Once over lightly

John L. Kelley

John J. Kelley (1989), Once over lightly. In: A Century of Mathematics in America, Part 3, pp. 471–493. Edited by Peter Duren. American Mathematical Society. ISBN 0-8218-0136-8. https://www.ams.org/publicoutreach/math-history/hmath3-index

Reprinted with permission from the American Mathematical Society.

J.L. Kelley received his Ph.D. in 1940 from the University of Virginia, studying under G.T. Whyburn. He taught at Notre Dame, then served during the war as a mathematician at the Ballistic Research Laboratory, Aberdeen Proving Ground. Following an appointment at the University of Chicago, he moved to the University of California, Berkeley in 1947. In 1950 he refused to sign the loyalty oath imposed by the University Regents, was dismissed from his tenured position, and taught at Tulane and Kansas until the oath was declared unconstitutional. He then returned to Berkeley and later served two terms as chairman. His books include Exterior Ballistics (with E. J. McShane and F. V. Reno), General Topology, Linear Topological Space (with I. Namioka and others), and Measure and Integral (with T.P. Srinivasan). Concerned with problems of mathematical education, he wrote elementary texts and lectured on Continental Classroom (NBC-TV) in 1960. He retired in 1985.
Peter Duren to J. L. Kelley, 10/2/87, for the AMS Committee on History of Mathematics:

“... We invite you to write some kind of autobiographically oriented historical article for inclusion in a centennial volume. We rely on you to make an appropriate choice of topic.”

J. L. Kelley to Peter Duren, 10/28/87:

“I’m pleased and honored by your invitation to write an article for one of the Society’s centennial volumes ... I want to write about the mathematics that most interested me and about the changes in mathematics and mathematical education during my time. I also want to write about universities and about mathematics and politics in war and in peace, and about students.

... All of this is too much on too many topics, so I propose to try a sketchy autobiography, touching lightly on these matters and full of gossip and name dropping ...“

I am a member of a threatened species. For the first thirteen years of my life my family was not urban, nor suburban, but just country. We lived in small towns, the largest with fewer than 2500 inhabitants; the roads were unpaved, we had no radio and television hadn’t been invented. I was born in my family’s house (there was no hospital in town) and about the only hint of modernity at my birth was that I was an accident, the result of a contraceptive failure. But I was a genuine, twenty-four-carat country boy, a vanishing breed in these United States.

My schooling began in Meno, Oklahoma, which was then a village of a few hundred people, two churches, one general store, a blacksmith’s and a one-room school. There was no electricity and the town center was marked by a couple of hundred feet of boardwalk on one side of the road. I went to school at a very early age because my mother was the school teacher and there weren’t any babysitters. I remember the first day of school; I got spanked.

There were about thirty students in the school, spread over the first eight grades. Most of the time was devoted to oral recitation, reading aloud, spelling, and arithmetic drill, with various groups performing in turn. We were supposed to study or do written work while other groups were reciting, but listening wasn’t forbidden and we often learned from other recitations (simian curiosity is not a bad teacher). The first couple of years of arithmetic were almost entirely oral, quite independent of reading. We recited the “ands” and the “takeaways”, as in “seven and five is” and “eleven take away three is”, and we counted on our fingers. Eventually, we got so we could do elementary computations without moving our lips, but it was a strain.

The arithmetic I was taught by my mother during the two years in Meno, and thereafter by a half dozen different teachers in four or five other small towns, was mostly calculation. Compared with today’s programs: there was more oral work then, and less written; the textbooks then were unabashedly problem lists with a minimum of explanatory prose and they weren’t in color, but then and now not very many students read what prose there was; the textbooks then were much shorter. Then and now, most teachers assumed that boys were better at arithmetic, especially after the third or fourth grade; and the end result, then and now, of the first half dozen or so years of arithmetic classes was the ability to duplicate some of the simpler answers from a five-dollar hand calculator. Of course we didn’t have hand calculators so this seemed much more important than it does now.

Perhaps it’s worth recounting that the mathematics program I was taught in the first six or eight years differed from that taught my father. Somewhere about the seventh or eighth grade there used to be a course called “mental arithmetic”, which was problem solving without pencil and paper or, in my father’s time, without slate and crayon. He also studied “practical arithmetic” where they learned about liquid measure and bulk measure, liquid ounces and ounces avoirdupois, bushels and pecks, furlongs and fortnights, gallons and pints and gills, interest and discount, and other esoteric matters. Some of these subjects still appear in the late elementary math curriculum, but even though the French Revolution did not overrun England, its system of measurements is conquering the world.

But the mental arithmetic course has apparently vanished from our schools. I regret its demise. A modest competence in mental arithmetic and a fivedollar calculator would, I think, ensure arithmetic competence as measured by the usual standard tests, as well as saving an enormous amount of student and teacher time.

But to return to my own schooling. After arithmetic and a rather muddled study of measurement, I entered high school and an algebra class. The former experience was frightening; the latter devastating. I didn’t understand why letters at the beginning of the alphabet were called constants and those at the end were variables; it seemed odd to me that a variable could take on a value, or several different values if it wanted to; I didn’t know what a function was, and why a string of symbols should be called an identity some of the time and an equation, or a conditional equation, at other times; and disastrously, I decided that our teacher, who was inexperienced, did not understand these things either. This was quite unfair although it was comforting and the real difficulty was probably my own pattern of being literal-minded (or perhaps simple-minded) in times of insecurity. But the mathematics was abominably organized, and the quantifiers “for every” and “there exists”, weren’t mentioned, so no one without prior information or divine inspiration could tell an equation from an identity. At any rate, my teacher indicated by her grading that she agreed with my assessment of my understanding of the course.

The following year I took my last high school mathematics course, geometry. It was a traditional course, very near to Euclid; it talked about axioms and postulates, defined lines and points in utterly confusing ways. The woman who taught us had a chancy disposition and she had been known to throw erasers at inattentive students. It was the loveliest course, the most beautiful stuff that I’ve ever seen. I thought so then; I think so now.

One would suppose that I, having fallen in love with geometry, would immediately have pursued mathematics passionately, and one would be wrong. The mathematics course that, then and now, follows euclidean geometry is algebra again. In my junior year in high school I decided to be an artist (we had a sensational art teacher that year) and in my senior year I decided to be a physicist (I had a sensational physics teacher).

