Years ago, when I was an undergraduate, specializing in mathematics and physics at the University of Toronto, my colleagues and I were filled with an inflated sense of our abilities and were inclined to dismiss anyone outside our realm as irrelevant. However, as time unfolded, life taught us lessons in humility. Two years ago, I reported one of these lessons in my book, Intelligence. An excerpt is given below.
Though we had convened just two days ago, our group decided to meet to prepare for the international Putnam Competition on Saturday. The William Lowell Putnam Mathematical Competition, founded in 1927 by Elizabeth Lowell Putnam in memory of her husband, is considered to be the most prestigious university-level mathematics examination in the world. Its difficulty is such that the median score is usually zero or one (out of 120) despite that fact that its competitors are mathematics specialists.
I had just come from a mathematics tutorial that ran late, and had to sprint across campus to make up time. When I reached the Arbor Room coffee shop, I could see that our group was already engaged in discussion.
“You’re all outta breath, Brendan; has the Putnam got you all excited?” asked Sean.
“Actually, it’s this week’s problem set that has me breathless,” I responded. “I wanted to check on an integration technique with one of the teaching assistants.”
“I don’t go to those help sessions,” interjected Eldon. “It’s faster to figure out the answers myself than to watch those TAs bumble through a series of false starts.”
“Ya, that’s the second one I’ve attended. The tutorial leaders are usually graduate students, but today I had a little old man who came up to me and asked in a very soft voice if he could be of help. He had been cleaning the blackboards, so I assumed he was one of the janitorial staff. I was about to tell him that I wanted assistance from someone who understood calculus. However, he seemed eager to help, so I told him that I needed to know how to integrate the function f(x) = xx, so that I could integrate the expression xx–1 + xx(log2x + log x). He smiled and picked up a piece of chalk. His chalk moved fluidly across the blackboard, as he substituted elogx for x, reminding me that the exponential and logarithmic functions are inverse, so their composition leaves x unchanged. Then he performed an integration by parts with the alacrity of a master chef composing ingredients for a pièce de résistance. At last he displayed the result, xx log x with an inaudible voilà and a joyful smile. Watching him sprint effortlessly through mathematical manipulations, told me he wasn’t a janitor.”
Everyone had been surprisingly quiet during my animated dissertation.“Do you know who you were talking to?” asked David, in a tone that suggested I was missing the obvious.
“No, but I know that he’s a mathematician.”
“That was H.S.M. Coxeter,” he said with bated breath.
“Who’s H.M.S. Coxeter?” I asked.
Everyone laughed, and then David said, “It’s H. S. M. Coxeter, not H. M. S. Coxeter; he’s not Her Majesty’s ship.” Everyone laughed again.
“Alright, so I’m outta the loop. Who is this guy?” I asked.
Gulping the last fragment of his donut, Sean came forth, “Only the most celebrated geometer in the world. This guy can actually visualize how four- and five-dimensional solids project onto three-dimensional space. Everyone in the international math community looks to him as the world’s preeminent geometer.”
“Wow, I sensed he was something special, but I had no idea…”
At this point Eldon, who had been merely observing, took a different tack. “Brendan, how could you not know about Coxeter? He’s considered a demigod by a lot of the mainstream mathematicians. Although synthetic geometry is somewhat passé, he’s still respected as the guru in this field.”
“Eldon, I enjoy being out of the loop. In the words of Groucho Marx, I don’t want to be a member of any club that will accept me as a member.” …
Indeed, Professor Coxeter, the man I had summarily dismissed as a being beneath our level, was a legend in the mathematics community. The next time I saw him, he was seated among a handful of people in the audience during my Ph.D. dissertation defence. When he raised his hand to ask a question, I feared that he had discovered an error in my thesis that would cause three years of intensive work to evaporate in a flash. Instead, he asked a couple of insightful questions. Then, after my presentation, he graciously said that he had learned something interesting from my work–I suspect that I didn’t teach him anything that he didn’t already know. Professor Coxeter was exceptional as a scholar and a human being, and on first encounter his powerful intelligence was disguised in the demeanor of a humble concierge.
