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Lipman Bers

Lipman Bers

Born: 23 May 1914 in Riga, Russia (now Latvia)
Died: 29 Oct 1993 in New Rochelle, New York, USA

Lipman Bers, always known as Lipa, was born into a Jewish family. His
parents Isaac Bers and Bertha Weinberg were teachers, his mother being
head at an elementary school in Riga where teaching was in Yiddish
while his father was head at the Yiddish high school in Riga. Born in
1914, Lipa's early years were much affected by the political and
military events taking place in Russia. Latvia had been under Russian
imperial rule since the 18th century so World War I meant that there
were evacuations from Riga. The Russian Revolution which began in
October 1917 caused fighting between the Red Army and the White Army
and for the next couple of years various parts of Russia came first
under the control of one faction then of the other. Lipa's family went
to Petrograd, the name that St Petersburg had been given in 1914 when
there was strong anti-German feeling in Russia, but Lipa was too young
to understand the difficulties that his parents went through at this

At the end of World War I in 1918, Latvia regained its independence
although this was to be short-lived. Lipa spent some time back in
Riga, but he also spent time in Berlin. His mother took him to Berlin
while she was training at the Psychoanalytic Institute. During his
schooling mathematics became his favourite subject and he decided that
it was the subject he wanted to study at university. He studied at the
University of Zurich, then returned to Riga and studied at the
university there.

At this time Europe was a place of extreme politics and, in 1934,
Latvia became ruled by a dictator. Lipa was a political activist, a
social democrat who argued strongly for human rights. He was at this
time a soap-box orator putting his views across strongly both in
speeches and in writing for an underground newspaper. Strongly opposed
to dictators and strongly advocating democracy it was clear that his
criticism of the Latvian dictator could not be ignored by the
authorities. A warrant was issued for his arrest and, just in time, he
escaped to Prague. His girl friend Mary Kagan followed him to Prague
where they married on 15 May 1938.

There were a number of reasons why Bers chose to go to Prague at this
time. Firstly he had to escape from Latvia, secondly Prague was in a
democratic country, and thirdly his aunt lived there so he could
obtain permission to study at the Charles University without having to
find a job to support himself. One should also not underestimate the
fact that by this stage his mathematical preferences were very much in
place and Karl Loewner in Prague looked the ideal supervisor.

Indeed Bers did obtain his doctorate which was awarded in 1938 from
the Charles University of Prague where he wrote a thesis on potential
theory under Karl Loewner's supervision. At the time Bers was rather
unhappy with Loewner [1]:-

Lipa spoke of feeling neglected, perhaps even not encouraged, by
Loewner and said that only in retrospect did he understand Loewner's
teaching method. He gave to each of his students the amount of support
needed ... It is obvious that Lipa did not appear too needy to

In 1938 Czechoslovakia became an impossible country for someone of
Jewish background. Equally dangerous was the fact that Bers had no
homeland since he was a wanted man in Latvia, and was a left wing
academic. With little choice but to escape again, Bers fled to Paris
where his daughter Ruth was born. However, the war followed him and
soon the Nazi armies began occupying France. Bers applied for a visa
to the USA and, while waiting to obtain permission, he wrote two
papers on Green's functions and integral representations. Just days
before Paris surrendered to the advancing armies, Bers and his family
moved from Paris to a part of France not yet under attack from the
advancing German armies. At last he received the news that he was
waiting for, the issue of American visas for his family.

In 1940 Bers and his family arrived in the United States and joined
his mother who was already in New York. There was of course a flood of
well qualified academics arriving in the United States fleeing from
the Nazis and there was a great scarcity of posts, even for the most
brilliant, so he was unemployed until 1942, living with other
unemployed refugees in New York. During this time he continued his
mathematical researches. After this he was appointed Research
Instructor at Brown University where, as part of work relevant to the
war effort, he studied two-dimensional subsonic fluid flow. This was
important at that time since aircraft wings were being designed for
planes with jet engines capable of high speeds.

