From at-net@leeor.technion.ac.il Sun Feb 5 03:59:58 1995 From: Allan Pinkus To: Multiple recipients of list Subject: AT-NET SPECIAL BULLETIN: Szego X-Comment: AT-NET -- Approximation Theory Network @ AT-NET @ AT-NET @ AT-NET @ AT-NET @ AT-NET @ AT-NET @ AT-NET @ ================================================================= Messages for possible distribution over AT-NET should be sent to approx@math.technion.ac.il (note NEW e-mail address) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ February 5, 1995, AT-NET Bulletin Szeg\H{o} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Dear Subscribers, Due to the length of this "announcement" by Paul Nevai, it was decided to send it out separately from the regular monthly bulletins. The Editors ######################### START ############################################# Dear Friends: G\'abor Szeg\H{o} was born on 1/20/95 (1895) in Kunhegyes, (amazingly still) Hungary, so the enthusiastic citizens of this small town of (approximately) 9000 souls organized a a little celebration on 1/21/95 (1995) which was endorsed and co-organized by the J\'anos Bolyai Society and the Hungarian Academy Sciences. So yours truly flew to Budapest on 1/19/95 BUT his plane did not succeed in landing. Because of the killing snow storm after 30 minutes of circling over Ferihegy (the airport in Budapest), our pilot took a U-turn and we ended up in Vienna. From Vienna we took a bus and within a less than 9 hour delay we finally arrived to Budapest. At 7:15 am on 1/21/95 a historic event happened: we established a new record for mpcm^3. Guiness, are you listening? For the uninitiate, mpcm^3 = mathematician per cubic centimeter. The following were packed in a fSoviet made Latvija minibus: P\'eter V\'ertesi, Cili Kulcs\'ar (aka Szabados), Gyuszi Katona, Vera T. S\'os, \'Akos Cs\'asz\a'r, Pista Vince, Gyuri Petruska, yours truly, and G\'abor Hal\'asz (in seating order). PUZZLE OF THE DAY: how many apcm^3 does that make (apcm^3 = member of the Hungarian Academy Sciences per cubic centimeter)? Yours truly, being a guest, had been provided the most space: I was given two seats and ended up with the biggest butt/back ache since there was a vertical shift between the two seats. Before you ask me why didn't I just sit on one seat, I add that the seats were sized to fSoviet standard which is about 60% of what people in the Western civilization would consider as minimally adequate. Amazingly, noone complained (but my butt). To get to the point, we also established a new cpcm^3 (cpcm^3 = caught cold per cubic centimeter). To my best knowledge, at least three of us are sick now, since, in case you did not learn in high school, the Latvija is unheated which probably makes it a great vehicle in the subtropical Latvia (notice difference in spellings) but not for Hungary which was recently promoted from the Balkans to Central Europe. Anyway, we made the (approximately) 150 km (roughly 93.225606 mile) trip southeast from Budapest to Kunhegyes in less than 2.5 hours and just arrived to be met in the city's Cultural Center (7, Liberty Square) by Mr. P\'al Baranya, the city clerk (the #2 person in the local government). Another amazing fact: after traveling 150 km in an almost straight line we have not left Hungary yet. We were quickly whisked into the VIP room where guess what was waiting for us. Hint: according to Pali Erd\H{o}s, TP (Paul Tur\'an) used to say that this substance goes into mathematicians and what comes out are theorems (BTW, I believe that TP was wrong although what comes out is still related to mathematics, more precisely to 3.14). The program started at 10 am (GMT+1) sharp. The gentleman as ever, \'Akos Cs\'asz\a'r was the master of ceremony and the introduction was made by Mr. Baranya. There were four speeches about Szeg\"{o}'s life so every aspect of it was repeated and analyzed four times from at least four (entirely) different points of views. The ailing Barna Sz\'en\assy's essay was read by Erzs\'ebet Dar\'oczy, n\'ee Kotora (I believe she is herself a historian of mathematics). Dick Askey's and Lee Lorch's speeches (which were translated into Hungarian) were read by Gyuri Petruska. My talk was a spiced up and updated version of my obituary article ``G\'abor Szeg\H{o}'', Magyar Tudom\'any {\bf 8-9} (1986), 728--736. (see also Nyelv\"unk \'es Kultur\'ank {\bf 65} (1986), 57--63). With the permission of Dick and Lee, I attach their talks at the end of this report. What I found incredible was the audience; over one hundred local people came to the celebration. I wonder how many would have come if this celebration were held in Palo