It is time to pause a bit, with me proudly graduating from high school, to explain what was going on with the rest of the world. We had moved to California in 1930 along with the rest of the “okies” and so my last high school year was in a downtown high school in Los Angeles. Times were hard. One-third of the men in LA County were out of work and no one counted how many women needed work. But women weren’t neglected. There was considerable rumbling about women taking jobs away from men that needed them and, for example, the state legislature in Colorado passed an act denying teaching jobs to married women (this was one of the reasons we emigrated from Colorado); but women had not yet advanced to the dignity of unemployment statistics.

We were poor and it was not a good time to be poor. One summer a couple of years later I worked with my father trucking oranges from the LA basin up to the central valley and peddling them, buying potatoes and fruit in the central valley and peddling it in LA. I remember the Los Angeles basin with stacks of oranges a hundred and fifty feet long with purple dye poured over them so people couldn’t steal them to eat or sell; and I remember the camp outside Shafter where hundreds and hundreds of “okie” families lived and everyone, including children of four, picked up potatoes and sacked them following the potato digging machine. There was food rotting, and people hungry, and my view of the glories of unrestrained capitalism became and remains a trifle jaundiced.

But I digress.

One of California’s truly great educational innovations was tuition-free junior colleges. I entered Los Angeles Junior College in 1931, at the bottom of the depression, faced only with a three-dollar student activity fee and a block-long line to see a dean for permission to pay the fee with four bits down and four bits a month. But the fee included admission to LAJC’s little theater productions, football games and many other goodies and my sister worked in the bookstore and got books for me, so I really had it made.

Besides four semesters of physics (I was still going to be the great physicist) I took of necessity Intermediate Algebra, College Algebra, Trigonometry, Analytic Geometry (even the words have archaic significance) and finally a year and a half of calculus. Calculus was almost as nice as geometry (analytic geometry wasn’t really geometry, since Descartes muddled over what Apollonius discovered). And experimental equipment displayed a distinct antipathy towards me. So I entered UCLA, well-trained by very good teachers at LAJC, wanting to be a mathematics major and wondering just how a mathematics major made a living.

As far as I could find out, there was very little market for mathematically trained people. Teaching, actuarial work, and a very few jobs at places like Bell Labs, seemed to be the size of it. I had no money so graduate school seemed unlikely, and high school teaching looked like the best bet. Consequently I undertook three courses in education in my first three semesters at UCLA in order to prepare for a secondary credential. The courses were pretty bad and besides, the grading was unfair, e.g., I wrote a term paper for Philosophy of Education and got a B on it; my friend Wes Hicks, whose handwriting was better than mine, copied the paper the next term and got a B+, and our friend Dick Gorman typed the paper the following term and got an A.

Of course teaching is a low prestige field in this country. The prestige of a field of study is apparently a direct function of the technical complexity of the surrounding society. Engineering, and especially civil engineering, seems to be the prestige field at a relatively early developmental stage (e.g., pre-World War I U.S., pre-World War II India), to be overtaken by chemistry and chemical engineering as technology develops (World War I was a chemist’s war), followed in turn by electrical engineering and physics (World War II, radar and nuclear weapons). It has been said that the last war will be a mathematician’s war, so mathematics is now deadly and hence reasonably prestigious.

Fortunately for history, the precise time that mathematics acquired prestige among students at Berkeley is recorded. My student Eva Kallin explained to me that during her first couple of years at Berkeley she suppressed the fact she was a math major when talking to an interesting new man; later it was OK to be a math major, and a little later it was a very definite plus.

Back to UCLA. Los Angeles itself was then a gaggle of small towns held together by a water company, and UCLA was on a new campus, plopped down on the west side of town in the middle of an expensive real estate development. Too expensive for most of us students, so we drove, hitchhiked, car pooled or bussed from our homes to the school. There were about 4500 students and the math department was on the top floor of one wing of the chemistry building. It was definitely not a prestigious location. But mathematicians were usually viewed with an uneasy mixture of awe and contempt like, say, minor prophets. Our prophetic powers were used: math courses were prerequisites for courses in other fields, and math grades were often used to section physics classes into fast and slow groups. But mathematics was scorned as being irrelevant to the “real” world.

E. R. Hedrick, of Goursat-Hedrick Cours d’analyse, chaired the department — he later became chancellor. I enrolled in the last term of calculus, won the departmental prize for a calculus exam ($10), then blew the final on my calculus course and got a B (Wes Hicks said they should have offered a fifty-cent prize). I got shifted from my part-time job in a school parking lot to a part-time job in the math department office keeping time sheets for readers, recording grades, and whatever. I took all of the courses in geometry, mostly from P. H. Daus, admired Hedrick’s flamboyant lecturing style, conceived quite a fancy for my own mathematical ability, and quit taking education courses, thus abandoning a career as a high school teacher. (I could always go back and get a teaching credential if I had to.)

In midyear 1935–1936 I graduated and was given a teaching assistantship in the department at $55 a month, which was enough to live on, and so became one of the multitude feeding at the public trough at the taxpayers’ expense. Of course I could never have gone to college except at a public school — I could barely manage to cope with UCLA’s $27 per semester fee — so I like public schools, and the public trough is just fine. The fall of 1935 was notable for another event: I received my first college scholarship. It paid $30.

During my last year at UCLA I began to learn how to teach (I was terrified) and I was first exposed to the R. L. Moore method of instruction, which was fascinating (more on this method anon). W. M. Whyburn, who took his degree at Texas, introduced me to the Moore methodology in a real variable course, told me I had to leave to get a Ph.D. (I didn’t even realize that UCLA had no mathematics doctoral program), and arranged a teaching assistantship at the University of Virginia for me. In 1937 I was granted an M.A. and headed for Virginia.

I crossed the Mississippi river for the first time that September, carried in a brakeless old Packard 120 by a maniac who had advertised in an LA paper for riders going east. He dropped me off in Knoxville, I took the train to Charlottesville and enrolled in the university.

I didn’t know what to expect. I’d consulted the U. Va. catalogue about requirements and it stated that “The requirements for graduate degrees in mathematics are the province of the School of Mathematics”, which is not very informative although it’s a classy way to go. (Consider the number of deans and faculty committees that are bypassed! But wait until I get to Witold Hurewicz’ theory of deanology.)

As it turned out, I didn’t need to know what the requirements for a degree were. G. T. Whyburn, E. J. McShane, and G. A. Hedlund told me what to do and I did it. That first year I took Point Set Topology from Whyburn and Calculus of Variations in the Large from McShane. The C of V was horribly difficult for me in spite of valiant attempts by A. D. Wallace, George Scheigert, and B. J. Pettis to teach me enough algebraic topology to understand the lectures. But the topology course was geometry, and she was my friend. Here are some results that we proved in the course, to give the flavor of the material.

