Eye of the Hurricane

By Richard E. Bellman (World Scientific, 1984).

Overview

This is a book I read a while ago, which I found immensely interesting and would highly recommend. Of course, everyone in CS knows the name of Bellman (for the Bellman-Ford algorithm or dynamic programming, and some people may know the large number of books Bellman edited). Yet, I found I knew so little about Bellman after reading the book. Here are a few excerpts to intrigue you.

Chapter 1: Growing up in New York city

• Bellman’s family came from the Kiev area. The name Bellman is Swedish, as historically the Swedes went down as far as Kiev. (reminds me of the TV show Vikings)

• The two curses of Bellman’s childhood were bed-wedding and fear of the dark. The bed-wetting went away at a relatively late age, about thirteen.

Chapter 2: High school and college

• I got my copy of Whittaker and Watson, suitably inscribed by Harris F. MacNeish. The first book I bought was Titchmarsh’s “Theory of Functions.” I had that inscribed by my father. The second book I bought was also by Titchmarsh, “Fourier Integral.” I worked through all three books, and then started writing papers.

Chapter 3: Graduate school, marriage and war

• There was a famous feud between Wintner and Zariski. What the origin of the feud was I don’t know. But, whenever one spoke at the weekly seminar where attendance was so compulsory, the other would turn his back to the board and just smoke. Another famous feud was between Vandiver and Moore at the University of Texas. Finally, the situation got so bad that a separate department, a department of applied mathematics was created for Vandiver. What makes it particularly amusing was that Vandiver’s field was number theory. Such feuds are very common in academic life.

• Charlie Chaplin: Comedy is tragedy at a distance.

• Murnaghan was not happy that I was married. He felt that graduate students should not be married. He was probably right.

• An all-purpose insult is rarely effective. One has to know a great deal about a person to insult him effectively.

Chapter 4: Belleville 1942; I learn electronics

• He (John A.) became a bum and wandered about the country. Whenever he wanted a meal, he would go to a restaurant and wash dishes. When this failed, he would go to the local whorehouse. He said that it was true that whores had hearts of gold. He always got a meal there.

Chapter 5: Madison, Wisconsin, 1942-43

• My procedure for doing mathematical work was simple. I would thumb through the latest issue of the Duke Mathematical Journal or the Bulletin of the AMS and see whether there was something which interested me and was something I wanted to do.

  (This was how he discovered the Bellman-Gronwall inequality. The above two journals no longer represent the entire mathematical field.)

• There are a few papers in my bibliography which I would gladly withdraw. I console myself philosophically with the thought that “even Homer occasionally nods” and that Shakespeare and Beethoven wrote some stinkers.

Chapter 6: Princeton 1943-44

• Solomon Lefschetz (who lured John Nash to Princeton) had been born in Iran, raised in Moscow, went to school in Paris, and then came to United States as an engineer. While working as an engineer, a wire fell across his hands severing both. … He was very proud of the fact that he was the first Jewish professor to have a permanent appointment at Princeton.

Chapter 7: San Diego and sonar 1944

• Oppenheimer came from a very wealthy background, and his pet trick was to borrow a book from a graduate student, and slip a $10 bill in the book when he returned it.

  (Those who borrowed books from me: you know what to do now 😉)

Chapter 8: Los Alamos 1945-46

• Why he, Bethe, and Flanders bothered with me I will never understand. Whenever I lose patience with a graduate student, I think of how patient they were in the middle of a war with lots of more important things to do.

• Betty Jo, however, was determined about joining WAC. I was very unhappy about this and felt deserted.

  (Bellman eventually divorced Betty Jo but he did not disclose many details in the book other than blaming WAC’s bad reputation in the 50s. History about WAC seems like an interesting read for another day.)

• I found an elegant way of using the representation of a group and integration to generate invariance. Later, I found that I had been anticipated by Hurwitz. I never minded being anticipated by a famous mathematician since it showed I was working on the right problems. I always felt it was a matter of time before I found new results.