Alto (population at least 6 times greater than that of Kunhegyes). I also point out that one single person knew in the audience where Palo Alto was (not counting the mathematicians) so I also gave a short course in geography (Kunhegyes, Szolnok, Budapest, Vienna, Berlin, K\"onigsberg, St. Louis, Palo Alto, just to name a few). The morning session ended at 12:18 pm (GMT+1) and the main event started soon. Yes, you guessed it right, I am referring to the lunch (free for VIP's) held in the local pub. Everything was fine. Even my vegetarian requests were attempted to be observed although I had difficulties explaining that neither chicken nor fish are really vegetarian (I mean the poor souls may be but consuming them is not a vegetarian act). Plenty of (free) drinks. I was sitting opposite from Mrs. Erzs\'ebet Ferencz, n\'ee Kocsis, the local school superintendant, who mentioned that there maybe a problem naming a street after Szeg\H{o} since the city council has accepted a resolution not to change the name of any existing street (yes, Virginia, in Hungary there used to be at least 10^4 Lenin Blvd's and such, and it took probably a (not so) small fortune to get rid of the past and put other equally shortlived politicians' names on them). What about a statue for Szeg\H{o}? No way. ``Until Leopold Fej\'er has no statue in Hungary, Szeg\H{o} will NOT get one either'' declared some big shot (somewhere in Budapest) who, I guess, controls who gets what in Hungary. I don't know whether or not Fej\'er's statue exists but according to some well informed sources (Vera S. S\'os and Gyuszi Katona) there is a bronze relief somewhere so at least Szeg\H{o} is qualified for one too. Alas, it's gonna cost approximately 2*10^5 forints which is roughly speaking equivalent to $1,851.8519. I immediately volunteered to help to get the money from my rich American friends. ############################### TIME OUT ################################### My dear (American or not) reader, I am now very serious. Please send me whatever you can afford, say $1 or $5 or $10 or $20 or $100 or more (in checks payable to Paul Nevai, Dept Math - OSU, Columbus, Ohio 43210-1174, U.S.A.) and I will make sure that all the money collected will be sent for some type of a memorial dedicated to G\'abor Szeg\H{o} in Kunhegyes. Depending on the money collected, I promise to add a substantial amount from my own resources. My final goal is in the neighborhood of 5K. ############################# EOF TIME OUT ################################# Now comes the main event in the main event: yours truly was presented with a LIFETIME MEMBERSHIP in the J\'anos Bolyai Mathematical Society and a diploma signed by its President (\'Akos Cs\'asz\a'r) and its Secretary general (Gyuszi Katona). It is like a dream came true. I mentioned this to Cili Kulcs\'ar as one of the things I most wanted in life. I really appreciate this. After lunch we went to see the Szeg\H{o} exhibit in the basement of the City Library. Among others, a number of letters by Peter Szeg\H{o} were on display. I noticed that Peter misspelled his father's name in one of the letters. It was typed "Gabor Szego" and the accents were inserted by hand BUT it became "Gab\'or". Well, I can't help, I even proof read cereal boxes these days. It was a marvelous job done by kids form one of the local elementary schools. For me the most touching was seeing a pair of benches from the local Jewish school from the very beginning of the century so that Szeg\H{o} himself may have sat behind them. As it turns out there were a couple of hundred Jews there up until 1944 when, thanks to our former sponsors, they were almost all murdered. Some later returned but now there is only one single Jewish family left in Kunhegyes. The Jewish temple is closed and its belongings were either moved to the Budapest Synagogue (Doh\'any street) or buried in the Jewish cemetery. PUZZLE: if you are the only Jewish family in a town then how do you keep up with the Greenbergs? The afternoon session consisted of a few short (15 mins max) talks about Szeg\H{o}'s influence on Hungarian mathematics. It was organized by G\'abor Hal\'asz. The speakers were G\'abor Hal\'asz, Gyuri Petruska, yours truly, and P\'eter V\e'rtesi. So who were the listeners? Besides us, mathematicians, a number of teachers from the local high school were present as well. Inequalities, power series, Szeg\H{o}'s theory, interpolation\dots Around 4:30 we were whisked back into the minibus/refrigerator Latvija but not before I grabbed the remains of the marvelous pastry (cheese rolls, cream puffs, etc.) which raised eyebrows among the local