Suppose that X is a separable topological space whose topology has a countable base, and that each neighborhood of a point contains a closed neighborhood of the point (i.e., X is regular). Then X is normal, and in fact metrizable. If X is locally connected, then it is the continuous image of a closed interval (it is a Peano space) and it is itself arcwise connected. Moreover, if two distinct points of a Peano space are not separated by some cut point x, i.e., don’t lie in distinct components of X ∖ {x}, then the two points both lie on some simple closed curve.

The course on point set topology contained beautiful mathematics and it was done in a fascinating way. Whyburn stated theorems, drew pictures, gave examples, and we were left to find proofs. Each day he listened with enormous patience to our clumsy presentations of proofs of previously announced results. If no one of us had a proof of a result and we all gave up on it, he presented a proof himself. Otherwise he just listed more results, all chopped up into lemmas and propositions that we might be able to prove. It was often brutally difficult and it was always enormous fun. It gave us great self-confidence and a really deep understanding of a body of material.

By the end of the year I’d written a couple of papers and considered myself a mathematician. Indeed, mathematics has been my pleasure and my support since then, and it sure beats working for a living. Of course there is some drudgery. The last two years before my Ph.D. I taught thirteen hours a week (the same course at 8:30, 9:30, and 11:30 — Whyburn didn’t believe in having his students do too many different preps because it took too much of their time). But I had an assistant, Truman Botts (later the Director of the Conference Board of Mathematical Sciences), who tried to teach me to fence and, pounding out the Revolutionary Etude on a beat-up old piano in the gym, explained to me that composing was certainly a better idea then returning from France to Poland to fight.

My self-satisfaction after the first year at Virginia knew no bounds, and so it was probably just as well that during my second year I was taken down a notch. I tried to solve a problem of K. Menger: is it possible to construct a metric for a Peano continuum X so that X is (metrically) convex? I spent months on the problem, couldn’t do it, and was abashed when both Ed Moise and R. H. Bing, independently, established the conjecture.

Before leaving the lovely lawns of Mr. Jefferson’s University let me mention two more notable facts, the first about the mathematics that was being done in this period, and the second about the university students’ honor system and why it worked. First, during my second year there I was taught J. Alexander’s duality theorem about the relation of the homology of a nice subset of n space and that of its complement. It was a major turn-on for me, and so I read Pontrjagin’s beautiful proof of the duality theorem for compact subsets of n space, but then I didn’t know how the necessary duality theorem for locally compact groups was proved so I had to read that, and to straighten this out, I went through Emma Lehmer’s translation of Pontrjagin’s book on topological groups, and so (it was a year or two after my Ph.D. by now) I wandered into functional analysis.

At the University of Virginia the honor system worked. Partly this was because it was a university of reasonable size (four or five thousand), rather than a megaversity, but most importantly because the faculty and administration stayed out of it. The only possible penalties, if guilt was established, were resignation from the university or dismissal, and dismissal showed on one’s record. To the best of my judgement, this worked better and with fewer injustices than faculty or administration systems. I think the governing principle is that students are better at this sort of problem than professors.

Let me describe, with some nostalgia, what being a mathematician was like in the decade or so after 1938. First, there weren’t so many of us. About 100 Ph.D.s a year were granted except for the war years, and even the Christmas meeting of the Society drew only four or five hundred people. Society meetings were always held on college campuses, virtually all of the participants lived in the college dormitories and ate in the cafeteria, and almost everyone knew everyone else. Irving Kaplansky could say with only mild exaggeration that he knew every mathematician in the United States. It was a smaller world.

The mathematicians then were like mathematicians now, only more so. John Wehausen, an early editor of the Mathematical Reviews, once told me that mathematics was one of the psychologically hazardous professions. “Every mathematician, for most of his early life, is the brightest person he knows, and it’s a great shock when he finds there are people that can do easily things that are very hard for him” according to John. I think that this is true, and that within every mathematician, more or less suppressed or laughed at, is an arrogant little know-it-all, and simultaneously a stricken child who has been found wanting. Johnny von Neumann has said that he will be forgotten while Kurt Gödel is remembered with Pythagoras, but the rest of us viewed Johnny with awe.

Arrogance in good graduate students is much admired though one usually hopes that they will grow out of it. I remember Murphy Goldberger’s description of a physics student: “He understands everything, he knows everything, he’s incredibly quick, he can barely contain his contempt for the rest of us.” Students in theoretical physics are much like math students, although Feynman insisted that the difference between math and physics is the difference between masturbation and sexual intercourse.

Perhaps a few anecdotes about mathematicians will help characterize the breed. Paul Erdős was one of the characters. For many years Erdős wandered about the world in almost periodic fashion with a long list of mathematical problems in his head and the rest of his possessions in two suitcases. He must hold the record for writing the most joint papers with the most different authors. He had an elaborate code: “epsilons” were children and very young epsilons with that profound look knew all of mathematics, but couldn’t talk; “bosses” were wives, and “slaves” were husbands. He enjoyed being an eccentric, and was a charming but absent-minded house guest.

Witold Hurewicz, for a brief period, expounded a theory of “deanology”. It began like this: Let S be the set of frustrated scholars, let B be the set of frustrated businessmen, and let D be the set of deans. Axiom: D = S ∩ B. And so on. The fascinating part of the theory was the method of reproduction. Sons of deans are not deans, but potential deans marry deans’ daughters. He expounded this theory once at a rather formal dinner given by a rather pompous host, and his hostess said, “But I’m a dean’s daughter”, and that stopped the conversation. Afterward Witold, looking mischievously penitent, said to me, “But what could I do? It’s exactly what I meant.” Witold was a gentle, elfin man, incredibly insightful and inventive, and he wrote mathematics like poetry.

No list of eccentric mathematicians would be complete without Norbert Wiener. Many mathematicians like to show off, a sort of delayed “show and tell” syndrome, but Wiener really demanded attention. He was short, a bit plump, and had a neat pointed beard that he wore pointed up in the air. It was rumored, and it was quite possibly true, that he wore his bifocals upside down. He feared that his students called him “Wienie” (they called him Norbie). His standard ploy when attending a lecture was to walk in late, walk down to the front row, take out a magazine, read ostentatiously, then sleep ostentatiously, wake abruptly at the end of the lecture to ask a pointed question, or sometimes to make a little mini-lecture of his own. For awhile he had a game of asking others for a list of the ten finest American mathematicians. At one math meeting (Duke, sometime in 1938–1940) a number of people concocted a response. They would run briskly through a list of nine mathematicians, omitting Wiener’s name, and then look thoughtful and puzzled about the tenth until Wiener’s squirming was unbearable. It sounds cruel, but I suspect Wiener knew what was going on and enjoyed the attention.

