Edwin Hewitt autobiography

Edwin Hewitt wrote So Far, So Good: My Life Up to Now in 1988, two years after he retired, giving details of his life. Sadly he suffered a severe stroke in January 1989. We give a version of Hewitt's article below.

So Good: My Life Up to Now, by Edwin Hewitt

I was born in Everett, Washington (USA) on 20 January 1920. I am the youngest of three children born to Irenaeus Prime Hewitt and Margaret Guthrie Hewitt. I had two siblings: William Guthrie Hewitt (1916- 1983) and Helen Hewitt Arthur (1918-1953). Our parents were old American stock. On my father's side we (and myriad other Hewitts) are descended from Thomas Hewitt, who flourished, as the saying goes, in North Stonington, Connecticut, in 1639. On my mother's side there are a lot of Pennsylvania Dutch ancestors, some with a wild streak that keeps cropping up unto the third and fourth generation. My father was trained as a lawyer, but in my lifetime never practiced law. My mother had a bachelor's degree in English from the University of Nebraska. During my first decade she was a housewife, but also taught English as a freelance and for two years studied English in the graduate school of the University of Washington.

My early memories are for the most part happy, though I carry to this day recollections of stern discipline meted out for this or that childish crime. I suppose I was precocious, though by no means a prodigy. An early memory is of being taken to a meeting of the Everett Rotary Club and being stood up on a table to recite the Gettysburg Address. My mother began to teach all three of her children French, using a little book called French without Tears. I can still quote passages from that little book, and recite the Gettysburg address.

I was an insufferable child. I had - and still suffer from - a terrible habit of mouthing off. Recognising this weakness has at least preserved me from the folly of becoming a department chairman or dean: I knew that at some inopportune moment I would lose control of my tongue and then lose my job.

My mother was devoted to literature. During summer vacations in the 1920s, she and her children read aloud to each other Pilgrims Progress, David Copperfield, Dombey and Son, Oliver Twist, and finally Vanity Fair. I recall my pride at being given the honour of reading the last instalment of Vanity Fair to my mother and siblings.

In 1931, my mother took all three of her children to St. Louis, Missouri, where she enrolled us in the Principia Academy, a Christian Science school. I have no idea where she got the money, I know now that she was determined to get out of Everett, Washington, and away from my father. I spent three academic years at Principia and two at a Christian Science country boarding school called The Leelanau School, located 30 miles west of Traverse City, Michigan. I got a good education at both schools, though I had unhappy times at both. Part of the process of growing up, no doubt.

I learned mathematics and French with little effort. In grammar school I had a hard time with written arithmetic, though mental arithmetic and word problems were simple. At ten years of age I heard about logarithms, at thirteen about trigonometric functions. I had a marvellous mathematics teacher at Principia, Paul C. Dietz. He gave me my head and the run of his exiguous mathematical library. I read trigonometry on my own, ditto Euclid (I loved ruler-and-compass constructions), built models of the regular solids, wrote out on tape an estimate of 1200!, found in Thornton C Frye's probability text, and enjoyed wielding a Keuffel and Esser log log duplex slide-rule, which I still have. Of course, it is only an antique now. I had a fine teacher of French at Principia, Moniseur Robbins. He gave me a good start in French, and turned me loose to read Les Misérables on my own: this was my first experience of reading a seriousbook in a foreign tongue. The Latin teacher at Principia was a Mrs Semple, a lady of the old school. We learned our Latin from her and much more about what the Germans called Umgang mit Menschen.

I entered Harvard in 1936 on a Samuel Crocker Lawrence scholarship in the amount of $500 per annum. A half-century ago Harvard charged $400 per annum tuition and $100 per annum for dormitory rooms [at least for the needy among us]. With waiting on tables for my meals and savings from summer jobs, I had no money problems.

My six years at Harvard were happy. I melted into the crowd, no longer an underage, undersized misfit. The mathematics faculty was awe-inspiring. George David Birkhoff, an Olympian figure, was also dean of the Faculty of Arts and Sciences. William Caspar Graustein was a dignified man who always wore black three-piece suits. Edward Vermilye Huntington was an elderly scholar, plainly not part of the power structure. Joseph Leonard Walsh was greatly respected for his flawless lectures, though not for the Walsh- Rademacher functions: we had not heard of them. The younger faculty included David Vernon Widder, Saunders Mac Lane, Garrett Birkhoff, Willard van Orman Quine [I think he was in the Philosophy Department: he gave brilliant courses on mathematical logic], and Marshall Harvey Stone.