dignitaries not used to the idea of doggie bagging but my action was finally endorsed by the proud hostess. As it turned out these pastries later saved our lives on our long way back to Budapest in freezing rain. The driver had to stop regularly to de-ice the windshield and for 90% of the time he had zero visibility. Let's put this way, if you are a fan of the Yugo then you will love the Latvija. We got back to town at 6:56 pm (GMT+1). I can't speak for the rest of the crew but I am still sick (as of Sat Jan 28 09:22:02 EST 1995). (Added on Fri Feb 3 11:04:06 EST 1995: I am no longer sick.) I finish by thanking the great citizens of Kunhegyes and my fellow travelers for this wonderful day. Paul Nevai pali+@osu.edu Department of Mathematics nevai@math.ohio-state.edu The Ohio State University http://www.math.ohio-state.edu/~nevai 231 West Eighteenth Avenue 1-614-292-3317 (Office) Columbus, Ohio 43210-1174 1-614-292-5310 (Answering Machine) The United States of America 1-614-292-1479 (Math Dept Fax) ############################################################################# These are the talks by Dick Askey and Lee Lorch. Your job is to identify which one was written by Dick and which one by Lee. ############################### #1 ########################################## G\'ABOR SZEG\H{O}-ONE HUNDRED YEARS by mystery person #1 It is 100 years since G\'abor Szeg\H{o} was born and 80 years since the publication of his first paper. Before this publication he had already shown a strong talent in mathematics by winning the E\"otv\"os competition in 1912. His first paper contained the solution of a problem of George P\'olya. However, he had earlier, in 1913, published the solution of another problem of P\'olya. For the nonmathematicians it should be remarked that there are problems at various levels. Some, like those you did in school, are ones which everyone should learn how to do. Then there are contest problems, like those in the E\"otv\"os competition. These are harder and frequently require deeper insight than seems so at first reading. The problem of P\'olya which Szeg\H{o} solved and published in 1913 is an example of a harder type, which has long attracted prospective mathematicians. Hungary has long specialized in the use of problems to attract young students to mathematics, and other countries have learned from you and have contests of mathematics problems to encourage students to think harder than is needed for the typical school problem. The problem of P\'olya which made up Szeg\H{o}'s first published paper was an open problem and there is still great interest in extensions of Szeg\H{o}'s solution to more complicated problems of this nature. Since Szeg\H{o} had been a mathematical prodigy himself, he was an ideal person to be asked to tutor one of the great mathematical minds of this century, John von Neumann. Here is what Norman Macrae wrote in his book "John von Neumann". "Professor Joseph K\"ursch\'ak [of the Lutheran School in Budapest] soon wrote to a university tutor, Gabriel Szeg\H{o}, saying that the Lutheran School had a young boy of quite extraordinary talent. Would Szeg\H{o}, as was the Hungarian tradition with infant prodigies, give some university teaching to the lad? "Szeg\H{o}'s own account of what happened was modest. He wrote that he went to the von Neumann house once or twice a week, had tea, discussed set theory, the theory of measurement, and some other subjects with Jancsi, and set him some problems. Other accounts in Budapest were more dramatic. Mrs. Szeg\H{o} recalled that her husband came home with tears in his eyes from his first encounter with the young prodigy. The brilliant solutions to the problems posed by Szeg\H{o}, written by Johnny on the stationery of his father's bank, can still be seen in the von Neumann archives in Budapest." Macrae was wrong in saying K\"ursch\'ak was at the Lutheran School. He was a professor at the university. He was the appropriate contact between the mathematics teacher at the Lutheran School and Szeg\H{o}. Szeg\H{o} served in the army in the First World War, but continued to do mathematics, and received his Ph.D. in 1918 in Vienna. Fifty years later he returned to Vienna for a celebration of this, and I still remember how pleased he was with this when he described it to me a few years later. After temporary positions in Hungary, Szeg\H{o} went to Berlin in 1921. P\'olya was is Z\"urich and they started to work on a problem book. It turned out to contain too much material for one volume, so was published in two volumes. P\'olya wrote the following about their work together on these books. "It