Math in the Lives of Two English Professors
By Dr. Eugene Maier
They had much in common. Both were born in the 1860's and both died in the 1940's. Both attended Yale University as undergraduates and both, after receiving Ph. D. degrees in literature, taught at Yale. They became full professors within a year of one another and remained colleagues until their retirements. Both wrote autobiographies. Even their names were alliterative. But they differed vastly in one respect. William Lyon Phelps abhorred mathematics. Wilbur Lucius Cross relished it.
"Mathematics," Phelps wrote in recounting his school experiences, "were the curse of my life at school and college, and had more to do with my unhappiness than any other one thing, and I bitterly regret the hours, days, weeks, months and years that I was forced to spend on this wholly unprofitable study." He promises to return to this subject later in his autobiography with "more venom." And he does.
While describing his college days at Yale, Phelps digresses to vent his rage at all things mathematical: "…for those who have no gift and no inclination, mathematics are worse than useless—they are injurious. They cast a blight on my childhood, youth, and adolescence. I was as incompetent to deal with them as a child to lift a safe. I studied mathematics because I was forced to do so…. After 'long division' nearly every hour spent on the subject was worse than wasted. The time would have been more profitably spent in manual labor, in athletics, or in sleep. These studies were a brake on my intellectual advances; a continuous discouragement and obstacle, the harder I worked, the less result I obtained. I bitterly regret the hours and days and weeks and months and years which might have been profitably employed on studies that would have stimulated my mind instead of stupefying it."
It's not only his own circumstances he deplores, but the tragic fate of "hundreds who were deprived of the advantage and privilege of a college education because of their inability to obtain a passing mark in mathematics. They were sacrificed year after year to this Moloch [an ancient deity worshiped by the sacrifice of children]."
Cross, on the other hand, found arithmetic easy and prided himself on his ability to make mental calculations. In college, he recalls, " I was almost equally interested in pure and applied mathematics. Euclid…fascinated me, not because it added anything new to my knowledge of geometry, but by the art portrayed by the old Greek mathematician in proving by a strict deductive method the truth of propositions which any one might see were true at a glance. It was like traveling over a beautiful road to the foreseen end of one's journey. Likewise, in a course in analytical geometry…, we played with the curves of algebraic equations which fell into strange and wonderful patterns, rivaling anything I have ever seen in the most fantastic designs of wallpaper. Though drawn in the first instance to higher mathematics by a kind of artistic sense, I maintained a secondary interest in mathematics as the foundation of science. The more difficult the problem, the more intense was my desire to attempt its solution."
Though each is treated in the other's autobiography as an esteemed colleague, no mention is made of any discussion between them about their polar views of mathematics. If there were, I suspect it did nothing to change these views, which in all likelihood were deep-seated, emotionally-laden beliefs springing from their childhood experiences and the messages they received from the authorities in their lives.
Phelps says nothing of his mathematics teachers or classes. Whatever went on in school or at home, it's clear he heard some of the saws about mathematics that still hold sway today, e. g., some people simply do not have a mind for math—which he accepts and cites as the cause of his struggles with the subject—and, everyone should study mathematics because of its usefulness and the intellectual discipline it develops—with which he vehemently disagrees.
Cross offers some clues for the felicity he found in mathematics. He mentions a teacher to whom he owes "a lasting debt for the practice he gave me in mental arithmetic" and he cites a teacher in the college preparatory course he took in high school that "was one of the best teachers I have ever seen in action. He knew well how to keep his students steadily at work. And yet he was not a drillmaster. Rather, he assisted his students in laying good foundations in mathematics…."
Whatever the case may be, Phelps emerged from his schooldays seeing math as drudgery, entailing long hours of burdensome work for very little return and no satisfaction. While Cross emerged from his seeing math as an aesthetically pleasing and absorbing subject to which he willingly gave his time.
So what made the difference? According to Phelps—and Cross might have agreed if they had ever discussed the matter—it was their nature: some people are endowed with a "math mind" and some aren't; Cross was; Phelps wasn't. But I think not.
Rather I think it more likely that Cross was fortunate enough to have had teachers who, rather than drillmasters, were educators. They connected to the nascent, naturally curious, mathematician within Cross and nurtured it. Consequently, for Cross, math became a natural and intriguing subject which he willingly encountered.
As for Phelps, I suspect he was victimized by a mythology that still surrounds the teaching of mathematics: Math is a collection of procedures entrusted to authorities that pass them on to students regardless of their appropriateness or their significance to the learner and his inherent mathematical knowledge. Furthermore, if the student doesn't acquire mastery of these, despite prodigious effort, it's because the student doesn't have a math mind and not the fault of the instruction to which they were subjected. And further, the failure to master these procedures has dire consequences, since the mastery of them is critical for success in all but the most menial tasks, as well as being a measure of one's capacity for analytic thought. One can understand Phelps' anger when he came to realize he had been forced to struggle for years to master something that made no sense to him, only to find out in the end, the misery he experienced in doing so had been in vain. Math played no role in the considerable success and satisfaction he experienced in his profession.
The Cross/Phelp story has intrigued me ever since I stumbled upon it leafing though autobiographies. First, I find it interesting that a couple of close associates with so much in common could have such a divergent outlook on mathematics. Secondly, if I hadn't known it's a century-old story, I might of thought it took place yesterday, so familiar is the theme. Mathematics still catches the fancy of a few and repels a lot of others. And I continue to believe its neither in the nature of either human beings or mathematics that this is inevitable. I cling to the belief that if math were taught in ways appropriate for human beings, there would be lots more Crosses in this world and the Phelps would become all but extinct. Maybe next century.
A postlude : Cross gravitated into administration at Yale, becoming Dean of the Graduate School in 1916 and Provost in 1922. He retired from Yale in 1930 and shortly thereafter was elected governor of Connecticut, an office he held for four two-year terms. Phelps retired from his professorship at Yale in 1933. A popular teacher and prolific author, he received a number of honorary doctorates, including those from Brown, Colgate, Syracuse, Rollins, and Yale. The William Lyon Phelps Foundation, headquartered in Huron City, Michigan, where Phelps maintained a summer home, is dedicated to his "writing, values, life and times".