In the autumn of 1937, Stone accepted me as an advisee. Thirty-four years of age and an associate professor [shortly thereafter promoted], he was at the meridian height of his mathematical powers. He had the strongest mind I had ever encountered. He had written a huge and, to me, incomprehensible book; he was a son of the Chief Justice of the United States; his lectures were known for their clarity and vigour. I took but one course from Stone, the theory of functions of a real variable, in 1939-1940. This course put my feet on the path to becoming mathematician. The concepts set forth in this course have been with me for forty-nine years; some of them appear in the book that Karl Stromberg and I wrote. From Stone and his fellow mathematicians at Harvard, I learned vital lessons about our wonderful subject:
Rule #1. Respect the profession.

Rule #2. In case of doubt, see Rule #1.
My studies under Stone's policy of benign indifference led me into set-theoretic topology, to the neglect of much else. In 1941 I proved my first theorem, If X is a metric space without isolated points, then X contains complementary dense subsets. Early in 1942, I lectured on this and related matters to the Harvard Colloquium, G D Birkhoff did me the honour of attending. At the end he asked, "Mr Hewitt, how much of this would you have without the axiom of choice?" I replied, "Nothing at all, Sir." With that, G D said something like "hump" and turned about to register his scorn at a whippersnapper who couldn't construct the things he was talking about.

I got my Ph.D. in June 1942 for a theses on set-theoretic topology written under Professor Stone. Saunders Mac Lane read the manuscript and half way through found an unfortunate blunder. Luckily the lacuna could be filled. George Mackey got his Ph.D. the same day I got mine, also from Stone. Professor Stone has been a decisive influence in my life for over half a century. My debt to his is second only to that I owe my dear parents. It is a marvel that Stone took me as his protégé, and over the years increasingly as his friend.

Military service loomed for all young men in my position at that time. Nonetheless, I accepted an instructorship at Harvard in June 1942 and taught there happily for six months. This was a carefree time. I was the assistant senior tutor at a Harvard house and so had free room and board. I had my first serious girlfriend, an eighteen-year old Radcliffe sophomore. (She dropped me early in 1943.) I found mathematics of consuming interest and rejoiced in learning mathematics and in discovering new facts.

In January 1943 John M Harlan paid a visit to Harvard. He was a prominent New York lawyer who had been recruited by W Barton Leach to organise and run an Operations Research Section at the 8th Bomber Command in England. Someone, probably Oswald Veblen, had given Harlan my and Frank Stewart's names. Harlan offered us positions with his group. We thought for as long as thirty seconds before saying "yes," and in April 1943 found ourselves in High Wycombe, 30 miles outside of London. Harlan was a colonel, and there were perhaps two other commissioned officers in the group. The rest of us, some 40 in number, were civilian scientists. I was put onto the problem of defending B-17 and B-24 bombers against German fighter planes. Astonishingly, here was the B-17 with machine guns all over it and no doctrine whatever for gunners to aim by. I attended an RAF gunnery school, where a sensible and simple system was taught. I recomputed the RAF data for our ammunition and airspeeds, and added new rules to deal with head-on attacks, which the night-flying RAF did not have to cope with.

My first job was to convince Col. Harlan that I had the right answers. He gave me a lawyer-like grilling. Once satisfied that I was right, he turned me loose. I got great assistance. Major George R Weinbrenner was a great help until he was shot down. (He cold-cocked a guard on a train in Germany, walked through France, and lived the life of Riley on the Riviera until US forces liberated him in 1944.) I had able assistance from Sergeant John S Jillson, whom I had known at Harvard. There was a superb draftsman named Bosch. Porter Henry, a New York journalist, joined us and performed prodigies. I went all over the 8th Bomber Command, lecturing to bomber crews and passing out skilfully written training literature from Porter Henry. I felt it necessary to fly and wound up with seven missions to Germany and France as a bombardier-gunner.

In the late summer of 1944 I was rotated back to the USA. I spent some weeks with Saunders Mac Lane's Applied Mathematics Panel at Columbia University and about 1 January 1945 joined an Operations Research Section at the headquarters of the 20th Air Force in the Pentagon. I wanted nothing so much as to go to the Marianas and help bomb Japan, but I never got my orders. I learned 20 years later that my mother had telephoned a deputy secretary of the Navy and asked him not to let me be sent out a second time.

Altogether, my two and a half years with the Air Force were the best times of my life up to now. I've been a fortunate fellow. I've climbed some nontrivial mountains. I've skied across Lapland. I've driven 165 miles per hour in a motor car. I've known some wonderful women, two of whom I married. But nothing else even comes close to hanging around the Air Force and getting rides in their beautiful machines.

