Autobiography: My Life at Cornell

©1999 by Anil Nerode, Ithaca, NY

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Off to Cornell

Matthew Arnold, the noted English poet and critic of the late nineteenth century, has been quoted as saying "Cornell University rests upon a provincial misconception of what culture is, and is calculated to produce miners or engineers or architects, not sweetness and light". Although it surely produces engineers, and architects, there has been plenty of culture and plenty of sweetness and light in Ithaca during my life here. I received an invitation to join the Cornell faculty as Assistant Professor of Mathematics in December, 1959. This invitation was extended by then Chair Robert J. Walker at the instigation of J. Barkley Rosser, who heard my talks at the 1957 Cornell conference. I accepted by return mail, since the memory of Ithaca from my visit the summer of '57 was extremely positive and I liked having Rosser's sponsorship. Aside from logic, he had great influence as the head of many important national committees in pure and applied mathematics. I arrived in September 1959, to be housed in a decrepit building, Lincoln HallLincoln, while the Mathematics Department's White HallWhite was being renovated. My officemate was Simon Kochen, who was also a new assistant professor in logic that year. We had no blackboard, but scrounged one up from the basement of that building. But it turned out that it was the custodian's blackboard, which he ungracefully retrieved. Kochen left in 1964 after he and Ax had solved the Artin problem and won the AMS Cole Prize. He has spent his career at Princeton. I vividly remember one of his his family anecdotes. All his parents' friends left Antwerp at the beginning of World War II with assets in diamonds. His father had instead converted everything into Polish Zlotys. His father never heard the last of it.

The Mathematics Department then had about twenty faculty members. Chairman Bob Walker provided an immensely congenial atmosphere, centering around regular parties at his apartment overlooking one of the gorges. He had all sorts of games and puzzles from all around the world. The department at that time had more the atmosphere I associate with small liberal arts colleges than that of a great university. There was an office staff of one, Madeline Keady, who was also librarian for the math library. She had been typing mathematics papers for so many years that she could detect a lot of errors that seemed to require some technical knowledge. That was quite unnerving. Under the influence of Yitz Herstein's wife and Peter Hilton's professional actress wife Margaret, the math department produced its own plays in the Kimball auditorium in Goldwin Smith. I remember an excellent production of Chekov's "The Three Sisters", and another of Tennessee Williams' "Lady of Larkspur Lotion", in which my first wife learned that she could act.

At that time the Arts Quad was the most beautiful quandrangle in the United States, with great elms planted by the class of 1872elms in long rows. The Foresters gave them transfusions of new supposed cures every year, but they all died of Dutch Elm disease anyway. None of us will live long enough for the replacement trees to acquire the same majesty. The teaching load was three and three in 1959, gradually reduced to two and two and then two and one for tenured faculty over many years due to competitive pressures.

Bob Walker himself had his research career ended by spending nine years as chairman. He had started out by proving resolution of singularities of algebraic varieties in dimension 2 in 1935 and wrote a book on plane algebraic curves that is still a classic. But nine years as chairman wore him out. My own feeling is that it takes five years to accomplish much as a chair, but nine years is too much for those in the sciences if they want to continue research. He was followed as Chair by J. Barkley Rosser.

Rosser was not at Cornell in 1959-60 when I arrived. He was setting up the cryptanalysis unit of IDA in Princeton with Oscar Rothaus of NSA as his technical chief. Rosser put us both (Kochen and I) on an existing ONR summer contract that year. The next year, the NSF foundations program started. It arrived in the form of Ralph Krause, a recent Harvard Math Ph.D., who had the position of program manager for logic and foundations and topology. He held that position till his retirement in July, 1999. So I had the same program manager for 38 years. If that isn't consistent support, what is? The sole Ph.D. student in logic was Gerald Sacks, whom Rosser had said I should take good care of. I did. There was also a master's student Carol Wolf, whom I inherited from Rosser. Sacks learned everything I knew about recursion theory, and took off like a rocket. I was not impressed at the time, because he was exactly like my fellow Chicago students. He is now Professor of Mathematics at Harvard and MIT Sacks Home Page. For thirty years we cooperatively developed recursive function theory and placed Ph.D.'s in that subject over the whole country. As time went on, I realized what a rarified atmosphere Chicago had been, getting the world's best students at the time. My persona seems to have been well established, since my first course assignment at Cornell, again without asking me, was the required graduate analysis course.

After I got to Cornell, I participated in many educational activities beyond teaching. I was an MAA consultant to many small colleges on curricular matters. I think I went to 80 colleges over ten years before they discontinued the service. With NSF support I and Carl Herz constructed courses and a curriculum for MAT students who would become high school teachers. We wrote two book manuscripts, which were never published because he believed in absractness and I believed in concreteness, and the manuscripts oscillated and did not converge. I was chair for a very great number of NSF subsidized MAT students. I kept up my applied consulting with the same Laboratory at Chicago. Bartky died, and was replaced by Frank Bothwell, an MIT Ph.D. who had a President's medal for contributions to the Polaris submarine project. I became his personal scientific advisor. He moved on to run the Center for Naval Analyses in Washington, and I ended up as his scientific advisor there too and also at the short lived Institute for Naval Studies in Boston. Meanwhile, Rosser asked me to come down to IDA Princeton. That required a top secret compartmented clearance. In those days, they had to check on all your addresses to birth, to be sure you had not been replaced at an early age by a Russian mole. This took a very long time due to the sheer number of addresses, many at hotels that had since been torn down. I was told it had taken a hundred thousand 1960 dollars of investigative time. addresses

I was promoted to the rank of Associate Professor in 1962 and went on leave to IDA and IAS. Gödel was again very helpful on a weekly basis. The most exciting thing that year was that my Chicago graduate schoolmate Paul Cohen solved the independence of choice and the continuum hypothesis. He was unsatisfied with the proof checking of the West Coast logicians and came to get Gödel's approval. I dropped him off at Gödel's house and scheduled a talk in a small lecture hall of IAS for the logicians. The permanent members were unwilling to sponsor Cohen before the proof had been checked by Gödel, but we wanted to hear it. When he gave the talk , with overnight notice on one bulletin board, two hundred people turned up. It had to be moved to the main IAS auditorium, and Gödel had not yet finished checking it!