But to return to the autobiographical business. In 1940 I wrote a thesis, Whyburn made me revise it, McShane made me revise it again, and Hedlund said he’d make me revise it except it was too late in the year. So it was accepted and then Sammy Eilenberg spent a couple of weeks revising and making me revise. This training, with a post-graduate bit from Paul Halmos a few years later, is how I learned to write mathematics.

On a rainy day in Charlottesville in June 1940, I was granted a Ph.D. degree. But this remarkable occurrence was overshadowed by the commencement address. Italy had just entered the War and Franklin Roosevelt said, “... The hand that held the dagger has plunged it into his neighbor’s back ...”. It seemed pretty clear that the war that had begun in Spain in 1937 would now engage us, and within a year and a half it did. So I’ll be getting on to the bit about how I won the war.

The Christmas meeting of the Society in 1941 was held in Chicago, and was titillated by the news that three aliens, two of them enemy aliens, had been caught taking pictures near a radar station on Long Island. They offered the unlikely story that they were on their way from Princeton to Chicago. Further details were soon available. It turned out that their names were Paul Erdős, S. Kakutani, and Arthur Stone. Oswald Veblen of the Institute for Advanced Study, also known by his irreverent young admirers as his Grey Eminence or the Great White Father, finally got them out of stony lonesome. Oswald Veblen, Jimmy Alexander, and Gilbert Ames Bliss were at the Ballistics Research Laboratory at Aberdeen Proving Ground in World War I, and they redid exterior ballistics following the methods of computational astronomy. In the second war Veblen acted as recruiting agent for mathematical types for Aberdeen. There was already a mathematics unit at Aberdeen under Franklin V. Reno, who was trained in astronomy. He had set up a system of cameras obscura to obtain ballistic data on bombs, and he devised the standard method for constructing bombing tables. He was meticulous; at the laboratory the smallest known unit of measurement was called the Reno. It was defined as the width of a milli-frog’s hair.

Veblen talked to Reno and asked if he needed help. Reno said yes, but he wanted someone he could boss around or else someone who would boss him around, and Veblen got Jimmy McShane to be the big boss. A little later McShane wanted me. I was teaching at Notre Dame; they didn’t want to let me go. Veblen sent his assistant, Gerhard Kalisch, who was an alien and couldn’t work at Aberdeen, to teach in my place, and I went to Aberdeen. Veblen had persuasive ways.

Our group at Aberdeen, known at various times as the math unit, the math section, and the theory section, set up new computational procedures for exterior ballistics and did troubleshooting on all sorts of projects. The construction of artillery firing tables had long since been turned over to the computing branch, as had the tables for level bombing a few years before. Theory section projects during the war included such exotica as: tables of Fresnel integrals, as well as of various statistical variables; reduction procedures to obtain aerodynamic constants from spark range (shadowgraph) data; ballistics for dive bombing; ballistics for the Draper-Davis lead computing gunsight; construction of ballistic theory and procedure for range firing and making tables for rocket air-to-ground firing; taxonomic work on known aerodynamic data for bomb shapes; measurement of aerodynamic constants for some bomb shapes; and emergency work on a variety of fouled-up ordnance and projects.

Let me try to sketch the path of a single continuing problem.

Suppose an arrow moving through the air is yawing; i.e., the axis of symmetry is at an angle to the velocity vector. Then there are forces of drag and lift and, if the yaw is small, one can measure them in dimensionless constants (or functions, if the velocity varies over much of a range) and these can be used to predict, after a fashion, the behavior of the projectile. But what if the arrow is spinning? Of course there are inertial effects, but are there nontrivial aerodynamic effects?

Here is an experiment devised by Bob Kent, head of interior ballistics at Aberdeen. He constructed a “bomb”, a wooden cylinder with a couple of lugs at the side and a weight in the front. When fired from a “smooth bore” shotgun (no spin) it wiggled its tail a bit and then flew like an arrow, stable as can be. When fired from a “rifled shotgun” so that it rotated, it started out well, then developed a flat spin and tumbled. This worked every damn time, and the most reasonable explanation is that the aerodynamic Magnus force and couple can cause instability.

On the other hand, the British had a high-accuracy bomb (I think it was called the Tall Boy) which they deliberately spun, to average out asymmetries, so not every spinning bomb is unstable. We (the theory section and Alex Charters of the spark range group) measured the aerodynamic coefficients for real bomb shapes in the twenty-foot wind tunnel af Wright Field (at night because 35,000 h.p. takes more power than the City of Dayton can spare during the daytime). Tare effects (effects of the suspension system) messed up results on the small standard practice bomb but the results for the general purpose bombs were consistent and useful. “Statically” stable bombs can be dynamically unstable, and increasing static stability can remedy matters.

A stability problem of just this sort came up very late in the war. After the Allied invasion of Europe a minor scandal erupted. Alongside the roads of Normandy a lot of American 2000-pound bombs were sprinkled; the fusing wasn’t designed for every possible landing position and reports said that the bombs went into flat spins. The problem wound up at Aberdeen.

Of course one could redesign the whole thing, but that’s very expensive and very slow and so a simpler fix seemed very important. A hydraulic engineer from Cal Tech, Bob Knox, suggested running water channel tests on an (interval × bomb body shadow) and try various tail patterns, all this on the basis of an analogy (with the wrong γ) between rotationally symmetric flow and two-dimensional flow. A couple of GI’s and I tried this in Bob’s lab at Cal Tech. (I ran into a friend, Hans Albert Einstein, there and introduced him to Bob, who turned out to be his colleague.) The experiments suggested adding to each flat plate of the tail a plate so the cross section was a line interval with a triangular form on the rear third of the plate (making the cross section a rough cusp, point forward). So we designed a fix, had it made, and it worked.

There was a little fuss at a conference later involving some high brass (civilian and military) about who deserved credit for this remarkable wing design and this flattered me. Bob Kent told me later that he’d looked through my notebooks and he thought that the design was a pretty wild guess, if it was based on that data. But a bit of Irish luck never hurts.

Jimmy McShane had a health problem and had to go back to Charlottesville, Reno’s health was not good, and so I ran the section for the last year or so. The astronomer Edwin (Red Shift) Hubble was my boss. He was a pleasant well-spoken man, still very much influenced by his Rhodes scholarship. He talked of “shedules” and “leftenants” and such and his irreverent underlings spoke behind his back of “that skit about the shedule” and so on. Hubble was rather reserved and we saw nothing of him outside of ofice hours, but we understood he read Horace with the commanding general. Bob Kent, who never entirely grew up, was known to remark, “Dr. Hubble, known to his intimates as Dr. Hubble, ...”, but in fact we all worked together very well.