• I have found that colonels and generals and their navy equivalents captains and admirals are generally nice people. It is the junior officers that one must steer clear of.

• Bochner had arranged that I have a National Research Predoctoral Fellowship waiting for me at Princeton.

Chapter 9: Princeton 1946-48

• (Paul) Erdős has great talent, even genius, but he has no judgement. He does not match the problems he works on with his ability.

• One of Pete’s (Peter Lax, whose functional analysis book is one of my favorites) aunts was Emily Post (who wrote the bible on etiquette). Gábor Szegő is Peter Lax’s uncle by marriage.

• The method I used was the following. There is a German review journal, Zentralblatt fur Mathematik. I read all the reviews on differential equations. If the review seemed interesting, I read the original. The American counterpart, Mathematical Reviews, was started in 1941 when it was recognized that it was impossible to depend on a German journal.

• He (Solomon Lefschetz) said that once he had written a letter like this and paid very dearly for it. He advised me in the future to say what I wanted in person or over the phone, but never in a letter.

• There was an episode with Carl Siege that ended Bellman’s dream to study number theory under him:

  Princeton University Press was very anxious to get a book from Siegel who had not written one up to this time. Shiffman and I were to take notes, these notes were to be sent to Gordon Pall, who was to work them over and then send them on to Siegel for the final polishing. First, Shiffman dropped out, then Pall wrote that he was too busy, then Siegel decided to take a European trip. Since I was busily writing my thesis, I should have taken heed of all this and postponed the whole thing. However, I was anxious to please, and, therefore, I undertook the publication myself. The press insisted that it be a joint work, Bellman and Siegel. … Artin pulled me into his office. Siegel didn’t like my notation! As a matter of fact, he disliked it so much that he demanded that the press suppress the edition. Artin demanded that we go over to Siegel’s house and that I apologize. I, of course, was quite willing. Siegel was not at home. … Copies had already been sent out to the major libraries. For years afterwards one of my hobbies was seeing if a university library had this edition. Siegel rewrote the book, Number 18 of the Annals of Mathematics Studies. In my bibliography, I list it as “Limited Edition”.

  I will never forget Neugebauer saying to me, “Let Siegel write his own books.”

• A few bizarre episodes with Paul Erdős:

  Shapiro wrote many papers himself. Erdős was the referee for these papers. Each time that Shapiro wrote a paper Erdős would improve the result a little. Consequently, Shapiro would withdraw the paper.

  Unfortunately, the editor, A. A. Albert, had gone off to Brazil for six months and left the journal in the hands of Kaplansky. Our paper was refereed by Erdős who accepted it. Kaplansky, however, asked Erdős whether he couldn’t get a better proof than ours. Erdős supplied one, and Kaplansky transmitted it to us. We wrote back, pointing out if Erdős’ proof were written up in the same detail as ours it would be just as long. Kaplansky persisted, and Erdős supplied a very elegant shorter proof. Kaplansky suggested then a joint paper. I refused, saying that we would add Erdős’ proof as an appendix if he desired. … it seems that Erdős had gone around the country saying that we were stealing our result from him. Shapiro wanted to withdraw the paper. I didn’t think that was a good thing to do but one paper more or less meant little to me, and I was in this for Shapiro’s sake anyway. I wrote to Kaplansky telling him we wanted to withdraw the paper if possible.

  We heard nothing for several weeks. Then we received a letter from Kaplansky saying that the type was destroyed and the bill would be sent to us.

  I wrote back, saying that he had misinterpreted my letter and that we had no intention of paying the bill, about $300. By this time Albert had returned, and heard Kaplansky’s version of the story. We received a vitriolic letter from Albert telling us that either we pay the bill or face expulsion from the American Mathematical Society. I have often thought of the expulsion ceremony. I think our pencils would be broken in front of us.