was a wonderful time; we worked with enthusiasm and concentration. We had similar backgrounds. We were both influenced, like all other young Hungarian mathematicians of that time, by Leopold Fej\'er. We were both readers of the same well directed Hungarian Mathematical Journal for high school students that stressed problem solving. We were interested in the same kind of questions, in the same topics; but one of us knew more about one topic and the other more about some other topic. It was a fine collaboration. The book `Aufgaben und Lehrs\"atze aus der Analysis, I, II', the result of our cooperation, is my best work and also the best work of G\'abor Szeg\H{o}." It is hard to argue with P\'olya's assessment about the quality of the problem books. They set a standard for others who would later write books of problems and no one has come close to the level achieved by P\'olya and Szeg\H{o}. Not only are their problems interesting and important, they build on each other, so that working the problems in a section allows the reader to grow and learn new mathematics and techniques. Szeg\H{o} spent more than ten years in Germany, first in Berlin as privatdocent and then in K\"onigsberg as professor. His first two Ph.D. students were in K\"onigsberg. He was a beloved teacher, and when the situation in Germany became hard and then impossible for Jewish mathematicians, and Jews in general, Szeg\H{o} was one of the last to suffer because he was so highly respected by students and colleagues. While in Berlin, he was awarded the Jules K\"onig prize in 1924. F. Riesz gave the report for the prize committee, and this is reprinted in Riesz's "Oeuvres completes". In 1934, G\'abor Szeg\H{o} moved to the United States, first to St. Louis, Missouri, where he taught for four years at Washington University, and then to Stanford, California, where he was chairman of the mathematics department for 15 years, building it into an excellent department. At Washington University, Szeg\H{o} wrote the other great book of his, the first and still the best book on orthogonal polynomials. The study of these polynomials started in the 19th century, and continues to the present. In the 1920's, Szeg\H{o} found a variant on the earlier work, and one of facts he discovered was eventually used in speech synthesisers. A Ph.D. student from Stanford, Paul Rosenbloom, wrote about life as a student under P\'olya and Szeg\H{o}. In addition to the mathematical education he received, Szeg\H{o} looked out for his cultural education, giving Rosenbloom a ticket to Bart\'ok's concert at Stanford. In 1952, Szeg\H{o} published an extension of his first paper. About this paper Barry McCoy wrote: "It is easily arguable that, of all Szeg\H{o}'s papers, `On Certain Hermitian Forms Associated with the Fouries Series of a Positive Function' has had the most applications outside of mathematics. In the first place, the problem which inspired the theorem was propounded by a chemist working on magnetism. Extensions of this work made by physicists have led to surprising connections with integrable systems of nonlinear partial difference and differential equations. \dots In addition Szeg\H{o}'s theorem has recently been used by physicists investigating quantum field theory." One way mathematicians are honored is to have something they discovered named after them. There is now the Szeg\H{o} kernel function, the Szeg\H{o} limit theorem and the strong Szeg\H{o} limit theorem, Szeg\H{o} polynomials orthogonal on the unit circle, the Szeg\H{o} class of polynomials. Another way we show that the work of a mathematician is deep enough to last is to publish their selected or collected works. Szeg\H{o}'s "Collected Works" were published in 1982. I first met G\'abor Szeg\H{o} in the 1950's when he returned to St. Louis to visit old friends, and I was an instructor at Washington University. Earlier, when I was an undergraduate there, I had used a result found by Hsu in his Ph.D. thesis at Washington University under Szeg\H{o}. This was in the first paper I wrote. While at the Univ. of Chicago in the early 1960's, Szeg\H{o} visited. I still remember seeing him at one end of the hall and a graduate student, Stephen Vagi, at the other end of the same hall. They walked toward each other and both started to speak in Hungarian. I am certain they had not met before, and I have always wondered how Szeg\H{o} recognized another former Hungarian. In 1972 I spent a month in Budapest and Szeg\H{o} was there. We talked most days, and though his health was poor and his memory was not as good as it had been a few years earlier, we had some very useful