The war ended for the theory section, not with a whimper, but a bang. The European war had dribbled out in daily rumors of new coups, new crises, and new German governments, so we were unprepared for the end. But for the Pacific War we were prepared. We’d hoarded ration tickets for liquor and the entire section, mathematicians, secretaries and computers (people who used desk calculators) had a historic party at Tony Morse’s house in Aberdeen, and within weeks we began to drift away, out of town.

I wanted to get back to mathematics, get the rust out of the tubes. For three years, except for some conversations with Herb Federer and Tony Morse about set theory and a bit with Chuck (C. B. , Jr.) Morrey on area, I’d only thought about useful (i.e., potentially murderous) mathematics. I asked Veblen for help and he helped. He arranged that my new boss, the University of Chicago, and the Institute for Advanced Study split my salary for a year and I went to Princeton.

At that time the Institute was mathematics heaven, the place all good mathematicians wanted to go, and it really was heavenly. It was the first time I’d had no responsibility save mathematics, and the fabled characters of my time drifted in and around the Princetitute. Veblen, Alexander, von Neumann, Weyl, Lefschetz, Eilenberg, Montgomery. The words make a litany.

The social life and the social knife at Princeton were a revelation to me. “The Veblens live a very simple life. I think it must be very expensive to live so simply”, said Dolly Schoenberg, married to Iso and daughter of Landau, who married the daughter of Ehrlich, whose wife was related in some fashion to one of the Minkowski brothers. (I’ve probably mixed up a lot of this — my memory isn’t too good.) “You know he’s a son of a bitch, but you have to like him because he’s so sincere about it,” said one anonymous friend of mine about another ditto.

Something I like to remember. My father-in-law was the physician for Hans Albert Einstein’s family in Greenville, S.C., and we knew Hans and his wife and made acquaintance with his aunt Mrs. Winteler, who took a liking to my young son. While Mrs. Winteler was visiting her brother (Hans Albert’s father) Albert Einstein in Princeton they invited my son, my wife and me to tea at his house on Mercer Street. I’d known Albert Einstein to speak to (the Institute wasn’t crowded that year) but this was the first time we’d actually had a conversation. He was gentle, he was thoughtful, he talked about mathematics and physics and me, and I remember his saying, “Your job is easier than mine. What you do only has to be correct, but what I do has to be both correct and right.” He was absolutely without pretension, without condescension, and he impressed the bloody hell out of me.

There was only one other famous person who, in person, so surpassed my expectations. The first professionally produced play I saw was Lillian Hellman’s “The Children’s Hour” and I was enormously impressed, and later I liked her plays, her other writing, and her politics. So in 1960, somewhat embarrassed with myself, I got my Tulane philosopher friend Jimmy Feibleman to take me to lunch with her. She was great. I think I’ve read everything she wrote, as well as some of the snide stuff that was written about her after.

But I digress, and so back to mathematics. In 1946–1947 there was a lovely seminar at Chicago. It started out with functions of positive type and carried on through works of M. H. Stone, Gelfand, Raikov, Shilov, Tannaka, and others. Seymour Sherman, Paul Halmos, Irving Kaplansky, Will Karush, Al Putnam, Marshall Stone sometimes, and I took part. In a certain sense I at last began to understand the role of linearity, and the wobbly path that led from Alexander’s duality theorem to the Fourier integral became clear.

The Chicago seminar had a decisive effect on the direction of my work. In Berkeley, in 1948–1949, I was booked to teach algebraic topology, and I asked if I could do topological algebra instead. I got an absent-minded approval, which is what I’d hoped. It was sort of a topics course, not yet approved for the catalogue, and neither algebraic topology nor topological algebra had ever been taught at Berkeley, and I doubt that my question was really understood.

But back to the real world for a little. The hot war was over and the cold war had begun. Our intelligence services imported and/or protected a most unattractive batch of German and Japanese war criminals on the grounds that we needed their expertise. Allen Dulles’ amateur spooks were legitimized as the CIA, and the domestic spook front also brightened up as a massive “security” program was put in place to harass the citizenry and provide program music for that thrilling melodrama, “China is getting lost, or the battle against monolithic, atheistic, godless communism”. In particular, a bill was passed that denied federal employment to members of the Communist Party and required federal employees to sign a statement as to whether they were or had been members of the party. All federal employees had to sign, at least if they wanted to remain federal employees. All of this seems pretty routine now, but it did take a little time for our gallant ally Russia to become the evil empire Russia.

At any rate all the employees of the Laboratory signed a statement that they weren’t and hadn’t been communists. Then, sometime in the years 1946–1948, McShane and Everett Pitcher and I were called before a Federal Grand Jury in New York and questioned about Frank Reno. It turned out that Frank had been a communist, that he had known Whittaker Chambers, and that Chambers had denounced him. There was also some talk about Reno giving documents to Chambers, but no charge was ever made. However, Frank had signed a statement saying he had never been a communist, and so his federal employment was over permanently.

Frank tried to get all sorts of jobs without much luck. Jimmy McShane and I both recommended him, explaining why he could not have a federal position, to a number of people including Abe Taub at his computing laboratory at the University of Illinois, the only computing lab in the country that was not on federal money. As a result Abe Taub was hauled before a loyalty board under threat of losing his own security clearance.

Reno was never again able to use his very considerable talents as a practical astronomer, statistician, and applied mathematician. The FBI kept potential employers informed as to his past and they pressured him to register as a foreign agent. On the basis of his signed denial of earlier membership in the Communist Party, he was charged with fraud (accepting his salary falsely) under an act that was passed because of Anaconda Copper misdeeds. He was convicted and sentenced to two years imprisonment and, with time off for good behavior, he served the sentence. When I visited him in Leavenworth sometime in 1952–1953 he said it wasn’t too bad, that one had to be careful of psychotics and never to settle a bet even though the inmates called him “doc” and appealed to him as an authority. He said most inmates were wild kids who’d driven stolen cars across state lines which made it a federal beef.

I saw Reno just once after that visit in Leavenworth. My family and I were car camping around Boulder, I picked up Frank in or near Denver, he camped with us for two or three days, and we talked a bit. He told of his mining engineering father; of violence in Leadville, not far from where we camped; of his graduate school days in the observatory at the University of Virginia. After the University of Virginia he got a job as a statistician in the agriculture department in Washington — he was probably a bearcat at civil service exams — just about at the bottom of the depression. He was recruited into the Communist Party (by Steve Nelson I think), was active in the Party and knew Whittaker Chambers. He told me that Chambers used to demand, cajole, and threaten in order to get money from him and other party members. Reno left the Party when he got the Aberdeen job, and he heard no more from Chambers.

