Barry Simon, IBM Professor of Mathematics and Theoretical Physics at Caltech, is without a doubt a giant. He’s the Simon in Reed-Simon’s four-volume masterwork Methods of Modern Mathematical Physics, which has been cited over 21,000 times since it was published in the seventies; generations of physicists used his text as one of their standard references all over the world – it was so important that it was brought behind the Iron Curtain during the Cold War and translated into Russian so as to be used over there. On MathSciNet he’s second only to the French nonlinear PDE specialist Pierre-Louis Lions, who won the Fields Medal in 1994. On Google Scholar he has 75,112 citations from 755 publications, including a staggering 390 with 10+ and 289 with 30+ and 220 with 50+ and 127 with 100+ and 21 with 500+ and 10 with 1,000+ (none with 2,500+ aside from his textbook series, which means he “did it the hard way”, like Noga Alon). The Notices of the AMS talks about how “Barry Simon’s influence on our community by far transcends his approximately four hundred papers, particularly in view of 126 coauthors, 50 mentees, 31 graduate students, and about 50 postdocs mentored”.

Great statistics, all of them. But what does that look like in terms of personal anecdotes from the people he’s touched over the years?

I enjoyed this collection of reminiscences by his friends, colleagues and relatives on the occasion of his 60th birthday. Here are some of them. The most salient theme that emerges is that Barry is fast, really fast, at everything, and he was really good at multitasking (writing papers while listening to lectures and offering shorter proofs after their conclusion etc). He just has this tremendous dynamo of a brain.

Gary Chase:

As undergraduates at Harvard, several of us took the Real Variables course given by Professor Lynn H. Loomis. Loomis came to class with few or no notes and lectured fluently. One day he was writing a proof on the blackboard and paused briefly, scratching his head. He stepped back from the board and looked into the audience where he saw Barry. Loomis said “Are you thinking what I’m thinking?” and Barry said “Yes.” Loomis said “I thought so” and then went back and completed the proof. The rest of us had no idea what this thought was, since it was not verbalized by either of them! This incident was one of many that convinced us that Barry was uniquely gifted in such matters.

Yosi Avron:

At Princeton there were the lunch time seminars and the Math-Phys seminars. In the lunch time seminar, Barry was the prima ballerina. (Can you imagine Barry on his tiptoes?) He would normally either tell a new result of his or a new result of someone else. With Dyson, Lieb and Wightman in the audience, most grad students and postdocs, were too terrified to expose their slowness if they were to ask an innocent question. Most of the time, nobody dared open his mouth. The notable exception was the fresh grad student from Harvard, Alan Sokal, who never had a fear of authority and was sufficiently smart and self-confident to argue with Barry.

The math phys seminars were a different business. There was an outside speaker most of the time. Wigner would usually show up and ask his typical Wignerian questions. Barry would sit in the audience and write a paper. From time to time he would look up from his notes and ask a question that would unsettle most speakers: Someone in the audience seemed to know more about what he was talking about than himself. Sometimes, at the end of the talk, Barry would go to the board and give his version of the proof, which was always slick.

E. Brian Davies:

In 1983 Derek Robinson invited me to visit him at the Mathematical Institute in Canberra for a month. As one of the inducements he mentioned that he had also invited Barry Simon for the same period. The prospect of seeing Barry, Derek and kangaroos was enough to make my decision, and in July 1983 I set off on the gruelling journey.

I was very surprised shortly before my departure to hear from Derek that he was unable to avoid a commitment to go to a conference in Japan, and would not return until ten days after my arrival. Barry arrived about the same time as myself, and I asked him a problem about heat kernels of Schrodinger operators which I had solved in one dimension by a method that could not be extended to higher dimensions. At that time I had read several of the papers on hypercontractivity, a concept that was invented specifically to solve problems in quantum field theory, in which there are an infinite number of degrees of freedom.

Barry listened to my question carefully and agreed that some progress should be possible. The very next time I saw him he told me that he had solved the problem by an improvement of the standard hypercontractive estimates that made use of the finite dimensionality. He then proceeded, without notes, to give me a lecture on the subject, explaining every step in detail, including the infinite summation procedure that allowed one to pass from L² ® L^p bounds to L² ®  L^¥ bounds by controlling the constants involved.

Although very impressed, I had the temerity to suggest at the end of his lecture that although he had clearly done what was needed, I did not like his solution aesthetically, and would prefer an account that depended on differential inequalities. I had the feeling that this would yield better constants and be in some sense more natural. On the next occasion Barry rewrote the entire account in this language, and we realized that this was going to have enough ramifications to occupy the entire month. By the time Derek got back we were fully committed to the project, and I now feel embarrassed that I did not spend nearly enough time talking to him. Derek was, however, the person who coined the term ultra-contractivity, which was the focus of almost all of my research over the next ten years.