  At this point, I went to Lefschetz. I felt that the function of the referee was not to improve a paper. Lefschetz handled the problem in a characteristic fashion. He didn’t waste any time on the problem. Rather, he wrote a letter to Albert pointing out various indiscretions which Albert had committed in his youth.

  Thereupon we received a very nice letter from Albert and the matter was ended. However, we never published the paper nor did Erdős publish his proof. That is a great shame since Erdős really had an elegant method.

• Lefschetz loved to taunt Shapiro because Shapiro reacted so strongly. As a matter of fact, most of the graduate students were terrified of Lefschetz. When they saw him coming they would hide. Shapiro used to retaliate by telling Lefschetz that I was doing number theory. One day, Lefschetz stopped me and said, “Which end is turning out the papers on number theory?” “The same end that is turning out the papers on differential equations,” I said.

• The ONR grant also supported my office mate, Joe LaSalle.

  (the “bang-bang” control.)

• At tea, I was introduced by Chevalley to Weyl as the young man who had proved this conjecture. I had to tell Chevalley and Weyl that the proof was wrong. Weyl was very nice. He pointed out that if the world knew the mistakes that famous mathematicians made at their desks their reputations would not be as high.

  Weyl was not as nice when it came to the inequality which I had discovered in Madison. He and Levinson had become interested in the result which had generated this inequality and in 1946 published papers in the American journal of Mathematics on this subject. I went to Weyl very diffidently and showed him my paper of 1943. He said casually that he had known the result for many years, back in Zurich.

  I vowed then and there that I would never treat a young mathematician this way. I complained about this to Lefschetz. His name for Weyl was “Holy Herman”.

• Before the war, a Russian paper had a complete translation in French, German, or English with an abstract in one of these languages.

  It was clear that I learn how to read Russian or else I would be cut off from a very important source.

  I use the Shleimann technique. I took a book which I knew well, Bernstein, “Lecons sur Meilleure Approximation” which had a Russian translation. Using the Russian translation, the French original, and a dictionary, I went through the text word by word.

• Lefschetz taught me a great deal about how to handle committees. For example, he would often put very trivial material at the top of the agenda and discuss it in detail. After several hours, he would say, “I will handle the rest of the material.” I have often used this trick myself.

• Playing with Chevalley one never won a game. If one had a winning position Chevalley would sweep the pieces off and start a new game. If one had a losing position Chevalley insisted that the game be played out.

• Bohnenblust was also a very good mathematician. He knew many fields of mathematics and could produce very elegant proofs of many results. He was a fine teacher. However, he was not a creator, a “selfstarter” in Lefschetz’ words. His notes on real variables were a bible for the graduate students.

• Wigner was saved from the Nazis by von Neumann who went to the Princeton authorities and had his salary cut in half so that Wigner could be invited

• Hua give several lectures on his extension of the work of Vinogradov.

  Hua went back to China when the communists took over and became a top scientific man. He was reported shot in various purges but always survived.

• Selberg had made an essential step forward and told this result to Erdős. They went home and were able to push the result through to obtain the complete theorem. The next day Selberg obtained an independent proof, using a different method.

  They were supposed to write a joint paper. Somehow this did not happen. Selberg wrote his paper, then Erdős in self defense was forced to write his.

  It became a matter of national honor. In the Scandinavian books, it is called Selberg’s theorem, in Hungarian, it is called Erdős’ theorem.

• Ernst was Einstein’s assistant, and thus I had access to Einstein whenever I wanted. However, I didn’t feel it was right to bother him since I was not interested in relativity theory, Zionism, didn’t play the violin and spoke execrable German.

  Characteristically, Einstein took the small office and gave the large one to Straus.

  Einstein said that there was no difficult mathematics, only stupid mathematicians. I think that the history of mathematics is on the side of Einstein.

  Einstein’s next assistant was John Kemeny. Now John is president of Dartmouth.

