I am very honored to receive the Van Doren award. It has special meaning for me, first, because it comes directly from the students, and second, because of the illustrious list of past winners. The more distant winners are legends; the more recent ones are colleagues for whom I have the greatest admiration. In addition to gratitude and pride, I feel a sense of obligation and responsibility. I hope I will be able to live up to the high standard and great tradition of this award.
There are many people I should thank, but to thank them individually would take up all my allotted time. I do want to thank the two pillars of undergraduate education in the Mathematics Department: Professor Hervé Jacquet and Professor Pat Gallagher. I also want to thank my wife Judy Moore and my two daughters Sophie and Jessie: there is nothing like seeing college through the eyes of a parent to change one's attitude about teaching. I thank David Koenig and Professor Dave Bayer for doing such a marvellous job of speaking on my behalf. Finally I want to thank the students I have taught in my twenty five years at Columbia.
I don't often have the opportunity to address this eclectic an audience, so I hope you will indulge me if I talk a few minutes about two of my favorite writers, Edward Gibbon and Richard Feynman.
You all know Edward Gibbon as the author of the Decline and Fall of the Roman Empire. Richard Feynman, on the other hand, is known to the scientists in the audience as one of the great physicists of the twentieth century. Others may know him as the scientist of the investigatory commission of the space shuttle Challenger disaster - the fellow who dunked the O-ring in the glass of ice water - or as the author of two entertaining volumes of autobiography, or perhaps as the subject of James Gleick's biography Genius.
I know Feynman best as the author of Lectures on Physics, ostensibly a three volume freshman and sophomore introduction to physics, which I bought many years ago, and which I reread from time to time. I bought the book thinking it was a textbook. In reality, it is much more than that. In the words of Alan Lightman in the New York Review of Books, it is a "triumph of human thought", deserving of "a place in the history of Western culture, along with Aristotle's collected works, Descartes's Principles of Philosophy and Newton's Principia." The course on which the book is based was given as a first and second year physics course at Caltech in the sixties, and it was not a success. According to Gleick, as the year went on, fewer and fewer freshman came to the lectures, "but at the same time, more and more faculty and graduate students started attending, so the room stayed full, and Feynman may never have known he was losing his intended audience." [This makes for a nice story, but it is a bit hard to believe since we know that Feynman was aware of how poorly the real students were doing on the exams. So surely he knew the enrollment.]
In the book's introduction, which I read for the first time a few years ago, Feynman himself says that the course was a failure. He does acknowledge that the course was a success for "one or two dozen students" who understood the material, were excited by it and in the process acquired a "first-rate background in physics. But then, " he continues, quoting Gibbon "the power of instruction is seldom of much efficacy except in those happy dispositions where it is almost superfluous."
This is a shocking statement, especially for educators. It says first that most students are uneducable; second that the most of the rest can learn on their own. It is clear that Feynman is mainly invoking the first statement, since he does admit that the course gave the gifted students a first-rate background in physics, showing that it had not been "almost superfluous".
Still, the quote bothered me. I could not believe that Gibbon had actually written it. A couple of weeks ago, when I found out that I would receive the Van Doren award, I decided to find the context of the quote to use in these remarks-- Feynman does not give a reference. It occurred to me that it might be from Gibbon's autobiography, which I had never read and has the advantage of being short. The autobiography contains a number of interesting remarks about education, but not what I was looking for. It made the quote seem even less likely, since Gibbon describes the fourteen months he spent at Oxford as "the most idle and unprofitable of my whole life", and blames this on poor teaching and the antiquated organization of the University. So apparently teaching does matter.
Having failed to find the quote in the Autobiography, I was left with the Decline and Fall. I did not think I could reread the whole thing in two weeks, no longer having the stamina of a Lit Hum or CC student, and having a few lectures to prepare in the meanwhile. Fortunately my colleague Peter Woit helped me locate a web site that had the full text of the Decline and Fall. I downloaded it, searched it electronically, and in a few seconds found the quote.
It occurs very early on in the Decline and Fall and refers to the emperor Commodus, whose reign (AD 180-192), in Gibbon's view, marks the beginning of the decline of Rome. Commodus's father, Marcus Aurelius, was the last and much admired emperor (and stoic philosopher) of the period "during which the condition of the human race was most happy and prosperous", in Gibbon's words.
As Gibbon says, "the monstrous vices of the son" - Commodus - "have cast a shade on the purity of the father's motives", because, " he sacrificed the happiness of millions to a fond partiality for a worthless boy" in making Commodus his successor. The vices of Commodus are described at length by Gibbon, and I refer you to chapter IV of the Decline and Fall for details. Gibbon goes on to say:
Nothing was neglected by the anxious father, and by the men of virtue and learning whom he summoned to his assistance, to expand the narrow mind of young Commodus, to correct his growing vices, and to render him worthy of the throne. But the power of instruction is seldom of much efficacy except in those happy dispositions where it is almost superfluous. The distasteful lesson of a grave philosopher was, in a moment, obliterated by the whisper of a profligate favorite; and Marcus himself blasted the fruits of this labored education, by admitting his son, at the age of fourteen or fifteen, to a full participation of the Imperial power.
So this is the context of the sentence lifted by Feynman.
I will now leave it to you to decide whether it is fair to apply Gibbon's aphorism to education in general, or just to one particular slow learner, the emperor Commodus.
Needless to say, I myself don't believe that it applies - for starters because it would put all of us out of business. It is especially important, it seems to me, not to believe this for mathematics. In the United States, more than anywhere else in the world, we tend, at a very young age, to characterize ourselves and each other as either "good in math" or "bad in math". Every year, as they advance through the educational system, students of mathematics fall by the wayside not because they are bad at math, but because of bad teaching, inadequate individual attention and -- so not to blame the teachers for everything -- lack of understanding, on the part of students and their parents, that mathematics is a cumulative topic where one cannot afford to fall behind. I try to do my part, at Columbia, to reduce this attrition.
Thank you for your attention, and thanks again for the award.