths. Moving the words (symbols) around to get the clearest connection is crucial to proving your point. This is obvious to mathematicians who love math, for math’s sake. It wasn’t totally clear to me because I didn’t have anything I wanted to argue, mathematically. Once I could relate the tricks of working through math problems to the tricks of writing effectively (another struggle of mine) I got it.
In short, Helen proved that math is a language, to me. Again, I had heard that math was a language countless times from my teachers! But none had put it so clearly, “the dog bit the boy” = “the boy was bitten by the dog”. None had proved it.
I matter not in the mathematics world. But here is a truth. In my ranking, it is Walker, Euclid, Newton, etc. Without Ms. Walker, I could only take it on authority, of other men mathematicians who taught me, that those mathematicians were great. Ms. Walker gave me the insight that unlocked mathematics. She reached out to me, from her outsider status as lowly educator, and proved the most important mathematical theorem in my life. She did what others couldn’t do, despite years and years of effort on their part and mine.
So back to my friend. She believes she isn’t qualified to teach. Who is? I later learned that Helen Walker became the first female President of the American Statistical Association in the late 1940s. But I didn’t know that when I was reading. When she wrote the book in the 1930s, she was an outsider, who toiled away on a refresher math book for adults.
Who knows whose life my friend might change? Who knows what she may accomplish if she continues to teach? Who knows what brilliant insight she may put in a book? Helen Walker didn’t, but she did.
Thanks to Thomas Donahue who found an online link to the book.