I was discharged in September 1945. Powerful forces were guiding my destiny - I suspect Veblen or Stone. At any rate, Henry Allen Moe of the Guggenheim Foundation awarded me out of the blue a $2500 fellowship for reconversion to civilian life. Though I was of two minds about taking up mathematics again and thought of having a whirl at law school, I took the money and with my beautiful young wife, Carol Blanchard Hewitt, went to Princeton for the year 1945-1946. There was a galaxy of eminences at the Institute for Advanced Study: Albert Einstein, Carl Ludwig Siegel, John von Neumann (who was around only part of the time) Hermann Weyl, Kurt Gödel, James W Alexander, Marston Morse. Richard Arens was Morse's assistant; Ernst Strauss, Einstein's. At Princeton University there were Wedderburn (a man of small stature, no longer young, who wore well-cut tweeds), H.P. Robertson, L P Eisenhart, Salomon Bochner, Ralph Fox, Emil Artin, Solomon Lefschetz, Claude Chevalley. I was very much an Unterspieler but enjoyed watching the big shots, attending their seminars, and observing their foibles. I was horrified one day to watch Chevalley bait Weyl like a terrier nipping at a water buffalo, while Weyl was trying to give a lecture on Lie groups.

My own research paid off quickly, though of course with the usual struggles. I solved tow old problems posed by Paul Urysohn in the 1920s and discovered what are now called realcompact or Hewitt spaces. This came about through my efforts to understand the ring of all real-valued continuous [not necessarily bounded] functions on a completely regular T0-space. I was guided in part by a casual remark made by Gel'fand and Kolmogorov (Doklady Akad. Nauk SSSR 22 [1939], 11-15). Along the way I found a novel class of real-closed fields that superficially resemble the real number field and have since become the building blocks for nonstandard analysis. I had no luck in talking to Artin about these hyperreal fields, though he had done interesting work on real-closed fields in the 1920s. (My published "proof" that hyperreal fields are real-closed is false: John Isbell earned my gratitude by giving a correct proof some years later.) In fact, what I got from Artin was a quick brush-off. My ultra-filters also struck no responsive chords. Only Irving Kaplansky seemed to think my ideas had merit. My first paper on the subject was published only in 1948. It got a lukewarm review from Dieudonné. Later Leonard Gillman, Meyer Jerison, and Melvin Henriksen put me under a great debt by taking the matter up afresh and doing a whole lot with rings of continuous functions. A lost of citations published a few years back by Joseph Schatz lists my 1948 paper as one of the most cited papers of the past fifty years. Three Soviet mathematicians came to the hyperreal field problem many years later: the hugely talented brothers Gregory and David Chudnovsky and that great fellow Misha Antonoviskij. The four of us published a joint paper in 1983 on rings of continuous functions. Nothing like coming back to a problem after 35 years!

In 1946-1947, I taught at Bryn Mawr College. I was not housebroken enough for Bryn Mawr. Although John Oxtoby and Anna Pell Wheeler were wonderful to me and expressed regret at my departure after one year, they must have felt relieved to have this loose cannon out of their pleasant demesne. I made friends among students at Bryn Mawr whom, 42 years later, I still cherish as my close friends.

I went to the University of Chicago in 1947 to take a half-time position with a military research project called CHORE [Chicago Ordnance Research] and a half-time position with the Department of Mathematics at the University of Chicago. This move was a disaster. I lost the military job by running afoul of the regular army colonel, Frank Fenton Reed, who was the Army liaison officer. I then found that Marshall Stone had no interest whatever in hiring me full time in his department. The man in charge of CHORE, Dean Walter Bartky, was decent enough about my plight but could do nothing to mitigate it. So I served out my one-year appointment in wretched circumstances.

In the spring of 1948, I generated job offers from two large midwestern universities and from the University of Washington. All salaries offered were $4250 for the academic year. One of the Midwest schools offered me twelve hours per week of teaching: four sections of beginning calculus. The other Midwest school is in an agricultural state. I had enough Harvard snobbery to refuse to go where I thought I would be in the middle of cornfield.

The University of Washington offered a nine-hour teaching load, a course in the theory of functions of a complex variable, and the opportunity of living in Seattle, which I remembered pleasantly from my childhood. So in August 1948 my young wife and I, with most of our worldly goods in a station wagon and accompanied by my recently widowed father, set out for the Pacific Northwest.