discussions. Three years earlier, also in Budapest, Szeg\H{o} had mentioned two papers of his which he said should be studied. I did not do it immediately, but three months later did. One contained the solution of a problem I had been trying to solve for three years. His paper had been written 40 years earlier. I learned from this that when a great mathematician tells you to look at a paper of theirs which they think has been unjustly neglected, one should do it rapidly. Szeg\H{o} left a memorial for us, his mathematical work. It continues to live and lead to new work. One of his main areas was orthogonal polynomials and this is now a very active field. I often regret that he is not here to appreciate all of the work being done on problems he started. ############################# EOF #1 ######################################## ############################### #2 ########################################## G\'ABOR SZEG\H{O}-ONE HUNDRED YEARS by mystery person #2 G\'abor Szeg\H{o} was a great mathematician. His profound contributions are gathered in the three large volumes of his Collected Papers (edited by Richard Askey) and in the six books he authored or co-authored. They influenced greatly the content and direction of both pure and applied mathematics. They will continue to do so in the long future. His writings, like his lectures and discussions, were lucid. They led directly and gracefully to the essence. The breadth, depth and precision of his knowledge of mathematics were legendary, but never paraded. He helped; he did not overwhelm. One story, presumably apocryphal, came to me from one of his contemporaries, probably Karl Loewner. The young Szeg\H{o} was undergoing his doctoral examination. From the examiners came question after question, all answered swiftly, completely and correctly --until one stumped him. Another professor turned to the questioner, saying that he found that question most intriguing but could not think of the answer himself, and asked his colleague for the answer. Came the reply:"I don't know. Had I known, I would not have bothered to ask." He was only twenty when he published a seminal paper in one of the world's most distinguished mathematical journals. By 1925 he had published thirty papers, all noteworthy. That same year witnessed the publication of the celebrated P\'olya-Szeg\H{o}, Aufgaben und Lehrs\"atze aus der Analysis." These two volumes changed the landscape of advanced instruction and research in mathematical analysis, becoming world-famous immediately. Translated into Chinese, English, Hungarian and Russian, they remain beacons today. The next year, only 31, he was appointed Ordinarius (Professor) in K\"onigsberg, heir to the mathematical legends Jacobi, Hilbert, Hurwitz, Minkowski, to the philosopher Kant, city of the artist K\"athe Kollwitz. Years later, he would become Head of the Mathematics Department at Stanford University, one of America's most famous universities, and develop that Department so dramatically that it became one of the world's meccas of mathematical analysis. From all this it would seem that his path was smooth, from one triumph to another. Yet the very opposite was the case. It required his strong character to preserve his mathematical talent and give the world his memorable contributions. Serving as a frontline officer in the Austro-Hungarian army in World War I, he worked on his doctoral dissertation. That massive slaughter, in G. H. Hardy's words, of young men sent off to die by old men, left a lasting impression on him. It may well have intensified the passion he lavished on mathematics his entire life. It certainly affected his view of society. He supported later World War II against fascism, seeing no alternative, but he was an outspoken opponent of the Cold War which followed it. He opposed the development, use or testing of nuclear weapons and sought to moderate the growing international tensions which could have destroyed humanity. There had been but few opportunities for mathematical employment in pre-World War I Hungary or in the post-war Horthy times, for both economic and political reasons. Like many other Hungarian mathematicians destined to become well-known internationally, he had to look abroad, first to Berlin, leading to the K\"onigsberg professorship in 1926. This distinguished post was to fall victim to the Nazi accession to power. The years of peaceful, productive scholarship soon were swept away. His life, those of his wife and two children, in danger, his post soon to be taken away, he had to flee abroad, this time to the US, there being no possibilities in Hungary or elsewhere where