Juerg Froelich:

I first met Barry(-boy) in front of the conference building of the Les Houches summer school, back in 1970. He introduced himself like this: “Hi, I’m Barry Simon from Princeton University.” I must have replied roughly as follows: “Good afternoon,  Professor Simon. I guess I am Juerg Froehlich, a student from ETH in Zurich. How are you?”
This was to be the beginning of a wonderful friendship that has lasted to this day.

Barry was a very lively “student” at that famous Les Houches school (constructive quantum field theory and statistical mechanics). He was already pretty voluminous, physically, but also mentally, as he appeared to always know more than the lecturer. He was engaged in a friendly competition with Alain Connes, also a student at that school: The competition was about who of the two was faster in simplifying the proof of the lecturer or rendering it more elegant. I will only say that both of them performed admirably!

Barry was almost always writing some manuscripts, even during lectures. Nevertheless he appeared to always understand what was being taught to us. In the library, a new Simon preprint could be found every week – the school lasted for eight weeks. These preprints were handwritten. Some of them were co-productions with people like Graffi, Grecchi (Borel summability of the anharmonic oscillator), or the  late Raphael Hoegh-Krohn (hypercontractivity). These preprints were consumed like French croissants by the other kids (like myself), because they were very clearly written and not enormously technical and could therefore be understood by people whose level was not terribly advanced yet.

David Ruelle presented some rather qualitative lectures about statistical mechanics. (He likes to be qualitative and write only few formulae, in his lectures.) Barry asked him: “David, when are you going to start to do some serious work?” David replied: “Go to the library and read my paper about superstable potentials. This is as serious as I can get.” I imagine that the contents of that paper will appear in Barry’s second book on statistical mechanics that we are all awaiting impatiently.

Barry had wonderful qualities of all kinds! For example, he always applied for money from the NSF, not just for himself but also for Valja Bargmann and for me, and probably for further members of the club. And he apparently got the money. He was unbelievably well organized and efficient! He would always write the paper when the research was done, and he did it in five percent of the time ordinary mortals need to write such papers. I once told Barry that I always wanted to be at a department with a colleague like him, who takes care of essentially everything and doesn’t forget anything. He said: “Juerg, I only know one place where you could have a colleague like me.” (He had already moved to sunny California.)

Fritz Gesztesy:

Barry’s lightning mental agility, his extraordinary talent to strip the unnecessary clutter surrounding an argument, getting straight to its core, and his remarkable ability to see connections to related topics other than the obvious ones in question, are legendary…

The following observations will sound familiar to many of us:

Scenario #1: You joyously walk into Barry’s office to present him with a new idea, just to exit a few minutes later, your idea having been shred to pieces. “Back to the drawing board” is sometimes his comment, with a broad grin on his face. All this sounds more cruel than it is: After all, you have just been saved from going down a cul-de-sac and you can start regrouping!

Scenario #2: You proudly walk into Barry’s office to show him something new. Barry thinks for a second, then jumps up to the blackboard and explains to you in no uncertain terms what you “really had in mind.” That’s great, because at this point you realize a joint paper will eventually be written.

Scenario #3: You march into Barry’s office and this time you’re convinced you have a blockbuster at your fingertips. You start to explain to Barry, and then he says “time out” and silence fills the room. After a bit of eerie silence you realize this time you’re going to write a very nice joint paper with Barry. Of course, after a few more moments scenario #2 will be repeated, but that’s quite alright!

Scenario #4: Barry asks you into his office and explains what he was struggling with lately. (He likes to put it this way, though: “I was banging my head against the wall about this…”) After he suggests jointly working on this you return to your office with a big puzzle in your hands. Those rare instances in which you can actually do the job asked of you and complete the argument are priceless.

Barry likes to pick on me since I’m usually not afraid of computing anything, well, almost anything (while he doesn’t have the patience to do so!). So once in July of 1997, he confessed to me that he had a terrible contradiction in his long manuscript on “The classical moment problem as a self-adjoint finite difference operator” (it later appeared in Adv. Math. 137, 82–203 (1998)), but he just couldn’t find the error. So I was supposed to look at this. It was an intricate puzzle! I spent a day on it and well after midnight was sure I had found the error. So I e-mailed him what I thought was the culprit and slumped home to the apartment. Next morning I opened my e-mail and there was Barry pointing out that I was dead wrong. It was “back to the drawing board” as he still grinned during our brown bag lunch meeting that day. I was dejected! Well, I had another day before going away with my wife to Hawaii, and I was not about to let this ruin our vacation! So I frantically computed like a dog and finally saw the light: This was it! I decided to treat myself to dinner and left after e-mailing him my second attempt to find the culprit. After returning from dinner late that night, I had received quite a different message from Barry. It started out: THANK YOU, THANK YOU, … and went on like this for half a page.