Cohen had always been ambitious. When he was a beginning graduate student, he decided that what would make him most famous was a proof of the inconsistency of first order arithmetic. After all, proving mathematics inconsistent would certainly cause a lot of consternation. I am not sure he appreciates being reminded of his early ambition. He did an analysis dissertation, and somewhat later took up consistency questions in set theory.

Unknown to us, among the two hundred in Paul's audience was MacLane's former student, Robert Solovay, previously a topologist. We had Cohen's paper and were starting to go over it at an Institute seminar a couple of weeks later, then Solovay turned up and offered to lecture and prove some further results. That was quite startling, since the incubation period was so short, and he did NOT have a copy of the paper. General interest was extreme. I has sent a very fine undergraduate to Princeton, Bill Easton. He had shown me his first attempt at a thesis under Church, which I pointed out was unfortunately mostly the same as Feferman's thesis a few years earlier. He attended the Cohen lecture, and produced in two weeks class forcing and his thesis under Church. This was the widely circulated first formal write-up of Cohen's proof.

During the same year I received a ballot for a vote of confidence called by Barkley Rosser, who was chair at Cornell. I voted confidence. When I got back, it turned out that only four professors out of twenty gave him a vote of confidence, and that he had then called up Kleene at Wisconsin, retrieved a former offer to run the Army sponsored Mathematical Research Center there, and left Cornell entirely. He was dissatisfied with the attractiveness of the Cornell Mathematics Department to applied mathematicians. Harry Pollard and Rosser were the only established applied mathematicians at Cornell at that time. Rosser was president of SIAM. He had arranged to set up a separate applied mathematics department. Some members of the mathematics department found out, and that led to his asking for a vote of confidence, which he lost. Once he had left, both the University and the Department simply HAD to do something about applied mathematics. To satisfy the mathematics department, the new entity was set up as the Center for Applied Mathematics with no faculty of its own, no undergraduate majors or courses, and a graduate field which takes on only Ph.D. students. We wrote a quick proposal to the state to get approval for the graduate program, and it was set up. Money was supplied to hire two P.D.E. persons, Payne and Bramble from Maryland. I am under the impression that both, having large families, came largely due to the free tuition for children at that time, a perq that has since vanished . They certainly did not come due to our strength in applied mathematics, Maryland was much stronger in applied mathematics at that time. Paul Olum succeeded Rosser as chair. Paul was a very accomplished parlimentarian, which made things go smoothly. A few years later, when Dale Corson became President of Cornell after the resignation of James Perkins in the great uprising of 1969, Paul wanted to be Provost and Corson did not want him. He left to be Dean of Arts and Sciences at the University of Texas, Austin, got in arguments, and ended up as President of Oregon State University in Portland. After the death of his wife, he married the ex-wife of the ex -premier Papadopolous of Greece whom he had known when the latter was head of the Economics Department at Berkeley in about 1940. In think Papadapolous married a big busted Olympic Airlines stewardess. Olum is still alive at this time with Alzheimer's disease. We heard that Papadapolous ran the Berkeley Economics Department in 1940 about the same way he ran Greece, that is, surrounded by syncophants.

The first Director of the Center for Applied Mathematics was Bill Sears, a man of good will, an aerodynamicist of note, and the founder of our Grumman funded Aerospace School. Almost as soon as appointed, he went on leave and asked me to replace him for 1964-5.

My First Administrative Experience

That was a fateful year for computer science at Cornell. With the encouragement of Vice President Frank Long, a famous chemist now deceased, we submitted a proposal to Sloan foundation, put together by Robert Walker (Mathematics), Richard Conway (Industrial Engineering) and myself, for Sloan money to fund for five years a new graduate computer science department. We also put in a proposal to the State of New York for a Ph.D. program in Computer Science. I wrote the charter for the new department. It would be joint between Arts and Sciences and Engineering, appointments to both faculties for everyone, budget from both colleges. I would have preferred a university wide department, but this was too radical. At that time, there was not even a Provost to report to. To the three of us it was obvious that CS would eventually change the way everyone works in every field of human knowledge, since properly applied, it speeds up routine intellectual tasks independent of area, and there are routine tasks in every area which have previously been thought of as research. Communication and information sciences are included here, for what else is the web but a speed up of the routines we used to use for locating and transmitting information.

I turned out to be the only one at Cornell who knew the small number of computer scientists in the country at the time. I used the new Center for Applied Mathematics and my Directorship to set up a fall topics course in computer science taught by me and David Block, so as to have an intelligent looking audience for the lectures of the computer science professor candidates coming in the spring. My candidate for chair was Juris Hartmanis of GE, who accepted. We also hired Jerry Salton and Pat Fischer from Howard Aiken's Labs at Harvard. Salton was a student of computer pioneer Howard Aiken, Fischer was a student of logician Hartley Rogers at MIT. Hartmanis, a Cal Tech Math Ph.D., was an unbelievably superb chair for ten years and is the one principally responsible for the high estate of that department now. In my 39 years at Cornell, he was far and away the best chairman of any department. The administration also gave me a budget for additional applied math professors, to be given to departments that accepted them. The candidates were world famous, but were rejected by the departments. Until then I was not aware that departments won't accept people foisted on them. I gave those positions back to the administration at the end of the year. So much for my first experience in administration. One win, one loss.