  (Like Eugene Wigner, John Kemeny was one of the “Martians” and he developed BASIC.)

• the only graduate student who had been kept on (at Princeton) was Tukey, and that was only half time.

• He (Lefschetz) was indignant, and wrote an outraged letter to Steinhardt accusing him of stealing his graduate students. As a result of this, Lefschetz got together with Tucker and they gave me a permanent position at Princeton as an assistant professor.

  But, I was not happy. I felt that Princeton was not a good place for a young mathematician. I wanted to work on problems which had a high probability of remaining unsolved. There was too much pressure that came from the Institute where there were many fine mathematicians and the pressure was overwhelming.

  Gábor Szegő offered me an assistant professorship at Stanford. I pointed out that I was already an assistant professor at Princeton. The next day he called again and offered me an associate professorship, which I accepted, provided that Princeton did not meet the offer. Princeton, of course, did not want to make me an associate professor, so at twenty-eight I was associate professor at Stanford at $5,000 per year.

  Lefschetz, Tucker, Wigner, and others thought that my leaving Princeton to go to Stanford was a serious mistake. But, I was firm, and we took off. I knew that this would hurt Lefschetz a great deal, and I was very unhappy about this. However, I felt it was the right thing to do.

Chapter 10: RAND, summer of 1948

• RAND is an acronym, standing for “Research and New Development”. A common joke is that it really stands for “Research and No Development”.

• The mathematics division, for example, had George Brown, Abe Girschick, Ted Harris, Olaf Helmer, Alec Mood, Ed Paxson, Lloyd Shapley, and others. The physics division had people like Herman Kahn, Dick Latter, and Jess Marcum; in social sciences there were people like Herb Goldhamer, and many others. It also had a very active summer program. Mathematicians like Beckenbach, Blackwell, Bohnenblust, Dantzig, Karlin, LaSalle, Tukey, Youngs, Widder and others came; mathematical economists like Arrow, Marshak, and Morganstern and Shubik were there; philosophers like Abe Kaplan worked on various problems; psychologists like Bales gave lectures.

• (Emile) Borel had worked on the theory earlier, unknown to von Neumann and had a partial proof of the principal result. Unfortunately, he made an arithmetical mistake and thought he had a counter example to the full result.

  (A little book about Borel, by Pierre Guiraldenq.)

• We (Ted Harris and Bellman) announced these results in the PNAS in 1948 and wrote a full paper for the Annals of Mathematics. We had the usual difficulties with referees. The third referee felt he owned one of the fields, and said that we had not given him sufficient credit. Actually, our results were quite different from his. However, when we saw his objections, we added a bit to the effect that this work was based on so-and-so’s work and then the paper was accepted.

Chapter 11: Stanford, 1948-51

• Bertrand Russell: Poverty is alright for artists and poets, but mathematicians need luxury.

• I believe very strongly in research programs and have always followed them.

  A friend got a summer position at an aircraft factory on Long Island in 1946 for the then magnificent sum of $35.00 a day. He reported bright and early on Monday and received a problem from the head of the section. Anxious to please, he stayed up all night Monday night and found a solution. On Tuesday morning, he came in, bleary eyed but triumphant, and showed his solution. The head of the section looked at the solution and groaned, “You have solved our summer problem.”

• As Galileo remarked, mathematics is the language of science, but, important clues about the behavior of various equations can be obtained by looking at physical processes.

• If you cannot stand the sight of your own blood on the page, don’t write.

• We often quoted to each other the well-known modification of the aphorism of G. B. Shaw, “Those who can, do; those who can’t, teach; those who can’t teach, teach teaching.”

• Henry (Scheffé) was an expert at mathematical statistics which had had a rough time at Princeton. He often complained about this.

  Lefschetz often remarked, “We have the mean and variance. What else do we want?”