Evans Harrell:

One of the rare categories in which I can compete pretty well with Barry is in the execrableness of our handwriting. I was at MIT as a postdoc when we wrote our long paper on the Stark effect. Back in those days, one actually wrote articles by hand and a secretary, using a device called a “typewriter” turned them into manuscripts, leaving blanks for formulae to be inserted. As a lowly postdoc I didn’t get first pick of the secretarial staff, and the manuscript ended up in the hands of a well-intentioned but struggling secretary who would produce about one page per day, which was usually sent back multiple times with corrections, often amusing. One day a favorite adjective of Barry’s, “operator-theoretic,” came back as “operator neurotic,” and I knew the manuscript was taking its toll on her. With lots of encouragement and little gifts she finished the manuscript after months of work, as the term ended. But she didn’t return the next term — it was doubtless the last mathematical manuscript she ever typed.

Barry has always been remarkable for his vast knowledge of mathematics, so it was many years before I can recall ever telling him a published theorem he didn’t already know. One day I saw Barry in Princeton shortly after a meeting and told him about an old inequality for PDEs, which, as I could tell from his intent look, was new to him. I said, “It seems to be useful. Do you want to see the proof?” His response “No, that’s OK.” Then he went to the board and wrote down a flawless proof on the spot.

Ira Herbst:

Barry, Yosi Avron and I were working on magnetic fields. As everyone knows Barry is a very fast worker and he writes up his work even faster. Barry and Yosi felt we should write something and as usual I wanted to get more done first. One day the two of them arrived in my office and began trying to convince me again that we should write something up.  I protested, at which point Barry took his hand from behind his back and with a smile produced a manuscript which he had presumably written the night before.

Woody Leonhard:

Many of you know Barry from his academic work and community achievements. I have a rather, uh, different perspective. I had the distinct honor and privilege of co-writing a handful of computer books with Barry, including several Mother of All Windows books, and The Mother of All PC Books. 

I’ll never forget Barry’s squeals of delight when he found foolish inconsistencies in Windows, the way his voice would drop low – and he’d talk fast – when he was working through a particularly snarly problem, and the way he’d rub his hands with glee when a solution suddenly appeared.

Barry wrote about PCs with extraordinary clarity and wit. The Mother books became (in)famous for their casts of characters – no dry technical mumbo-jumbo here. My favorite character from the early Mother books was the eight-legged cockroach (and bug expert) known as Erwin. We gave Erwin the enviable assignment of pinpointing and explaining bugs in Windows, a task for which he was eminently qualified. 

Barry’s one of the most intensely intelligent people I’ve ever met – and delightful, in every sense of the term. Except for the puns. The puns were really, really bad.

Ed Nelson:

In the late 1960s, Barry was a graduate student in physics at Princeton and attended some courses I taught. I soon learned that I did not need to prepare with great thoroughness; it was enough to get things approximately right and Barry from where he was sitting would tell us how to get them precisely right. I miss Barry.

Barry received an ugly, uncivil letter from a mathematician complaining that he had not been given sufficient credit in a volume of Reed-Simon for his work on a certain topic. Barry responded with a dispassionate two-page letter calmly reviewing the entire history of the topic and the contribution of each person to it. He concluded the letter with a one-sentence paragraph: “I hope that you will receive this letter in the same spirit in which you sent yours.”

Shortly after moving to Caltech Barry came east for a visit. He said that someone had stolen his attaché case. When we asked whether he had lost anything of importance, he replied, “Only the paper I wrote on the flight.”

Once Barry wrote a paper on hypercontractive semigroups and when he got it back from the typist, every instance of “hypercontractive” was rendered as “hypercontraceptive”.

Peter Perry:

As an undergraduate I took Quantum Mechanics from Barry, little knowing that I would later wind up a student. At the same time, I was taking Functional Analysis from Ira Herbst. The Quantum Mechanics course met on Tuesdays and Thursdays and there was a break in the middle of the lecture. One day I had my copy of Methods of Mathematical Physics, Vol. I, Functional Analysis with me. Barry walked up to me during the break and broke into a big smile followed by mock indignation when he saw that I had a copy of Reed-Simon. “Don’t read that stuff!” he admonished me. “It’ll pollute your mind! It’s worse than comic books!” Long before Barry became a department chair he was already a master recruiter. Several years later, I had the good fortune to begin thesis work with Barry as a graduate student.