Settling In

When I arrived at Cornell from Berkeley, I moved into a math professor's sabbatical house (Harold Widom). Since sabbatical houses were furnished with everything needed for life, I continued this way of life for seven years. When I spent a year in Thor Rhodin's house (Physics Department), I greatly admired a very much larger house next door. I said that if it came on the market, I would buy it. The owner of that house was then an orthopedic surgeon specializing in sports injuries with a large family, who decided to marry his nurse. He would have preferred to keep the house, but the wife he was divorcing insisted on selling it. So it came on the market, but the doctor was in the midst of remodelling, and it was a mess. The four hundred foot stone border wall and the huge stone patio were in a state of collapse, having been heavily damaged by the great flood of July 7, 1935, the heaviest rainfall ever recorded in New York. . He had a number of rooms in disintegrated state in the midst of redecoration. There was broken leaded glass due to children playing ball in the ballroom. It was on the market for a year. I made an offer in 1966 at half the asking price, which was still twice what my colleagues were spending for houses, and acquired a four story stucco and half timbered English Country House house1 , house2, house3 , house4with a forty by twenty Ballroom. Ballroom My friends thought this a bit grandiose. Michael Morley said he kept waiting for the real owners to show up. But my friends did not fully appreciate the effect of a vagabond childhood. I wanted a substantial dwelling that had a truly unmistakable feeling of permanence. I realized also much later that it has a resemblance to the on the surface stable base I had at the age of six at the Self Realization Fellowship Center on Mount Washington in Los Angeles. My childhood among the yogis It took 14 months of work to put my house in shape, and I have now been in it for 33 years. I have never regretted it. It made possible some very grand entertainments. I have had great difficulties in finding craftsman to repair things; I only got the exterior stone work redone, by a master craftsman, Martin Pirsic, a couple of years ago. It took two years for him to do it.

The surgeon who owned previously, by the way, built a large house on the other side of the lake, and had a large second family. But the second wife left for California leaving a note saying she was seeking a better life. He had a temper. He put all her possessions in the yard and burned them. The last time I talked to him was when my eldest son put his hand through a glass door and needed repairs. I called him at home, and he was very apologetic that he was drunk. He died very prematurely of drink, a broken man, a few years later.

The house itself is overbuilt of steel beam and concrete to the standards of 1920's grand hotels for Jerome Fried, a very exacting engineer, in 1922-26. It is very difficult to repair anything, the crafts have vanished. Fried owned a quarter of Thompson-Morse Aircraft in World War I, which manufactured a great number of Thompson-Morse scout planes for the Western Front. A quarter size replica of one of these scout planes hangs in the Tompkins County Airport. The Hanger of our Ithaca's Hanger Theatre was the hanger for this company. I found Fried's partnership papers when I moved in. Fried lost his money in the Great Crash, which was why the house was not kept up. My friend John Hsu, Cornell's eminent Viola de Gamba player and Professor of Early Music Performaance, said that the Ballroom was built as a performance chamber for the Cornell Chamber orchestra, that Fried was the Cellist for that orchestra for many years, and that Hsu and Fried and J. Barkeley Rosser, among others, played and practiced there regularly for many years.

Rosser was quite startled when he learned I had bought the house. He really liked my buying it, since he had many fond memories of it. Hsu was the one who found Fried at his death on one of his regular visits to the house. It was one of four houses designed by J. Lakin Baldridge, an Assistant Professor of Architecture at Cornell. Another of the houses is the current Cornell President's house. I was told years ago by Dean Mackesey of the School of Architecture, who was at Cornell in the 1920's, that Baldridge was quite gifted, but married money, and retired to be a big game fisherman. I later saw Baldridge's obituary in the New York Times, referring to him as "J. Lakin Baldridge, big game fisherman", not mentioning he had been a professor or an architect. Cornell students going to fraternity parties at fraternities on the same road invariably stop at my house by mistake.

Life as a full professor at Cornell. My first few Ph.D. students.

I was promoted to Full Professor in 1965. Kochen had moved to Princeton. Sacks, who had been hired in 1962 as Assistant Professor by Rosser soon moved to MIT, partially because he was angry that the department had not made peace with Rosser. I suggested that the department hire Michael Morley (1967), and later Richard Platek Platek Picture and then Richard Shore (1974) Shore Home Page. The first of my long string of Ph.D. students was Carol Wolf in 1964. I made an especial effort to give her research assistantships because her husband put up a lot of resistance to her getting a Ph. D., and that irritated me. There was also David Schroer who had earlier left with an incomplete thesis. Rosser also asked me to take care of him. Schroer did not like the Church-Rosser proofs, and had expanded on them at 900 pages length. The principal problem was to get someone to check those pages. I leaned on Myhill and he obliged. This was a great relief to me, otherwise I would have had to read them myself. The next year, a Stanford student did much the same work, but in 5 pages. Schroer also published a Fourier analysis of church bells, and observed that the best peal is the result of (I think) having two frequencies in the ratio of the golden mean. The next two were Alfred ManasterManaster Picture and Louise Hay in 1965. Hay was very active and became head of the Mathematics-CS department at the University of Illinois at Chicago, fostered women in mathematics, and died a premature death of breast cancer. An AWM prize is named for herThe Hay Award . She was also inherited from Rosser in that she had an MS from Rosser and taught at Mount Holyoke. She had a first husband who was a psychologist. She read Betty Friedan and came back to school. She wrote a spectacularly good thesis, and had twins at the same time, typing the dissertation in the hospital. Her total time with me in Ithaca was 15 months. Having supported her when she came back to school, her husband was unable to handle her successful career and her writing the math parts of his papers. He took up with one of his postdoctoral students, she found him out by stumbling upon a tryst. She divorced him, survived it all, and married a terrific person, her colleague Richard LarsonLarson Home Page. Manaster has spent his career at UCSD, with interests turned over the last twenty years to education and testing.

The next was Joe RosensteinRosenstein Picture in 1966. His interests later also turned to education, and he participated in the revision of the whole New Jersey math curriculum. The main problem when he was a student was to get him to stop proceeding toward becoming a chess grandmaster so that he would have time for his thesis.

Sacks and I had to put on a lot of pressure.

In 1966 I began a long-term collaboration with John CrossleyCrossleyPicture, right figure, then Fellow of All Souls at Oxford. His dissertation overlapped that of Manaster. Crossley invited me, Kochen, and SacksSacks Picture left to a meeting at Leeds, after which he visited me at Cornell with his family in 1966. This started a long collaboration in the area of recursive equivalence of structures. He held both a senior lectureship at Oxford and a permanent fellowship at All Souls. He set up the mathematical logic program there with the help of Michael Dummet and produced a string of excellent Ph.D.'s over four years. It was the program that Dana Scott inherited when he became the Professor of Logic at Oxford. But Crossley saw no real chance of further advancement at Oxford for himself, and in 1970 accepted a Professorship at Monash University in Melbourne, Australia. Many English scientists I met would not believe that someone would leave All Souls for Australia, but Crossley is an adventurous soul and has never regretted it. He took along his current student, Chris Ash (deceased) , who became a lecturer there, and they set up a fine graduate program in mathematical logic. After several visits, I convinced Chris that recursive algebra was something he would enjoy doing. That is the program that produced Rod DowneyDowney Home Page, now a chaired professor in New Zealand. My second son, Gregory, was born in this period.