I was taken with Seattle. We were welcomed by old friends from the 1920s, now rather grey at the temples. We found reasonable living accommodations. The department was a comfortable little group, which was for the most part unconcerned with research. Professors Z W Birnbaum (a Polish-born statistician), Ross A Beamont, and Herbert S Zuckerman rapidly became good friends. In particular, I found in Zuckerman a wonderful friend and collaborator. I learned most of my classical mathematics from him, a side that I had foolishly neglected in order to follow the sirens of functional analysis and set-theoretic topology. Herbert and I worked together from the autumn of 1948 until the day of his tragic and untimely death in June 1970. I am proud that my name stands alongside his, attached to now classical theorems in Diophantine approximation, the structure of semigroups, and abstract harmonic analysis.

In 1950 I attended the International Congress of Mathematicians at Harvard and met the great Swedish mathematician Arne Beurling. I had studied his enigmatic 1938 paper on the convolution algebra of functions of finite variation on the real line and asked him some questions about his proofs. Within minutes he invited me to spend a year with him in Uppsala. So my wife and I set about learning Swedish. In August 1951 we sailed for Copenhagen on the M S Stockholm. We had a splendid year in Sweden, though my hopes of achieving great things in research with Beurling never came to fruition. We made friends in Sweden who are today still close friends at the houseguest level. I can carry on a conversation in Sweden and read Dagens Nyheter.

In the summer of 1952 my wife was pregnant with our first daughter, Greta. We travelled in Germany, the Netherlands, France, Switzerland, and Britain. We met many interesting people, among them Wilhelm Blaschke, E Witt (who pointed out that I nearly stole his name, Hel Braun (who was a close friend up to her death), Helmut and Irma Grunsky (also lifelong friends), M. Plancherel (who gave me Kirschwasser in his garden in Züruch), Jean Dieudonné (who entertained me and others lavishly in Nancy), and Henri Cartan. We spent several weeks in Paris as guests of the late Leonard Jimmy Savage and his charming wife and young son Sam. They had an enormous apartment not far from La Santé. Jimmy and I did much of the research for our paper on product measures while sitting on a bench in the Luxemburg gardens, surrounded by nursemaids with prams. This paper contains the Hewitt-Savage 0-1 law, along with a construction of measures on extreme points of a convex set that is a special case of what later became Choquet theory.

Back in Seattle in the autumn of 1952 and settled down to a quiet life, I found myself picking up doctoral students. I was enthusiastic about mathematics; I gave lectures that were attention-getters though not show-stoppers; and over the years, a number of fine young men and women came to me for guidance as they worked toward the doctorate. The first was George H Swift (1954), who now is one of my best friends. Thirty-six others followed George over the years. Some have vanished to my sorrow. Many hold positions of great influence and trust in academe and industry. One has even been a university president: Albert J Froderberg. With Karl Stromberg and Kenneth Ross I have written many papers and three books. I am grateful to these fine scientists and good friends. It was seldom easy to work with me. Wis Comfort has maintained close ties of friendship as he has mounted to the academic empyrean. Leonard Yap, now a senior member of the faculty at the National University of Singapore, has been a stalwart friend. Those whom I don't list will forgive me. They know that I love them all and that I rejoice in their successes and mourn their misfortunes: and there are far more of the former than the latter.

In 1967 I met and instantly took to Mark Aronovich Naimark. In 1969 I went to Moscow for seven months to work with him under the inter-Academy exchange program. By this time, little Greta had grown into a sixteen-year-old woman, her mother had divorced me, and I had remarried. Great and I went to Moscow; my second wife joined us later and we had many an adventure. I had begun to study Russian during World War II, partly out of boredom when there was nothing better to do. I had continued my Russian study over the intervening years and was fluent when we arrived in the USSR. Greta, who had had one year of Russian in a Seattle high school, plunged into a Moscow high school and did very well. She made many Russian friends, received and declined a proposal of marriage, saw sights that no adult could have, and came away with a strong feeling for Russia and the Russians. She can speak Russian well enough to fool native speakers and can imitate both Moscow and Kishinev accents.

I took the academic year 1972-1973 at the University of Texas in Austin, intending to stay permanently. There too I had many dear friends, but I missed the rain in Seattle, and I missed my Seattle friends. After spending the summer of 1973 in Russia with Greta and her younger sister Lise, I went back to the University of Washington. Lise majored in Russian at Middlebury, has a master's degree in Russian, and is now a professional translator of Russian into English.