• “Where did the name, dynamic programming, come from?” The 1950’s were not good years for mathematical research. We had a very interesting gentleman in Washington named Wilson. He was Secretary of Defence, and he actually had a pathological fear and hatred of the word, research. I’m not using the term lightly; I’m using it precisely. His face would suffuse, he would turn red, and he would get violent if people used the term, research, in his presence. You can imagine how he felt, then, about the term, mathematical. The RAND Corporation was employed by the Air Force, and the Air Force had Wilson as its boss, essentially. Hence, I felt I had to do something to shield Wilson and the Air Force from the fact that I was really doing mathematics inside the RAND Corporation. What title, what name, could I choose? In the first place, I was interested in planning, in decision-making, in thinking. But planning, is not a good word for various reasons. I decided therefore to use the word, “programming”. I wanted to get across the idea that this was dynamic, this was multistage, this was time-varying — I thought, let’s kill two birds with one stone. Let’s take a word which has an absolutely precise meaning, namely dynamic, in the classical physical sense. … Thus, I thought dynamic programming was a good name. It was something not even a Congressman could object to.

Chapter 12: Princeton – Project Matterhorn, 1951-52

• I saved it for exercises for a later book. I used this technique frequently when I didn’t want to spend time on an interesting subject which was unrelated to my directions of research at the moment.

Chapter 13: RAND 1952-65

• I had to face the fact that I couldn’t do what I wanted to do. Possibly the state of mathematics did not allow this. Certainly, my state of knowledge was not up to it.

  I could either be a traditional intellectual, or a modern intellectual using the results of my research for the problems of contemporary society. This was a dangerous path. Either I could do too much research and too little application, or too little research and too much application.

  At RAND, I would have time for all this without any obligations of teaching, committee work, or contract proposals.

• My first task in dynamic programming was to put it on a rigorous basis. I found that I was using the same technique over and over to derive a functional equation. I decided to call this technique, “The principle of optimality”.

• Work on problems involving constraints had been done at the University of Chicago years before. For example, Magnus Hestenes had discovered what had become known as the Pontryagin Maximum Principle. Will Karush had discovered what had become known as the Kuhn-Tucker condition.

• With John Danskin we did a survey of the field (time-lag processes)

• a comment made by Felix Klein, the great German mathematician, concerning a certain type of mathematician. When this individual discovers that he can jump across a stream, he returns to the other side, ties a chair to his leg, and sees if he can still jump across the stream. Some may enjoy this sport; others, like myself, may feel that it is more fun to see if you can jump across bigger streams, or at least different ones.

• when working in the field of analysis it is exceedingly helpful to have some underlying physical processes clearly in mind.

• There are several ways in which a mathematician can proceed to extend his research efforts, particularly one who is deeply interested in problems arising from the physical world. He can, on one hand, examine the equations he has been working with and modify them in a variety of ways. Or he can ask questions that have not been asked before concerning the nature of the solution of the original equations.

  The well-trained mathematician does not measure the value of a problem solely by its intractability. The challenge is there, but even very small boys do not accept all dares.

  sidestep the equation and focus instead on the structure of the underlying physical process. How realistic were these assumptions? What state variables, and what effects did I ignore? …

• The Riccati equation plays an essential role. I had observed this but had published little on it, saving it for Norman for a Ph.D. thesis. Unfortunately, he decided not to go ahead. In the meantime, others, like Rudy Kalman, had observed this, and published various results.

  (Rudolf E. Kálmán is another “Martian”.)

• far more ability and sophistication is required to obtain a numerical solution than to establish the usual existence and uniqueness theorems. It is far more difficult to obtain an effective algorithm than one that stops with a demonstration of validity. A final goal of any scientific theory must be the derivation of numbers.

• The book (Applied Dynamic Programming) was dedicated to von Neumann. Stuart had wanted to dedicate the book to his mother. When the book was translated into Japanese, I wrote to the publishers and asked that the dedication read to John von Neumann and Stuart’s mother. I figured that this would be a good joke on Stuart. He certainly would not believe me, and would ask others who knew Japanese to translate the dedication. However, when they translated, he would think I had gotten there ahead of him, and finally he would have to learn some Japanese himself.