My next students out were Phillip Olin and Robert Soare Soare PictureSoare Home Page in 1967. Olin has spent his career at York University in Toronto. Soare is a chaired professor at Chicago, a leading expert in recursion theory, recursively enumerable sets and wrote the standard graduate text in r.e. sets. He also founded and was the first chair of the University of Chicago Computer Science Department. My first contact with Soare was a phone call while I was at the Institute for Advanced Study in 1962. He was a Princeton senior deciding on what graduate school to attend. It was always my policy to give objective advice, and not to push Cornell. At the end of the conversation, my office mate C.C. Chang said Soare would come to Cornell. I asked why. He told me that it was because Soare now knew someone at Cornell.

Barbara Falkenbach , Jack PlotkinPlotkin Picture and Manny Lerman Lerman PictureLerman Home Page got their Ph.D.'s in 1968. Falkenbach married a statistician, Ryan, and while still married to him, wrote the statistical package MINITAB. She is CEO Ryan Minitab of MINITAB now. She went away from logic immediately after her degree. Ten years later I got her to send her still not obsolete thesis in for publication by refusing to give her a reference till she did. The thesis was a nice piece of work. Plotkin's thesis was in generic models of structures in Choiceless set theory. Lerman wrote the standard text on degrees. He has spent his career at the University of Connecticut.

Robert Jeroslow and Herbert Shank got their degrees in 1969. I was a minor member of Jeroslow's Ph.D. Committee as he started graduate school in Operations Research. He was a star student there. His advisor there had him solve some problems, and of course the advisor put his name as well as Jeroslow's on the resulting paper. It was when the advisor wanted to put HIS advisor's name on the paper too that Jeroslow decided to move to mathematics. I was reproached for stealing a prize student, but I did not. He did an outstanding logic dissertation. He showed that the derivability conditions for Gödel's second incompleteness theorem as stated in Hilbert-Bernays were dependent, which surprised the experts. He returned to be a Professor of Operations Research a few years after his degree. First he was at Minnesota as an assistant professor in mathematics, then he was at Carnegie Mellon in the School of Management as associate professor, finally moving to Atlanta and Georgia Tech in order to relieve his son David from asthma attacks. He was a leading expert on integer programming. At my suggestion he was exploring the use of integer linear programming to implement logic proofs, when he suddenly died at age 47, just before he was to address a large international meeting in Japan on this work. He was a single parent at his death. His son David was infomed the cause of death was a heart attack, I was told that he had had a cerebral hemorrhage.

Shank was my age, and had worked with me at the Bartky Institutes. I invited him back under a National Defense Education Act fellowship. He spent a long time at the University of Waterloo, but more or less deliberately annoyed his Dean repeatedly before getting tenure, was denied tenure, and lost his job. The Canadian equivalent of AAUP defended his position, so he stuck around Waterloo for a number of years thinking that a later Dean would reinstate him because he had his department's support. I warned him at the time that having annoyed his Dean and having complained to the equivalent of AAUP, he would be regarded as a troublemaker by new department members and new Deans, and he would never be reappointed. Faces changed, the department hired new people, their support faded away, he became too old to get a tenure appointment anywhere. He never had a secure post again.

Don Alton and Taylor Ollman got their degrees in 1970. Alton did a nice recursion theory dissertation, which turned out to deal with what were later called speedable sets in computer science. He spent his career as a Professor of Computer Science at the University of Iowa, and has retired. Taylor Ollman did a model theory dissertation, and the last I heard many years ago was a financial trader. Paul Campbell did a thesis on Suslin Logic in 1971 and has spent his career at Beloit. His interest was always mathematical education, and he put together a nice book on great women mathematicians.

Collaboration with Metakides

I met George Metakides when he was twenty in 1965, when he was an undergraduate at Cornell in Engineering. When Sacks left for MIT in 1965, he told me to use Metakides as a grader, and I did. I did not know that Metakides was a prime figure in a group of Greeks that reinvented the Zorba tradition, already dead and buried in Greece long before the movie. But I found this out soon enough when he set up many elaborate parties for me over a number of years. We had all night parties, lambs roasted in the patio for fiev hours on a home made wooden spit, ouzo through the night. Greek music and dancing in all seasons. George had me as a minor member of his committee when he was in the fifth year engineering program in electrical engineering. It came time for his qualifying exam, and I believe that his major professor was trying to bring him down a peg (hazing is common in engineering) by asking mathematical questions substantially too advanced for a first year student. He passed, with some denigrating remarks on the part of that professor. But it irritated George enough to switch to graduate work in pure mathematics. The EE professors thought I had stolen a prize student, but this was quite false. By the way, in a later year my friend the famous statistician Jack Wolfowitz (now deceased) came to me in amazement. He said that same professor who hazed George had attended his information theory course, which was Wolfowitz's own creation, taken notes, and immediately published an information theory text elaborating on the notes not very much, and giving no credit to Wolfowitz. Mathematicians tend to suffer quietly, and that is what Wolfowitz did. The professor left for industry shortly after, of his own volition.

George Metakides got his degree in 1971, was a Moore Instructor at MIT and then an assistant professor at Rochester. He was a first class researcher and an absolutely extraordinary teacher. When he arrived at Rochester they had small calculus sections, perhaps twenty. In the first few weeks, hundreds of student moved to George's section, and they cancelled all the other sections. He won the university's teaching awards. In about 1972, my interest turned to determining the effective content of classical mathematics, particularly algebra. George Metakides joined me in that work during his sojourn in Rochester. We commuted back and forth for a couple of years till the subject jelled.