I spent the years 1973-1975 as vice-chairman and chairman of the University of Washington Faculty Senate. This was good sport but of negative value to my career as a mathematician. I took a lot of unpopular positions, presented honestly the faculty's point of view, and once got on the AP wire with a rash statement about not hounding faculty for overdue library books. The fact is, of course, that the faculty have no power in running the university. We're hired help without a union to help us. The occasional star gets exceptional treatment from the administration, especially if he is a surgeon with a large team and a large budget. But the hard-eyed businessmen who run the university are not really interested in research as such or even in teaching. Naturally they like intercollegiate football. What they are mainly enamoured of is garnering government contracts and trafficking in real estate.

My great friend Heinz Bauer of the University of Erlangen-Nürnberg put me in for an Alexander von Humboldt-Stiftung prize. Through his efforts I was awarded one of these marvellous prizes. With it I spent the months September 1975-April 1976 and September 1986-December 1986 at the University of Erlangen and the University of Passau. To live in West Germany was a superb experience. I love the country, and I love the language [which I learned in 1938-1940]; and I am - or was in 1975 - fascinated by the Wehrmacht's and the Luftwaffe's performance in World War II. In Erlangen I quickly met Gunter Ritter, a Ph.D. student of Bauer who was assigned the care and feeding of this eccentric American. Ritter and I hit it off at once. Over the past thirteen years we have written four or five substantial joint papers, and the Ritters have spent many months in Seattle.

In 1982 I taught for a semester at the University of Alaska in Fairbanks. This was a great adventure with good colleagues and interesting students at a fine university in a burgeoning state. The following year I accepted a permanent appointment at Fairbanks but at the last moment reneged. My friends were justifiably chagrined and angry. When the oil market collapsed a year later, they must have been relieved not to have an additional tenured professor to support. I continue to treasure my Fairbanks friends, in particular Jack Distad and Bill Phillips.

I've been abundantly blessed for many years by attracting gifted collaborators. I've already mentioned a number of them. Let me list some others. The great analyst and great gentleman Kôsaku Yosida spent 1950-1951 at the University of Washington under the auspices of our chairman, Roy M Winger. Yosida and I wrote a paper on finitely additive measures that is still well regarded. In Princeton in 1956 I ran into E P Wigner at a party given by Kees Gugelot and wrote a paper with him at the party. Shizuo Kakutani and I have written two papers about measures on groups. One of these includes the first construction of what are now called Kronecker sets, which are remarkable sets in topological groups.

I had the privilege of writing a paper with I I Hirschman, Jr, on Fourier transforms on groups and a paper with John H Williamson on Dirichlet series. Both collaborations gave me a lot of pleasure.

A casual remark made in Moscow to Dusa McDuff led to a paper with her in Mat. Sbornik that has not received the attention it deserves. It shows that M(G) for an infinite compact non-Abelian group G can have infinite-dimensional simple homomorphic images: a startling result in view of the docile behaviour of M(G).

Robert Edwards, who now leads a secluded life in Canberra, has been a good friend since 1952. We have collaborated frequently, with Robert applying his great powers to whatever problem is at hand.

Gavin Brown of the University of New South Wales has taught me a lot of classical analysis and neoclassical analysis on groups. Our labours have resulted in three papers.

Shozo Koshi of the University of Hokkaido is the hardest worker I've ever met. We have collaborated happily on two papers.

My final Ph.D. student, Nakhlé Asmar, with unrivalled generosity asked me to be his co-author on what is really his work, the last item in my bibliography.

Teaching has been a vital part of my career. I love to get in front of a class or a colloquium audience - any audience, in fact. Professor Stone will forgive me for quoting one of his great aphorisms: "Teaching is a form of public entertainment, much like acting, which it closely resembles."

In 1984-1986 I taught a two-year honours analysis class at the University of Washington. These splendid young people were the best undergraduates I ever taught. I recall especially Eric Stromberg and Marrena Lindberg, who have extraordinary talents in several fields and are blessed with ebullient personalities. Nakhlé Asmar took his Ph.D. in 1986. I knew that I would never again get students like these. I found that I could feather my nest nicely by taking partial retirement in 1986. [Did you hear about the chap who always gave his parties in the basement? He liked to nether his fest.] Other straws in the wind whispered plainly that it was time to go. And so I retired on 1 July 1986.

Since then I've taught part-time at the University of Washington, travelled and lectured in eleven countries, and done a certain amount of research. I am learning Chinese.

In May 1988 my friends put on the HEWITTFEST.

Here I am, still having fun and grateful for every new experience. As my dear friend Ursula Leonhardt-von Barchewitz says Jeder Tag ist ein Geschenk.

Department of Mathematics
University of Washington
Seattle, WA 98195 USA

Last Updated January 2021