he had personal connections. The depression and the growth of anti-Semitism also in the US did not make the transition easy, for him or for the numerous other refugees. However, his reputation and personality led to a temporary position at Washington University (St. Louis) --outside the normal university budget. The local Jewish community provided much of the requisite financial support. His presence and work added greatly to the prestige of that university, badly in need of someone of his standing. Its subsequent development into an excellent mathematical centre owes much to the years he spent there. He published while there a string of papers and a book, quickly classic, on Orthogonal Polynomials, which has undergone four editions, many printings and translation into Russian. In 1938 came the call to Stanford University where he spent his remaining years, except for occasional leaves elsewhere. He seized the opportunity to expand the Department with appointments of world-famous scholars, bringing first his teacher, collaborator and friend P\'olya (a Hungarian working in Switzerland), then Loewner, Bergman, Schiffer and younger analysts. His personal productivity never slackened. His capacity for work rivaled his talents. But he was far from being merely a mathematical machine. He was a modest, good-humored man, devoted to family and friends, reserved but warm, a pleasure to be with, ever helpful to those in difficulty. A strong character, but not domineering, he possessed a considerable personal charm and a remarkably wide culture. Mathematics for him was not just his own research. Generous with his time and experience, he sought out young people with whom he shared his knowledge and guidance and whom he assisted in their careers. Well read in ancient and modern literature, he worried that scientists who did not read the humanities could be ensnared by demagogues. He never stinted in seeking help for those threatened by Europe's fascist storms. In the post World War II era he gave moral and financial support to victims of McCarthyism in the US. He rose to the defence of the eminent Uruguayan mathematician Jos\'e Luis Massera, now the holder of a dozen honorary doctorates, but imprisoned for nearly ten years while a military junta ruled his country. He opposed racism and sexism. When the first campaign began to end the discrimination against African-American mathematicians then routinely practiced by US mathematical organizations, he quickly lent his aid. He also took time from his busy schedule to spend time at a college for Black students, helping and encouraging them. In his Will, he left money to one organization dedicated to opposing racism and to another supporting civil liberties in the US. The Cold War repelled him. He opposed nuclear weapons and the whole atmosphere and policy which the Cold War engendered in his adopted country. He was not given to initiating campaigns on the various social issues which commanded his attention, but he never with-held his open moral and financial support. Never did he forget his country of origin. He visited it often, even during the long, trying years of his final illness. A number of his distinguished publications are in Hungarian journals up to the end of his research activities. He translated and prepared for publication the notes dated March 12, 1944, left by "the young and able Hungarian mathematician, E. Feldheim," to quote the footnote G\'abor Szeg\H{o} appended, "a few months before he became the victim of the terror of the Nazis." He invited Hungarian mathematicians to visit Stanford and was in all ways in constant touch with Hungarian mathematical life and personalities. It gave him great satisfaction when he was elected to the Hungarian Academy of Sciences. To the end of his life, he remained true to science, to peace, to human values, to friends. His birthplace, his native land, his adopted country, scientists everywhere, have ample cause to celebrate the life of this eminent scholar and fine human being. He has brought honour to all. I congratulate you for organizing this celebration and thank you for allowing me to be with you in spirit on this day. ############################# EOF #2 ######################################## Richard Askey G\'abor Szeg\H{o} Professor of Mathematics Department of Mathematics University of Wisconsin 480 Lincoln Drive Madison, WI 53706 U. S. A. askey@math.wisc.edu AND Lee Lorch Department of Mathematics & Statistics York University North York Ontario M3J 1P3 Canada lorch@mathstat.yorku.ca --------------------------------- End of AT-NET Bulletin **************************