The collaboration with Metakides tapered off in 1980 when he accepted a Chair of Set Theory and Logic at Patras in his native land, Greece. He might well have stayed at Rochester, but they were trying out a new system of making you an associate professor without tenure for ten years, and then having a tenure hearing. He was not pleased with that. As we all know, Rochester adminstrations have not been able to handle mathematics with any grace. They had two great chairmen Lenny Gillman and my dear friend Gail Young. Gillman left for Texas, Young for Wyoming. But since then noone has been able to handle the administration there. They have excellent science departments, I hope this stabilizes sometime.

Metakides later served a term as President of the Science Council of Europe, was head of the EEC Esprit Program, and lives in Brussels. George is Director DG III - Industry Directorate F - RTD: InformationTechnologies, European Commission, in charge of research in telecommunications and computer science for both universities and industry in the European Economic Community. My colleague, Frank Spitzer, now deceased, liked George a lot. He said he had a ranking of mathematicians by the sum of the budgets of their students, grandstudents, etc., and that George by himself was enough so that I beat everyone else (George's budget is in the many billions.) He was very well known for the number and quality of his female companions over the years. He he recently surprised everyone and married and has a little girl named Clio.

Divorce, Remarriage

When Odysseus visits Menelaus in the Odyssey, Helen is there. She says that her running off to Troy was while under the spell of Aphrodite, which had since lifted. Perhaps also under the spell of Aphrodite, my first wife Sondra Raines Nerode left me in June, 1968, to marry a close friend and colleague Benjamin Gebhart, then a Cornell Professor of Mechanical Engineering specializing in heat transfer. I have concluded over the years that the reason for this disruption was that I hadn't a clue about women; she was my first girl friend in 1952. She was a scholarship student in Hutchins college, I was several years ahead. In 1952, I spent so much time with her that she was unprepared for her exams (on year long courses). I tutored her through the material and did not prepare for the MS exam, and flunked it. I took it the next year and passed it of course. A number of the Chicago professors thought I was an example of a late starter due to this initial failure. Not so; if she had not passed everything with high grades, she would have had to leave.

Released from the spell of Aphrodite after twenty years of a second marriage, she found a most estimable third husband, Tom Irvine, more satisfactory than either me or my former colleague. But Tom himself went through a lot of previous marital woes to achieve this.

In 1968, I was a single parent with custody of my oldest son Christopher, the younger Gregory being with her. When I was dating the next summer, frankly looking for a new spouse, Robert Soare, who visited Ithaca every summer, did not approve of the women I was dating. Without telling me, he asked around and made a ranked list of single women, each of whom had already been asked if it was OK for me to call. I always follow my friend's advice, so I called them all in rank order and took them all out. The one at the top of the list was Sally Sievers Sievers, who had been Bob's pal in graduate school. I married her and took her for our first Australian visit and a world tour. She is a mathematical statistics Ph.D. with Jack Kiefer as advisor and teaches at Wells College. We were married on May 16, 1970. Here are some wedding pictures. ( May 16, 1970. The wedding was held in my Ballroom. I decorated the wedding cake with an ounce of 24 caret gold leaf the night before. It is regarded as a stimulant in India. If you have ever worked with gold leaf you will know the problem. If you breath, it flys away. If you touch it, you are Goldfinger. Here is a picture of the cake and some pictures of the wedding.Gold Wedding Cake Wedding Ceremony, Wedding Ceremony2 , Wedding 2, Wedding 3, Wedding 5, Wedding 8, Wedding 9, Wedding 10. Here is a 1972 picture of me. anil 1972We have been married now for 29 years, and have one son, Nathanael, born in 1976. Pretty satisfactory match making! By the way, I still know all the women Bob disapproved of; they turned out to be just fine too.

Collaboration with Crossley

Crossley accepted a professorship at Monash in Melbourne, Australia in 1970. I never visited Crossley at Oxford, but starting in May, 1970 made many visits with second wife Sally Sievers to Australia. We took a great number of different great circle routes, stopping all over the world for sightseeing. I am an amateur archeologist, I even was president for two terms of the local chapter of the Archeological Institute of America. So many of the sites visited were of ancient civilizations such as Mohenjadaro in the Sind desert, Luxor and the Valley of the Kings in Egypt, the great Buddhist temple Borobadur in Java, the Ajanta and Ellora Caves in India, the Minoan city Acrotiri on the Island of Thera in the Mediterranean, and virtually all classical sites in Greece. I had avoided extensive travel since I matriculated at Chicago. The itinerant life of my childhood meant that for many years after travel held no charms. The trips to Australia with many other stops changed that. Recently I have travelled on airplanes so much on business that the allergy to travel has returned.