I digress to recall that Frank did all of the ballistics for horizontal bombing, adopting the drag data of the Gâvre commission as a guess at the drag of bombs (a reasonably good guess), making the necessary ballistic tables, designing and supervising the construction of instrumentation for range bombing, and establishing procedures for making bombing tables. It was a first-class job and he was decorated for exceeding his authority in doing it. The pickle barrel into which our bombers could drop their bombs under ideal conditions, from 20,000 feet, had a radius (probable circular error) of about 140 feet, which was better than that attained by any other air force.

Frank was very much part of the last hundred years of American applied mathematics, and he and his family are very much a part of American history. His grandfather was the Major Reno who fought under Custer at the Little Big Horn and later became a general and had a fort named for himself. Frank told me in detail of Custer, of West Point and the battle of Bull Run, and of the Indian Wars; of Custer’s last battle and of Reno’s fight — 30% casualties in twenty minutes; of the Sioux, of the Dakotahs and the Hunkpapas and the other subtribes; of statesman-sachem Sitting Bull, of Crazy Horse and Gall and the other two war chiefs.

All of this was related in the high mountains, under the stars, before sleeping. The last night he explained, to ears unbelieving of such jury-rigged Rube Goldberg gimmickry, how the astronomical scale of distance was established.

The next day Frank rode with us on our journey for fifty or a hundred miles, reluctant to part. I did not see him again, and except for a few letters, that is all. I mourn him and the way the country treated him, and that only a poor man’s Horatio speaks for him.

I arrived in Berkeley in 1947, just in time to observe the death of Joe College. He was done in by the returning war veterans who entered the University on the G.I. Bill of Rights. It was too much to expect a new freshman with thirty missions over the Burma-China hump to stay off the senior bench, or to wear a freshman beanie, and hazing was definitely out of the question. So, in spite of occasional revivals of fraternity rituals, Joe College died; the University blossomed.

It is easy to describe the Berkeley math department of that period: very strong in analysis, statistics, set theory and the foundations of mathematics, and not strong in other areas. It was a harmonious group, although there was a bit of jealousy of the statisticians because they could get consulting money and were generally a little more prosperous than the rest of us (something like the computing science people today). But this was temporary; statistics emigrated to become a separate department sometime in 1949. There was also occasionally a little nervous hostility toward the work in foundations, accompanied by a shaky lack of confidence that we understood the foundations of our own field. This hostility has now pretty well vanished, and unfortunately the intimacy and convenience of a small department has also vanished.

There was one curious action in the early 1950s that distinguished our department amongst other departments. In late 1949 or early 1950 we agreed that if any of us were dismissed, for any reason whatsoever, then each of the others would contribute up to ten percent of his yearly salary to support the dismissed person or persons. This agreement was called “Mathfund” and there was a reason for its existence. There was a peculiarly virulent outbreak of anti-Communist fervor in Sacramento and one of the University vice-presidents had a brilliant idea: Let’s stop attacks on the University by getting the faculty and other employees to sign a loyalty oath denying membership in the Communist Party. Of course the state constitution already required an oath of office, a promise to support the constitution of the U.S. and of the state of California, and forbade any other oath or test, but that sort of detail didn’t bother our administrative executive types.

The faculty got upset. The Academic Senate had a great deal of power at that time, because it won an argument with the University president in the early 1920s and was not yet being choked by sheer numbers, excessive structure, and a statewide superstructure designed to suggest that all the University’s campuses are like Berkeley.

The Senate held interminable meetings, a group of “non-signers” emerged, the Korean War began and a good many of the non-signers breathed a sigh of relief and signed on, the scared Senate passed a resolution that membership in the Communist Party was inconsistent with membership in the University, and a “compromise” was arranged. The Senate’s Committee on Privilege and Tenure resigned, a new blue ribbon committee was appointed, and each non-signer had the privilege of appearing before the committee.

In the spring of 1950 the various non-signers appeared before the committee, and the committee brought in its report in April or May. The committee argued sturdily for all the non-signers except five, and these it “could not recommend for continued employment” although there was no evidence of membership in the CP. So much for tenure.

If memory serves, two of the five people thus unceremoniously dumped were women, Elizabeth Hungerland of the Philosophy Department and Margaret O’Hagan of Decorative Art. The three men nominated for firing were Nevitt Sanford, Harold Winkler, and me. Sanford was a professor of psychology, a psychiatrist and author, and later founded the Wright Institute. Hal Winkler was in the Political Science Department and was later the first president of Pacifica, the mother foundation for the public radio stations, KPFA, WPFW, WBAI, WPFW and KPFK. And I was associate professor of mathematics, John Kelley.

I hit the panic button and wrote Veblen, Whyburn, McShane, Lefschetz, and a couple of others. It was June, I had a wife and three children and just two months’ salary in sight. Then Bill Duren called me from Tulane, told me that S. T. Hu was going to the Institute for a couple of years, and in that courtly southern way he gravely said that he understood I might be free to accept an appointment. Jeez!

Later that summer the Regents rehired the five, gave everyone thirty days to sign and then fired all the non-signers. Hans Lewy, Pauline Sperry, and I were fired from math, Charles Stein and Paul Garabedian left in disgust, R. C. James left soon after, S. Kakutani refused to accept a position because of the treatment of his mathematical colleagues, another of our department went on a self-imposed exile for three years, and I heard that preliminary talks about bringing the Courant group to Berkeley ceased abruptly. Chandler Davis and Henry Helson declined to take positions at UCLA because of the oath. (I only learned that this past summer.) This was a fair amount of carnage in just one field, and it’s hard to say how much the oath damaged the University. Postscript: The next fall Monroe Deutsch, former Provost of the Berkeley campus, and the faculty group called “Friends of the Non-signers” (chaired by Milton Chernin, with Frank Newman, later a justice of the California Supreme Court, as treasurer) took political command of the Senate and sent the Committee on P and T back to do its homework again, and they did. But we were long gone and the Regents’ edict was unchanged. Quite a few of the non-signers returned to Berkeley three years later under some sort of amnesty but our complete legal vindication by the California Supreme Court waited until 1956.