  Unfortunately, the publishers would not do that. I got back a letter saying it wasn’t customary in Japan to dedicate a book to a woman.

• Stuart Dreyfus was so bright that I wanted him to get a Ph.D. I used my influence at Princeton to have him admitted to the graduate school. After one year at Princeton, he transferred to Harvard and got his Ph.D. in a program of applied mathematics there, under Bryson. It reminds one of the old joke about the student who flunked out of Princeton and went to Harvard, thereby improving the academic level of both institutions.

• About twenty years ago, some people decided they were going to stake out the field of artificial intelligence. They proudly planted their flag and they loudly claimed that they had computer programs which would think, create, compose music, play chess, invest in the stock market, translate languages, prove mathematical theorems, and so on and so on.

  (Who’s the joke now?)

• I felt strongly that matrix theory was the arithmetic of advanced mathematics.

• the name index (referring to the book Algorithms, Graphs and Computers) for dynamic programming has Oveta Culp Hobby. If one looks on the appropriate page there is no mention of Oveta Culp Hobby. There is an exercise dealing with the preparation of vaccine. The story is the following. At that time, the Salk vaccine for poliomyelitis was perfected. Canada had enough vaccine for everybody. United States, which is far richer did not have enough. When Oveta Culp Hobby, then Secretary of Health, Education, and Welfare, was asked about this, she responded with the classic remark, “I didn’t know that poor people cared that much about their children.”

• Niels Henrik Abel: Read the Masters, not the pupils.

• Incidentally, one of the most valuable things that a senior mathematician can do is to guide younger mathematicians into meaningful theory and problems. For example, Weyl suggested to von Neumann that he could handle the ergodic theorem by means of his methods.

• The trigger was a postcard from Joel Franklin. He had been on a plane which had encountered some turbulence. To avoid the turbulence, which was uncomfortable for the passengers and dangerous for the plane, the pilot had changed course. Being a mathematician, Joel immediately thought of the problem of tracing a path of shortest length through a finite network. This was the problem he posed to me.

• Hans Bethe deserves a statue in every public square in every city. He gave up his scientific career to systematically show the mistakes and omissions in Teller’s argument. He effectively neutralized Teller.

• Often the objective of an investigation was to obtain an approximate value for a parameter. If we could start sufficiently close, there was no need for any further investigation.

  (Clearly, Bellman was not a fan of asymptotic or local convergence.)

• However, we were not prepared for the asininity of the educational establishment which gave up the alphabet in favor of hieroglyphics. … After several years, when it became imminent that this technique didn’t work it was given up. In the meantime, hundreds of thousands of students had been ruined.

• The airlines made every effort to make flying attractive. Someone even got the bright idea to write a letter to the wives afterwards. They stopped this in a hurry when they got back letters which said that the wife had never flown.

• A friend who worked in an aircraft factory said it was a good idea never to take a new plane until there were three crashes to eliminate all the bugs.

• Academic Press had been Academische Verlag. Hitler had confiscated the press and had driven out the owners.

• I am sorry that I didn’t keep all the referees’ comments. Some of them were helpful, but in general they would make a fine study of psychopathology.

• the associate editors would have the privilege of sending in a paper directly for publication. However, their name would appear underneath the author’s name, reading “submitted by … "

  (Some journals do this, but I didn’t know this was Bellman’s idea.)

  I chose, “Journal of Mathematical Analysis and Applications”, JMAA.

  (A respectable journal that is well worth reading, sometimes.)

• Mr. Jacoby was a charming gentleman of the old school and I greatly enjoyed our discussions. In particular, he showed me some pornographic poetry in Latin that Leibniz had written.