More Students

Charlotte Lin got her degree with me in 1977. She was a member of a very interesting group of students, the six year Ph.D.'s. In the 1960's, Max Black, a very clever Cornell philosophy professor, made a proposal to Mellon Foundation saying that humanities Ph.D.'s were taking 9 years to get their degrees, and this could be alleviated by a program which paid all expenses for a six year accelerated Ph.D. I have a feeling that Max knew what was going to happen, but others had to deal with the results. This was so attractive a program that while the program existed, Cornell skimmed the cream of US students who normally pick Harvard, Princeton, Yale, and Stanford as first choice. These were extremely self-motivated and creative people. They proceeded to go in all possible directions, studying whatever they liked and generally livening up the campus. Somehow I and H. Peter Kahn (deceased) became a center for a lot of their social life, and vice versa. They often offered to cater large parties (100-150) in my Ballroom. I invited my friends, they invited theirs. Everyone had a wonderful time. I don't think a single one got a Ph.D. in six years. They all lived interesting lives, at Cornell and after. Charlotte Lin was one of them She did a major in book-binding under H. Peter Kahn, and then decided to get a Ph.D. in mathematics. Being good friends with my wife, she arranged to move into one of my spare rooms for her thesis year without telling me in advance. I assume this was to guarantee access to her advisor. She cooked us wonderful Chinese meals that year but, after choosing a recursive algebra topic, never asked me a single question. She turned in her thesis with a beautiful red leather binding that she did herself, and went to work for Schlumberger International. This is a company supplying oil exploration equipment and software world wide. This was a big surprise to her dad, who was chief scientist of Boeing, and a former Assistant Secretary of Defense. He had hoped she would come to Boeing. She married her boss, Robert Porter, he became a vice president of Schlumberger and set up their Japanese operation. I think she was the first foreign employee of Hitachi Robots, where she wrote a lot of papers. He got tired of industry and became head of the EE department at the University of Washington. Charlotte returned to Boeing where she has been ever since. Porter was very good at investment and later took up investment management as a new career. He manages my investments and those of my friends. Another remarkable six year Ph.D. was Phil Lavori, who got his degree with Richard Platek, but spent most of his time in graduate school with me. He married yet a third six year Ph. D. , Kim McCullough, and took a Moore instructorship at MIT while she went to medical school at Tufts. It was apparent to me that theorem proving in pure mathematics was not how he wanted to spend his life, so I suggested he approach Moesteller, Chair of Statistics at Harvard, telling him he wanted to move over to statistics. I loved Tukey's exploratory data analysis and thought Lavori well suited. Moesteller invited him to his seminars in the Harvard School of Public Health. Lavori made the move, eventually became chief statistician for Mass General Hospital, rewrote the statistics standards for the New England Journal of Medicine articles, wrote many papers, and finally moved to the Stanford Medical school as Professor of Medical Biostatistics. This without ever taking either a probability or statistics course. He is now married to Sacks' first wife, McCullough is a cardiologist in Boston.

Later students

Collaborations with Remmel, Marek, Subrahmanian

Jeff Remmel got his degree with me in 1974 and has been at UCSD ever since. Jeff was transformed as a student by Transcendental Meditation and has been a serious meditator (four hours a day) ever since. He acquired incredible powers of mathematical concentration as a result of this training, being able to write out highly technical fifty page papers with gory details in a day at a sitting. He became my principal collaborator after 1980, first in recursive algebra, then in complexity theoretic algebra, then in non-monotonic rule systems, lately in Hybrid Systems.

I met Victor Marek first when he visited the US looking for a position, and then again at IVIC in Venezuela. I knew all about his work, since it overlapped Metakides in the early 1970's. He had headed the logic group at the University of Warsaw. One day his department head told him he had better leave the country immediately because he had aided Jewish colleagues. He and his family left and became stateless persons. I helped him move to the United States and into Computer Science, where he is very happy. Marek visited me in about 1990, interested me in non-monotonic logics, and became my principal collaborator in non-monotonic systems. He told me that after the fall of the Soviet Union he returned to visit Poland and found that almost all the scientists of his generation had been forced out of research into other things, administration and politics, and that being forced out of the country may have been a Godsend for his scientific life. You never know what Providence will provide.

A little later I started a long term collaboration with V. S. Subrahmanian , Ph.D. under Howard Blair at Syracuse, now in CS at Maryland College Park. We first worked on integer programming to compute models for general logic programs, then on the foundations of multimedia systems and distributed databases.

I first taught mathematics when I was a graduate student at Chicago. I taught in the evening school of the Illinois Institute of Technology. The three years experience of teaching tired adults was a good first entrance into designing courses and lectures for the audiences in front of you, not those that you might have preferred to have. There was no apprenticeship then in teaching at Chicago or in the other good private university. That has all changed. Over the years, I have taught a wide variety of pure and applied courses at all levels, undergraduate and graduate, including a shared course in mathematics and art with my close friend Art History Professor H. Peter Kahn, everybody's favorite Cornell professor, now deceased. I also taught history of mathematics courses, undergraduate and graduate, since I have read most of the sources anyway. I have probably never followed a textbook , including the one Shore and I wrote. I like to prepare afresh every year. In 1982, when I became Chair of Mathematics, I was removed from teaching, and this more or less continued while I ran the Mathematical Science Institutes till 1996. Returning to teaching in 1997 was more of a shock than I expected. The level of the courses we can offer to freshman has gone down substantially since the high schools eliminated Euclidean Geometry. Only the foreign students and the magnet school graduates reliably know something about proving theorems. Most other freshman now can't distinguish "a implies b" from "b implies a", or from "a if and only if b". I hope they can understand the newspapers. But since the latter have also eliminated logical structure along with proofreading, the students are probably just fine. Another change is that foreign graduate students are now the majority. This may all fit together in a grand pattern.

Collaboration with Peter Jutro and USEPA

I did primarily military consulting till 1970. In the 1970's my consulting turned from military to environmental. First of all, military investment during the Vietnam war turned from research to bombs. Second, after the Pentagon Papers affair, Nixon ordered the removal of all highly sensitive clearances from all consultants who were not government employees. I got a phone call de-briefing. During 1978 one of my luncheon companions at the late great Cornell faculty club (The Statler Club) was Peter Jutro. He had been counsel for the committe that wrote the clean air act. He was an associate professor in our business school and was working with the newly formed US Environmental Protection Agency. He asked if anyone might be interested in collaborating on quantitative risk assessment. Since I had done such work for the US Air Force, I expressed interest, and we got a USEPA contract for environmental risk assessment of the effects of sewage sludge, henceforth known as "The Sludge Project". He had chosen this topic because it was not fraught with business and industrial conflicts, that is, no one cared, even if it is quite important whether heavy metals enter the national diet through fertilization with sludge. We did one of the earliest papers on quantitative environmental risk assessment. It seemed far out to the environmental community then, but became the accepted methodology twenty years later. I worked over the years on many different USEPA projects, ranging from computerizing their offices to being Chair of their Technical Advisory Panel on Global Change for five years. I was a distinguished visiting scientist for them in AI and expert systems in the middle eighties for three years as well. The highest level assignment was for EPA Administrator Bill Riley under George Bush. I and three others were a FCRA committee to evaluate science at USEPA and to recommend changes. We were privileged to interview many scientists and executives from USEPA, from the universities, from industry, and from other branches of government, including the science advisor to the President and the Surgeon General. Our assessment was entitled "Credible Science, Credible Decisions" and many parts of it were actually implemented. At that time I found out that most of the environmental vice presidents of US corporations were former USEPA employees, and were indeed dedicated to protection of the environment. They are a powerful force now within even the largest corporations. I also discovered that since no other country spends much on environmental research, all the other countries of the world simply send their regulators to copy the USEPA standards. If USEPA makes a mistake, the whole world suffers. My last USEPA assignment was on NACEPT, which was a large advisory panel for USEPA Administrator Carol Browner.