A last word about our famous loyalty oath. The Regents’ problem with us non-signers wasn’t communism; it was insubordination. For example, in my case: at that time I did consulting work for Aberdeen Proving Ground, Redstone Arsenal, Sandia Corporation, and Los Alamos and was cleared for highly classified material. I see no way that the Berkeley administration and the Committee on P and T could have failed to know this; the problem with me was that I wouldn’t say that I wasn’t a communist.

But back to Tulane; it was lovely. Bill Duren, Don Wallace, B. J. Pettis, Paul Conrad, and Don Morrison were there, the graduate school was vigorous though not large, and the food was magnificent. Gumbo, oysters, shrimp, and crab; crayfish bisque! I drool to think of it.

I taught two courses; formally I was on half-time and the rest of my salary was covered by Mina Rees’ invention, an ONR grant. An unpleasant incident: a colonel wrote Bill and/or the ONR to complain that a known communist or at least an associate of a known communist was feeding at the Navy trough, but nothing came of it. It’s the sort of thing one expects of colonels. They’re always starting revolutions, or committing coups, or whatever; it’s part of their midlife crisis, the syndrome that we called “bucking for B. G.” at Aberdeen. If you are a colonel and haven’t taken the precaution of marrying a Senators’ daughter or finding a communist or otherwise displaying political acumen, you’re at the end of your line. That step from colonel to B. G. is the biggie.

There was a more upsetting occurrence. In 1951–1952 I was called to Albuquerque (or was it Los Alamos?) for a Loyalty Board Hearing. There were three charges: (1) I hadn’t signed the U. C. loyalty oath, (2) I continued to associate with a known communist, Frank Reno, and (3) I was careless in handling classified material and uncooperative with an FBI agent in Berkeley. Certainly (1) was true, (2) was true except that Reno wasn’t a communist and hadn’t been since I’d known him, and (3) contains a good bit of truth. I had some stuff from Aberdeen, some of it was marked “Restricted”, most of which I’d written myself, I had no private office and the stuff was kept in a couple of cartons in a non-private omce. I was also rude to an FBI agent. Later, under the Freedom of Information Act, I read his letter stating that since I was fired I would undoubtedly want to work again at Aberdeen and he recommended that I not be hired there. I wish I’d been ruder.

The Loyalty Board seemed very reasonable, they recommended clearance for me, the district manager concurred, Eisenhower was elected, the general manager appealed, and clearance was denied. For me no appeal, no witnesses, no hearing, no nothing. It ended my work for the AEC. A patent or two was taken out in my name (or my name plus Charlie Runyan’s) and an FBI agent in New Orleans got my signature and gave me one dollar in the coin of the realm. Some years later I got a notice that some patent was being released, but I don’t know what. Not sure I’m cleared to know.

I did retain security clearance, through “Confidential” at least, after the loyalty hearing and I continued to do some consulting for Redstone and for Aberdeen up to the time I returned to Berkeley. I wanted out of classified work entirely, but I was barely employable in the crazy freaked-out atmosphere of the witch hunt, and I hung on to security clearance as a possible protection, a security blanket.

The Tulane appointment was for two years. Rochester needed a mathematician and I’d thought an appointment was arranged there; but John Randolph wrote that his dean turned it down because it could make getting federal grants difficult — and it might easily have done so. Lee Lorch offered me a job at Fisk (he was fired from Fisk at the end of the following year) but Baley Price had just offered me a place at the University of Kansas. (It was May or June of the year again and I was jobless.) Baley had rescued Nach Aronszajn and Ainsley Diamond when Oklahoma State freaked out. Nach ran an excellent seminar, I made some good friends, and it was a good year. The following spring some signs of normalcy appeared at Berkeley and the University even agreed to put non-signers who returned on the payroll, and so I went back. I really didn’t expect to stay more than a year or so because I was still outraged by the University’s behavior. I had dreams of taking off my sandals, shaking off the dust and stalking out, but I never got around to it.

But before we relax in Berkeley’s ivory towers, let me announce a profound truth made clear by my eleven years experience and observation (1942–1953) of soldiers and spooks: The military, with assistance from security spooks, is deadly effective against both research and development. Here are some more or less current examples of what I modestly think of as the Kelley principle.

The September 1988 Scientific American carries a fascinating article on Halley’s Comet and its meeting with five spacecraft that obtained data to analyze the gases and dust in the vicinity of the comet and photographed the nucleus, the tiny solid body in the comet’s head. The space probes were the Sakigake, Suisei, Vega 1, Vega 2, and Giotto. Two were launched by Japan, two by Russia and one by Europe. U.S. science? Well, the Air Force is in charge. Their Challenger, a monument to the Wild Blue Yonder syndrome, is a press agents’ dream when it works, but it is obviously not a comet chaser. Not to worry: Halley’s Comet will be back in eighty years.

Another example: “Star Wars”, otherwise known as Pie in the Sky, is based more on fantasy than on science according to many scientists. And the project has already led to suppression of scientific dissent and dissemination of incorrect data (as revealed by the Woodruff affair at U. C.’s Lawrence Livermore Laboratory).

Here is a last picturesque example: The Stealth bomber stole onto the front pages of our local newspaper recently, after a long, well-announced development that began no later than Jimmy Carter’s presidency. It’s a swoopy looking machine, sort of an up-to-date Batmobile, but in spite of its long and public history, no prototype has yet flown (according to our local press). If this is indeed a military research and development project, for what war is it being prepared?

But we’re all tired of soldiers and spooks and so let’s go back to Berkeley, a quiet place in the mid 1950s. The students did not riot, except for panty raids, and a dog named Wazu narrowly escaped being elected president of the student body. Students were not very much involved in politics, and the university administration encouraged political lethargy. It was, for example, forbidden to invite a candidate for public office to speak on campus, and a firm foundation for the Free Speech Movement of 1964–1965 was under construction.

Toward the end of the decade the students showed a bit more initiative. They began to publish “Slate”, an evaluation of courses and teachers that appeared at the beginning of each registration period. It caused a flutter in the dovecote — not that students haven’t always evaluated faculty, but it’s not usually been systematic, with comments on lectures, exams, and grading patterns.

But the Berkeley students of the fifties were not confrontational, although one could say that some finished their political activities with a splash. You see, in those benighted days a sort of dog-and-pony show called the House Unamerican Activities Committee (HUAC) roamed the countryside in search of headlines, and in 1959–1960 they were booked into a hearing room in the City Hall in San Francisco. A bunch of U. C. students tried to attend the hearing, found themselves unwelcome, sat down outside the hearing room and were presently washed down the stairs by fire hoses manned by the San Francisco Fire Department. Unfortunately the cameras weren’t ready and almost none of the students could be identified, though a rough idea of HUAC tactics could be deduced. No one was hurt, no one was convicted of anything, and the general popularity of the dog-and-pony show took a satisfying drop.

