From at-net@leeor.technion.ac.il Sun Feb 5 03:59:58 1995
From: Allan Pinkus
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Subject: AT-NET SPECIAL BULLETIN: Szego
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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
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