Chair of Mathematics

I was Chair of the Mathematics Department in 1982-7. This came about because of a deadlock between candidates; Peter Kahn asked me to run to break the deadlock. I mention this because I never deliberately sought any administrative positions, but I always try to do what my friends ask. I think my main contribution as Chair was to get outside money from the Dana Foundation, the Pew Charitable Trusts, and the Exxon foundation to reduce the freshman calculus from large lectures to small sections, introduce alternate beginning courses, while bringing in small college teachers to help and to upgrade their backgrounds. I think our freshman and the college teachers who participated are greatly benefited, while we get far fewer complaints from the students. I have never felt that large lectures are useful. I tried to get the then Dean of Engineering to make a similar change for his students, but was told they did not need it. Eight years later, they followed suit to try to lower attrition rates of minority and female freshmen in Engineering. We knew these rates eight years earlier, but in the meantime I think the issue became more sensitive.

Another item was recruitment. I felt that Cornell Mathematics will always lose out to the six leading mathematics departments when we try to get beginning assistant professors, but that a lot of talent is developed after the PhD by many other institutions, and that Cornell can compete well for these late bloomers, and get absolutely first class people. This means offers at the tenure level, which Deans hate and hardly ever budget for. I took every opportunity to find candidates through our faculty and their friends, and to offer the Deans the opportunity to make these tenure hires. The Deans and Provosts went along with this every time, though not all those offered positions accepted. The Mathematics Department is very well served by those recruited. These include Guckenheimer, Hatcher, Smillie, and Vogtmann, among others.

A non-event of my chairmanship was a proposal accepted by the administration to move Mathematics from White Hall to Sage Hall with $8,000,000 of renovation. This was even announced in the papers. But it fell through when it was discovered that just bringing the 1870's building Sage up to minimal current building code would cost $40,000,000. At least the necessity of moving due to overcrowding was put on the university agenda. Later the School of Management , located in Malott Hall, managed to raise $50,000,000 for renovations of Sage. That school moved to a renovated Sage, and Mathematics moved in June 1999 into the renovated Malott Hall. Malott, after whom the building was named, was President of Cornell when I came in 1959. He had the estimable custom of interviewing all professors after they got tenure (for me 1962) in order to quiz them about their view of the strengths and weaknesses of their departments. He took copious notes. That custom has not survived.

Mathematical Sciences Institute

In 1987 Geoffrey Ludford, Professor of Theoretical and Applied Mathematics, wrote a five year proposal to the Army Research Office for a Mathematical Sciences Institute with the aid of Charlie Van Loan (Computer Science), Lars Wahlbin (Math) , and Narahari Prabhu (OR-IE). I organized support from several departments and from Ken Wilson and his new Theory Center, and Ludford won the competition. I was told by the sponsors later that we were the ONLY mathematics department that joined with science and engineering departments in making a proposal. Such is the insularity of mathematics, but not at Cornell. Ludford was diagnosed as having a fatal brain cancer the week the Institute was supposed to open. I ran it as Acting Director for the rest of the year while still math chair, and then as Director from 1987 to 1997. The successful renewal five year proposal 1992-7 I wrote jointly with James Glimm of Stony Brook. The Army Research Office has had its budget cut in half. They no longer can afford a large mathematical institute. I had the privilege of extending financial support for ten years to many outstanding mathematicians, young and old. It was a quirk of fate that Rosser had run the predecessor Mathematics Research Center at Wisconsin under the same funding, and that he was the one who brought me to Cornell. I was also privileged to have the most far-seeing and competent program manager I have ever encountered in any context, Jagdish Chandra. He was influential on the funding of excellent new mathematics in all agencies, not just the Army Research Office. He has retired happily from stressful government service. I miss him. I now run a small Center for Foundations of Intelligent Systems representing my Hybrid Systems interests and those of my direct collaborators. It is funded primarily through a Multiple University Research Initiative of the Department of Defense, with co-principal investigators Shankar Sastry Sastry of Berkeley Electrical Engineering-Computer Science and Zohar Manna Manna of Stanford Computer Science.

Applied Research

My specialty in applied research can be characterized as computational and mathematical modeling of large heterogeneous systems. I have been a consultant to many organizations, government and military and business since 1954.