But back to mathematics. There was a major development in the math ed business in the last half of the fifties. The war had focused a lot of attention on scientific training, and especially on mathematical training. A super-committee, the Commission on Mathematics, was formed (by ETS, AMS, and MAA if my memory is right) to investigate the situation and make such recommendations as seemed needed. The super-committee was set up in 1956 and found that the wrong math was being taught and often taught badly, and recommended a major effort to improve matters. A serious effort was begun in 1957 and then Sputnik was launched. It was like striking oil.

Sputnik raised enormous questions, and our own experts and newspaper pundits responded with something like panic. Was it possible that the Russkies were ahead of us on something? What was wrong with our own program (see the Kelley Principle)? Couldn’t an astronaut just throw nuclear bombs over his shoulder at us? All of a sudden there was a lot of money around for space flight and for technical training — enough money for technical training that some was even available for mathematics.

A long-term program improvement project, The School Mathematics Study Group (SMSG), was set up under E. G. Begle, first at Yale University in 1957 and then later at Stanford. The group labored for more than a score of years, with impressive results. Every high school program today shows improvements that began with SMSG, every university program is changed because of changes in the high school programs, and Begle’s bunch of Ph.D. students remain outstanding in the math ed biz. SMSG, the Madison project, the Ball State project, Minnemath, and many others changed the character of pre-college mathematics instruction. All of this and a theme song, New Math, by Tom Lehrer, to boot.

I got involved with the math ed biz because of an over-developed sense of outrage. I attended a conference in the 1950s that was re-examining the requirements for a California state secondary teaching credential, and neither the old nor the newly-proposed credential required, for example, that a teacher of ninth grade algebra had passed ninth grade algebra. At the time there was a tremendous shortage of math teachers, many high schools did not even offer four years of mathematics to their students, and now there was to be an emphasis on mathematics training! It sometimes seemed that requiring a math minor from physical education majors was the most constructive action possible, since athletic coaches often taught math on their sports’ off term.

But not all was lost. The California State Bureau of Secondary Education was headed by a sharp-tongued classical scholar named Frank Lindsay (“State buildings don’t have to be cheap, they just have to look cheap.”) who used the state textbook adoption system to upgrade the mathematical curriculum. E. G. Begle, who had moved to Stanford by then, served as adviser and a whole bevy of district math specialists, administrators, and pre-collegiate and collegiate math teachers became involved in the California program. The California Mathematics Council played a truly professional role and the statewise math curriculum, the teaching of pre-college math, and the preparation of teachers were all improved.

Of course nothing stays fixec without a lot of continuing attention. Thus, for example, an intern system of training teachers was set up successfully at Berkeley at the end of the 1950s by Clark Robinson, but as the pressure for schoolteachers slackened and the outside financing ended, the program was junked. Another example: The math department offered a Math for Teachers major (Harley Flanders and I set it up) that lasted for years. It was dropped only recently, in honor of my retirement and the current shortage of high school math teachers.

But let us look at Berkeley, and examine briefly the University itself during the decade of the 1960s. (See Education at Berkeley, Report of the Select Committee on Education, Univ. of Calif. Berkeley, Academic Senate, March 1966 for a detailed point of view.) Berkeley was the big U; its 27,000 students overcrowded the classrooms, jammed the libraries, and overwhelmed the faculty. It was very different from its pre-war counterpart — at least very different from UCLA a quarter century earlier, and it didn’t match the movies nor the stories of college. It was a new kind of animal, a megaversity, a maverick, a supermarket of ideas, but self-service only.

The customers at the big U were better off financially than pre-war students. It was possible, and quite common, for reasonably vigorous, reasonably able students to be entirely self-supporting, and this encouraged independence and self-confidence. And the increasing graduate enrollment maintained a reasonable level of intellectual and political sophistication on the campus.

In 1964–1965 the students demonstrated against restrictions on free speech on the campus and against over mechanization of the teaching process. (Do not roll, spindle, or mutilate me!) Several hundred were arrested for taking part in civil disobedience, the faculty was deeply concerned, a free speech policy was established, and something like a new kind of university seemed to be coming into existence (see Education at Berkeley, loc. cit.). This frightened the Regents, the newspaper reporters, and the voters, and before you could say 1968 Ronald Reagan was Governor, and at his first Regents’ meeting President Clark Kerr left his position as he had entered it, fired with enthusiasm. (I stole that last line from Clark Kerr.)

The University had no monopoly on turmoil. Voting rights, desegregation of schools, free speech, and above all ending the Vietnam War, made the 1968 Democratic Convention a noisy showplace for democracy. The antiwar movement, the war against the war, became the focus of American political activity. The Resistance, Stop the Draft Week, the War Resister’s League, Draft Counseling, the Vietnam Day Commencement, the Peace Brigade, the march to Kezar — these and many more events, organizations, points of view, became a single stream of protest, and finally, at long last, we stopped the war. Not when we wanted to, not the way we wanted to, but for the very first time the American people stopped a war. We won! (Read Mark Twain’s writing on the Philippine War, or U. S. Grant on the Mexican War. There have been unjust American wars opposed by strong, articulate people, but this was, I think, the first such to be stopped by the American public.)

Many of us have some unpleasant memories from the anti-war movement (be careful of shirt-sleeved policemen who wear black gloves) but we have good memories too. (My son announced his parents’ brief imprisonment with an engraved card.) But I think we all know, even the most burned-out of us, that what we did was important, perhaps the most important thing we have ever done.

Here is a last story to add here. It is a painful story because it concerns friends, acquaintances, and colleagues rather than anonymous administrators, politicians and officials.

In 1981 I accepted an invitation to lecture at Birzeit University on the Israeli-occupied West Bank. I gave a two-week series of lectures at Birzeit and a couple of talks at the University of Bethlehem. I lived on the West Bank at Ramallah, used public transportation, gossiped with local mathematicians and observed a visit of the Israeli army to the University.

In 1982 the Human Rights Committee of the AMS recommended that the Council of the AMS protest the continuing violations of academic privileges of Birzeit faculty by occupying Israeli authorities. The Council refused to take action and later, despite the representations of a distinguished former AMS president, refused to reconsider. I resigned from the Society in protest.

I do not believe that there was or is reasonable doubt as to the circumstances at Birzeit, and I think the Council has quite properly deplored repression in less severe cases. But the problems of our colleagues at Birzeit and the other Palestinian universities remain, and reproach us.