• (Norbert) Wiener was quite discouraged and wanted to know whether he had really done anything significant. I have always been a great admirer of Wiener and knew his work well. I convinced him that his work was fundamental and that he would be an immortal. During their lifetime, von Neumann had a greater influence. However, I think that Wiener’s work is more important. In 100 years, Wiener’s work will be remembered and I don’t think von Neumann’s will be.

  (Wiener is brilliant, but so is von Neumann? We have enough room for everybody.)

• The mathematical work at RAND made it world famous, and had a tremendous influence on research in this country and abroad. Ironically, there is no longer a mathematics division at RAND.

Chapter 14: Divorce and remarriage

• I knew enough not to take a drug where the dose was not known.

• Finally, in 1962, I left the house. I realized that Betty Jo and I were not good for each other. I knew this action would hurt Eric and Kirstie. As a matter of fact, the reason I had delayed in leaving was because of Betty Jo’s accident and because of the children. I felt, however, that the best example I could set for them was that each person should live his own life. I didn’t think they would be grateful later if I said that I had sacrificed my life for them.

Chapter 15: Guilt by association – 1954

• Bellman went through similar (spy) accusations as Oppenheimer. It didn’t help his case that he had learned to read Russian math papers and he lent his apartment to Greenglass (who took various secret papers from Fuchs to his wife who had then taken them to the Rosenbergs in New York). Eventually, the drama cost Bellman his job at RAND.

  While we are at this, let me also mention that Canada also wrongfully accused Israel Halperin, who improved von Neumann’s alternating projection algorithm to multiple hyperplanes. Tucker had worked very hard to establish Halperin’s innocence and to provide money for his family.

• Bellman had always been anti-communist.

  A man was crossing Union Square where a riot was in progress. The police were clubbing the rioters. As the man got closer a policeman started to club him. The man protested, “Don’t hit me, I’m an anti-communist.” The policeman clubbed him, saying, “I don’t care what kind of a communist you are.”

• No enemy agent could have caused so much damage. Why he (Joe McCarthy) had so much power, and why he was tolerated for so long, will interest social historians for hundreds of years. Incidentally, J. F. K. was one of the few senators who did not vote for the censure of McCarthy. He dodged the issue by spending a few days in the hospital claiming his back was acting up.

• It was interesting to see the reaction of various people at RAND. Some avoided me like the plague; some went out of their way to invite me to parties. I remembered who did what.

• Bellman had this to say about (Richard) Courant:

  Courant was a rare combination of a fine mathematician and a fine administrator. In addition, he knew how to handle young mathematicians and had helped many of them.

  (A bit strange to me: Did Bellman know Herbert Robbins who “coauthored” the book What is mathematics with Courant?)

• I was quite friendly with von Neumann at that time. However, he had just become an AEC commissioner and I thought that this contact would embarrass him. Consequently, I avoided him on his visits to RAND.

• Those were dangerous times. Everyone who wrote a letter was well aware of the danger. They felt, like I did, that it was a time to stand up and be counted.

• The hearing ended on a friendly note. One of the board members was an engineer who wanted to know about dynamic programming.

• In those days, this was the basis for a charge of guilt by association.

Chapter 16: USC 1965

• There had been some talk over the years about making RAND into a university, but nothing came of it.

• He asked Egeberg whether any committees had to be consulted. Egeberg laughed and said the committees would agree to anything he thought was right. And that is how I became a professor of mathematics, engineering and medicine at USC.

• One had to expect that many promising directions will not pan out.

• Most Ph.D.’s were unable to find positions. Chris had three offers. The point is that there is always a job for a person who fills a need. The reason that most of the other Ph.D.’s could not find positions was that there was no need for them. Many professors pay no attention to this. They are rather callous about what happens to their students after they got their degrees. I have always felt that a subject should be studied with a position in mind.

• When I lectured I always gave the material from a new point of view. It was seldom that I didn’t get several ideas this way.