Hybrid Systems and Wolf Kohn

In about 1990, an outstanding military officer and scientist, Col. John JamesJRJames, visited me at Cornell and queried me in a survey he was making about predictions of future technology for the Army. He was running a very successful hard AI unit at Ft. Monroe at the time. I assume that his visit was due to the active role I took at Army Science meetings, which I attended as the director of an Army sponsored research institute. I have always kept up with military technologies, and always have suggestions as to how to improve them. He arranged an invitation for me later to a meeting in Pacifica, California, sponsored by Lt. Col. Eric Mettala, an outstanding program officer at ARPA Mettala. They are both Ph.D.'s in electrical engineering. The meeting was devoted to the problem of how to develop control software for very large military systems. It was under the unlikely name "Domain Specific Software Initiative" , so I did not know in advance what the meeting was about. Many representatives of the control software industry were there. They assured the assembled audience that one just had to expand the scale of present software, and a budget of $900,000,000 a year for a few years was suggested to do it. They then sketched their ideas, and I realized that, except for implementation in software, these were the same techniques I had used a generation earlier, and that they could not possibly scale them up for the contemplated large distributed systems. There were two problems. One was that the large systems are full of major non-linearities, and the old control techniques usually can deal only with one source of non-linearity, and that not very well. The second was that the Army systems are interactions of physical devices, such as tanks and aircraft and artillery, and digital computer programs that the battle commanders use as assistants. The interaction of digital and continuous devices in real time had occasionally come up in the literature, and a few systems had been built, but there was no underlying mathematical theory of how to control continuous systems by digital programs analogous to standard linear control theory. At the end of the day, I wrote a two page definition of what the correct model of a system of interacting continuous and digital programs was, and why this required entirely new mathematics that did not exist and could not be approximated to using standard theory. I just dumped this on the display desk, along with lots of material distributed by others. I really did not think that the primarily software audience would get the point. But I was wrong. The paper was read, and a member of the audience moved that the definitions I had put down should be regarded as defining what we were trying to do. We divided into three groups, to write reports. Four people joined my group, including Jane LiuLiu Home Page of Illinois and Wolf Kohn Kohn , then at Boeing. They agreed with me, and wrote a report saying that the area involved was not developed enough yet, and possibly $10,000,000 a year should go out for a few years to research it, not $900,000,000 a year to write software. This was a suggestion that Mettala accepted. When the RFP (Request for Proposal) came out, I submitted one for $2,000,000 a year joint with Richard Platek's company ORA, and won. I had really expected to be the gadfly, since I did not see a path to solve the problems. I held at Cornell the first Hybrid Systems meeting in 1991, and invited everyone I could think of who had any ideas. The meeting was enthusiastically received, and Wolf Kohn had the clearest insights. I asked him for his papers, and was unable to figure out exactly what he was doing, but several ended up with PROLOG programs for controlling horrendous systems. I called up a friend who was Director of an Institute at MIT to ask what he knew, and was told Wolf was a brilliant person, had dropped by to see them with his ideas, but that they had not been able to figure out what he was doing either. I spent about 15 minutes a day on local perusal of the papers for about a year. Then the light dawned, in that I could connect a bit with what I knew, I e-mailed him, and our joint research was off to a solid start. It still took several years to get the area clearly delineated. We developed from his ideas a multiple agent hybrid control architecture (MAHCA). It turned out that the proper context was calculus of variations on manifolds, with a Finsler metric ground form induced by the Lagrangian of an optimization problem. This is a form of dynamic programming on manifolds. Dynamic programming in ordinary space was invented by Richard Bellman. By chance his daughter Kirsty was our ARPA program manager. The problems we look at are not convex. They usually have only weak solutions. The optimal control policies have as values measures on the space of connections. The executable control strategies are finite approximations to the optimal strategies. Logic and therefore PROLOG come in when implementing approximations to measure valued optimal control policies by finite automata. These finite automata can be simulated in real time by the PROLOG program. Logic also enters when there are mixed continuous evolution rules given by differential equations and discrete logic decision rules governing the same system. The logic rules are converted into continuous constraints so the whole problem can be solved by the differential geometry methods above.

The technology has a vast variety of possible applications. We have written many papers on them. We have received two patents: Kohn-Nerode-James, United States Patent 5,963,447, Oct. 5, 1999; Kohn-Nerode, United States Patent 6,088,689, July 11, 2000, each entitled "Multiple Agent Hybrid Control Architecture for Intelligent Real Time Control of Distributed Non-Linear Processes" These applications include distributed simulation, supply chain management, intelligent routers for communication systems, slightly noisy very high compression video and audio compression algorithms, distributed autonomous traffic control, distributed airborne traffic control, general enterprise management, etc. The special feature of this technology is that it allows one to extract real time algorithms for planning and control by distributed agents without arbiter which force the systems under control to meet mixed logical and continuous constraints. I initiated four hybrid systems meetings and published four volumes resulting from these meetings to establish a world-wide community in hybrid systems. Now there are many engineering meetings with hybrid systems sessions and many separate hybrid system meetings; there were none before these volumes were published. books.

And Now to Business

Wolf Kohn left Boeing and joined Intermetrics, which promised support to the project. Boeing gave him the rights to his ideas. I got some Army support for his work at Intermetrics, but it turned out that Intermetrics was in process of being reorganized for sale by its original founders who wanted to retire, so their promised support never really materialized. Afterwards I found out that supporting this project would have meant betting the bank; they really did not have much capital. Col. James retired from the Army and joined Kohn at Intermetrics. Since Intermetrics was changing shape and the support from them was not forthcoming, Kohn and James left Intermetrics. I got a sudden call from Wolf saying we were founding a corporation, and he was already renting and furnishing offices. He made the jump without getting new funding of any magnitude and without getting a release of rights from Intermetrics. Evidently he trusts Providence as much as I. We started out with me as Director of the Board, John James as President, Lennie Golub, a cousin of Wolf's wife, as business vice president, and a lawyer who knew the Golubs well, Howard Wolf. Howard was chief commercial lawyer for Fulbright and Jaworski in Houston, and is now retired. He was a godsend, the rest of us were business experience free. He negotiated the assignment of rights from Intermetrics in return for a modest portion of shares. We were also the full board of directors. I scrambled for some military contracts with unnatural haste with the help of Jagdish Chandra of ARO, who believed in the work. We spent a huge amount of time cultivating research vice presidents and chief technologists of large corporations who could use our work. We did not get a "not invented here" attitude, rather we got enthusiastic support. But it turns out that the businessmen running the large corporations pay no attention whatever to recommendations for investment coming up from the technologists, we were seeing the wrong people. Business executives with signatory power over large investments only talk to other businessmen of like ilk. How were we to know?
We also applied to NIST (National Institute of Technology) for a grant intended to carry technology companies from the highly risky category to the lower risk category which venture capitalists fund. This is a program with no strings, which offers all kinds of help from experienced entrepreneurs and accountants, to inexperienced start-ups. We had a million dollar a year grant for several years which allowed us to move from one risk category to the other, with the help of a terrific program manager from NIST, Barbara Cuthill. During this period, Wolf Kohn, chief scientist, and Howard Wolf, our lawyer, knew how to perform their functions. The other three of us were in new roles in business, quite a learning experience. There were too many possibilities, we did not focus on a single product. We were lucky to survive. Kohn is CEO, our company is Hynomics Corporation of Kirkland, Washington, Hynomics ., now concentrating on supply chain softwareSupply Chain We have a very distinguished Board of highly successful entrepreneurs from the software industry now Directors. Who knows what the future may bring?

My Childhood Among the Yogis

My Higher Education

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