Beth Ruskai:

After he moved to Caltech, Barry invited me to spend a month there, which, I think, ended up as April, 1984. Since e-mail was not yet widely used, he phoned me in February to arrange times for us to talk before his schedule filled up. 

While I was there, I sat in on some of his lectures. One day he wrote a bound on the board and claimed it followed from the Schwarz inequality. I interrupted and said that was not true. He stopped, said “You’re right”, paused about 10 seconds and proceeded to give a different, correct proof of the desired bound. He did this so quickly, that I assumed the second argument was what he’d prepared and the first was the kind of blackboard glitch I often make. Later I learned that the incorrect Schwarz claim was in his Trace Ideals book, and he’d come up with a different argument on the spot.

Yakov Sinai:

In the mid-1970’s, Barry visited Moscow. One day he went into a store to buy some eggs. He handed over a 10 ruble bill to the storekeeper and said “Eggs” in Russian; it was the only word in Russian which he knew. She asked him whether he wanted to spend all 10 rubles (a considerable amount in those days) on eggs. But this was a different phrase which Barry didn’t understand, and in reply he just smiled his charming smile. She then gave him a check for a hundred eggs.

The following day, Barry gave a seminar at the university. It was his last day since he was leaving Moscow the next day. After his talk, he distributed the eggs among the participants. Following the American tradition, undergrads and graduate students received the largest number of eggs and professors received almost nothing.

I also enjoyed this issue of the Notices of the AMS, also celebrating Barry Simon’s contributions and impact.

Evans Harrell:

The very first article in Barry Simon’s publication list, which appeared in Il Nuovo Cimento when he was a 22- year-old graduate student, was concerned with singular perturbation theory. This paper showed that a certain regularized, renormalized perturbation expansion for a two-dimensional quantum field theory model converges with a positive radius of convergence. As Barry candidly admitted in that article, in itself the result was of limited significance, but in a subject for which at that time “all the mathematically suitable results…are of a negative nature,” it announced a new, more constructive era.

To the reader familiar with Barry Simon’s works on mathematical physics of the 1970s, it is striking how many of the hallmarks of his technique are already apparent in this first article. Before entering deeply into the research, Barry first carried out a thorough and penetrating review of the entire literature on the subject. This signature of his method was something those of us who were students at Princeton in the 1970s would witness every time Barry began a new research project: Seeing him emerge from the library shared by Jadwin and Fine Halls with a mountain of books and articles, it was humbling to realize that Barry was not merely brave enough to collect all of the knowledge about the next subject he wished to study, but seemingly overnight he would absorb it in detail and carefully assess each contribution for its mathematical appropriateness. True to form, in that first article, Barry laid out which claims in the literature were established with mathematical rigor, which were plausibly to be believed, perhaps with some extra attention to assumptions, and which were frankly dubious. Finally, Barry’s own way of formulating the problem was sparse and clear, and his reasoning incisive.

Percy Deift:

The 1970s were a very special time for mathematical physics at Princeton. The list of people who participated in math-phys at Princeton University in those years as students, postdocs, junior faculty or senior faculty, or just visitors for a day or two reads like a who’s who of mathematical physics. Leading the charge were Arthur Wightman, Elliott Lieb, and Barry Simon. But there were also Eugene Wigner, Valentine Bargmann, and Ed Nelson. And in applied mathematics, there was Martin Kruskal, still flush with excitement from his seminal work on the Korteweg-de Vries equation, and across the way at the Institute were Tulio Regge and Freeman Dyson, doing wonderful things. Barry was a dynamo, challenging us with open problems, understanding every lecture instantaneously, writing paper after paper, often at the seminars themselves, all the while supervising seven or eight PhD students.

I was one of those students. I had an appointment to meet with Barry once every two weeks. I would work very hard preparing a list of questions that I did not know how to answer. Say there were ten questions; by the end of the first ten minutes in Barry’s office, the first six questions were resolved. Regarding questions seven and eight, Barry would think about them for about two or three minutes and then tell me how to do them. Regarding questions nine and ten, Barry would think about them, also for about two or three minutes, and say, “I don’t know how to do them. But if you look in such and such a book or paper, you will find the answer.” Invariably he was right. So in less than half an hour, all my questions were resolved, and as I walked out of the door there was the next student waiting his turn!