• Bruce Waxman at NIH was willing to give me five million dollars worth of computer provided it was IBM. Topping, probably under pressure from the board of trustees, wanted the computer to be Honeywell. This went on for several months and finally I had no computer. I did not want a Honeywell computer since I felt that the students would receive training in a computer which was not very common.

• I had done some work on learning processes in the early days of RAND, but I got seriously interested when I came across a paper by W. R. Thompson. This was devoted to the interesting question of how one introduces a new drug. I came across the paper in the usual way, by accident. I was looking through the American journal of Mathematics for a paper on analytic number theory when I spotted this. Since the title was “A Problem of Apportionment”, I was curious to see what anybody was writing on that in 1934.

  I finally decided to treat learning as changing an initial probability distribution on the basis of observation.

  the evolution of consciousness as a control process for overriding instinct.

• (Edward) Teller was mentioned a few times briefly, mainly as a maniac pushing for more nuclear tests.

  (There are some fine biographies on Teller, for another day.)

  On one hand, it is important to have weapons to deal with Russia. On the other hand, we have many other things to do with money. Consequently, there is no point in having too many weapons.

Chapter 17: The Center 1969-75

• it is always dangerous to interpret the results of a simple model for a complex society.

Chapter 18: Travels

• There is no Nobel prize in mathematics. Niels Bohr had a very simple explanation for this. He said that Mittag Leffler had seduced Nobel’s wife. When it was pointed out that Nobel never had married Bohr said, “Never let facts interfere with a good story.”

  The true story is the following. When Nobel got the idea of giving prizes, he went to Mittag Leffler, the leading man of Swedish science and a very well-known mathematician, to discuss it. Mittag Leffler thought the idea was bad and said so. Nobel went ahead anyway. But he was so incensed at Mittag Leffler’s attitude that he wanted to make sure that no prize be given for work in theoretical physics because he was afraid that Mittag Leffler would get a prize that way.

• Tukey used to stand up in front of the speaker if he spoke too long.

• Fortet had written an interesting paper on connections between dynamic programming and the principle of Fermat. Conversely, one can use dynamic programming for the minimum principles of mathematical physics. For example, with dynamic programming one has a very simple derivation of the eikonal equation. In addition, the Hamilton-Jacobi equation of mechanics can easily be derived.

• Jacques Lions was the head of the mathematics section of IRIA. They (Bob Lattes and Lions) wrote a book which I translated into English for my Elsevier series. It was on improperly posed problems, a topic which has always interested me.

• (Yakov Zalmanovich) Tsypkin had survived the war. The Russians had a very simple method for clearing mine fields. They used the first wave of the infantry. When infantrymen were too valuable, they used a special contingent for this purpose. Tsypkin had been in this contingent.

  (Polyak and Tsypkin wrote several papers on pseudogradient adaption and learning. One of their students is Alexandre B. Tsybakov.)

• Sunji Osaki described what he wanted in a wife. He went on and on about the virtues he required. Finally, this was too much for Yoshiko. She said, “Sunji, why do you think you deserve all this?”

• Bellman’s second mother-in-law, Andrea Day, was brought up in China. Chinese was her first language. Andrea was born in Kentucky but at the age of two her parents went to China. Her father founded schools throughout China. Her father sang at Chiang Kai-shek’s wedding and her mother played the piano.

• Bellman received an honorary doctor of Math from Waterloo in 1975.

To Read

• Bellman, R. and R. Kalaba (2017). Classic Papers in Control Theory. Dover (reprint).
• Bellman, R. and G. M. Wing (1992). An Introduction to Invariant Imbedding. SIAM (reprint).
• Bellman, R. (2003). Dynamic Programming. Dover (reprint).
• Bellman, R. and S. Dreyfus (1962). Applied Dynamic Programming. Princeton.
• Bellman, R. (2013). Stability Theory of Differential Equations. Dover (reprint).