Barry is one of the most prolific mathematicians of his generation. It was in the late 1970s, around the time that we were working on nonisotropic bounds for eigenfunctions, that I got a glimpse of the speed with which Barry did things. Soon after Volker Enss introduced his seminal time-dependent ideas on spectral theory and scattering theory, a few of us went to Barry’s house in Edison, New Jersey, to discuss a potential project inspired by Enss’s work. We spent the afternoon laying out in detail a list of problems that needed to be addressed and left in the late afternoon. The next morning Barry came into the office: Not only had he solved all the problems on our list, but he had in his hand the first draft of his subsequent paper [3]! We were overwhelmed. For a young person like me, this was most discouraging. And I was doubly discouraged: Barry was younger than I was!

Barry has many fine qualities as a colleague and as a researcher, but I would like to focus on just one of them, viz., Barry’s keen sense of fairness and correct attribution of results. People in orthogonal polynomials know well Barry’s insistence on calling the recurrence coefficients for orthogonal polynomials on the circle Verblunsky coefficients, in recognition of the almost forgotten seminal work of Samuel Verblunsky. But I would like to tell a different story. In the early 1980s Barry was in Australia, where he met up with Michael Berry, who was also visiting. Berry began telling Barry about some curious and puzzling calculations he had been making in quantum adiabatic theory. Barry immediately understood that what was really going on was a matter of holonomy, and with characteristic speed he wrote and sent off a paper to Physical Review Letters, pointedly titled “Holonomy, the Quantum Adiabatic Theorem, and Berry’s phase.” In this way, a major discovery that could quite easily have become known as “Barry’s phase” was fixed in the literature as “Berry’s phase,” and justly so.

Lon Rosen:

I must confess that my first meeting with Barry was far from auspicious. In 1967 I was in my first year of doctoral studies at the Courant Institute. Feeling isolated, I was reconsidering my decision not to have chosen Princeton for graduate school. I asked a friend to arrange a lunch meeting for me with a typical student of Arthur Wightman’s. I knew little about the “typical student” who was chosen (Barry Simon), although I was familiar with his name because Barry and I had both been Putnam Fellows in the 1965 competition.

Some typical student! He practically tore my head off. Whatever I said about my interests or ideas, Barry would trump it. I’d never met anyone else with such extensive knowledge, amazing recall, and proofs at the ready. I still haven’t. Thanks to Barry, I stayed put at Courant. Fortunately, James Glimm, who was to be my terrific thesis advisor, soon joined the faculty there. I learned later that Barry had been going through a rough patch in his personal and professional life around the time we met and that the fire-breathing dragon who had me for lunch was actually a gentle prince in disguise, if I may be permitted a fairy tale metaphor.

Three years later I gave a seminar at Princeton on the subject of higher-order estimates for the 𝑃(𝜙)^2 model. At the conclusion of the seminar Barry showed me a clever bootstrap trick that quickly established my most difficult estimate—or at least a weaker but perfectly acceptable version of it. I was grateful and revised the published paper accordingly.

This experience was not unique to me. As many speakers know, Barry’s rapid-strike ability could be unnerving at seminars. He would sit front row centre, working on a paper, only to surface with astute observations, counterexamples, or shorter proofs. This penchant for “tricks” arises, it seems to me, from Barry’s imperative to understand everything in the simplest possible way.

Mike Reed:

When people ask, “How long did it take for you and Barry Simon to write those four volumes of Methods of Modern Mathematical Physics?” I usually say, “About ten years,” since we started in the late 1960s when Barry was a graduate student and I was a lecturer at Princeton, and we finished in the late 1970s. Writing those books took 50 percent of my research time for ten years but only 10 percent of Barry’s research time, and that wasn’t because I contributed more—far from it. The reason is that no one works faster than Barry. He instantly sees the the significance of new ideas (whether in mathematics or physics), understands the technical structures necessary to bring the ideas to fruition, and immediately starts writing.

Barry’s legendary speed sometimes got him into trouble. I remember going to seminars at Princeton with Barry carrying new preprints from more senior mathematicians. As the seminar proceeded, Barry would read the preprint, absorb the idea, understand the correct machinery to prove a stronger result, and begin writing. No one is more generous than Barry at giving credit to others; he always does and did. Nevertheless, when Barry’s paper with a stronger result and a better proof would appear before the original result, the preprint’s author would sometimes have hard feelings. These feelings would usually dissipate when he or she actually met Barry and discovered how open and generous he is.

Of course, we were pleased and proud that so many colleagues and students found our books useful. We both still teach out of them and field email questions about the problems. Since we were so young when they were written, we got lots of funny remarks at conferences from mathematicians who didn’t know us, such as, “You can’t be the Simon who wrote those books; you’re too young,” and, “Hah! I always thought that Reed was Simon’s first name.”