Between 1945 and 1949 Bers worked at Syracuse University, first at
Assistant Professor, later as Associate Professor. Gelbart wanted to
build up the department at Syracuse and attracting both Bers and
Loewner was an excellent move. Here Bers began work on the problem of
removability of singularities of non-linear elliptic equations. His
major results in this area were announced by him at the International
Congress of Mathematicians in 1950 and his paper Isolated
singularities of minimal surfaces was published in the Annals of
Mathematics in 1951. Courant writes:-

The nonparametric differential equation of minimal surfaces may be
considered the most accessible significant example revealing typical
qualities of solutions of non-linear partial differential equations.
With a view to such a general objective, [Bers] has studied
singularities, branch-points and behaviour in the large of minimal

Abikoff writes in [1] that this paper is:-

... a magnificent synthesis of complex analytic techniques which
relate the different parameterisations of minimal surfaces to the
representations of the potential function for subsonic flow and
thereby achieves the extension across the singularity.

Bers then became a member of the Institute for Advanced Study at
Princeton where he began work on Teichmüller theory, pseudoanalytic
functions, quasiconformal mappings and Kleinian groups. He was set in
the right direction by an inequality he found in a paper of Lavrentev
who attributed the inequality to Ahlfors. In a lecture he gave in 1986
Bers explained what happened next:-

I was in Princeton at the time. Ahlfors came to Princeton and
announced a talk on quasiconformal mappings. He spoke at the
University so I went there and sure enough, he proved this theorem. So
I came up to him after the talk and asked him "Where did you publish
it?", and he said "I didn't". "So why did Lavrentev credit you with
it?" Ahlfors said "He probably thought I must know it and was too lazy
to look it up in the literature".

When Bers met Lavrentev three years later he asked him the same
questions and, indeed, Ahlfors had been correct in guessing why
Lavrentev had credited him. Bers continued in his 1986 lecture:-

I immediately decided that, first of all, if quasiconformal mappings
lead to such powerful and beautiful results and, secondly, if it is
done in this gentlemanly spirit - where you don't fight over priority
- this is something that I should spend the rest of my life studying.

It is ironic, given Bers strong political views on human rights, that
he should find that Teichmüller, a fervent Nazi, had already made
stunning contributions. In one of his papers on Teichmüller theory,
Bers quotes Plutarch:-

It does not of necessity follow that, if the work delights you with
its grace, the one who wrought it is worthy of your esteem.

In 1951 Bers went to the Courant Institute in New York, where he was a
full professor, and remained there for 13 years. During this time he
wrote a number of important books and surveys on his work. He
published Theory of pseudo-analytic functions in 1953 which Protter,
in a review, described as follows:-

The theory of pseudo-analytic functions was first announced by [Bers]
in two notes. These lecture notes not only contain proofs and
extensions of the results previously announced but give a
self-contained and comprehensive treatment of the subject.

The author sets as his goal the development of a function theory for
solutions of linear, elliptic, second order partial differential
equations in two independent variables (or systems of two first-order
equations). One of the chief stumbling blocks in such a task is the
fact that the notion of derivative is a hereditary property for
analytic functions while this is clearly not the case for solutions of
general second order elliptic equations.

Another classic text was Mathematical aspects of subsonic and
transonic gas dynamics published in 1958:-

It should be said, even though this is taken for granted by everybody
in the case of Professor Bers, that the survey is masterly in its
elegance and clarity.

In 1958 Bers address the International Congress of Mathematicians in
Edinburgh, Scotland, where he lectured on Spaces of Riemann surfaces
and announced a new proof of the measurable Riemann mapping theorem.
In his talk Bers summarised recent work on the classical problem of
moduli for compact Riemann surfaces and sketched a proof of the
Teichmüller theorem characterizing extremal quasiconformal mappings.
He showed that the Teichmüller space for surfaces of genus g is a
(6g-6)-cell, and showed how to construct the natural complex analytic
structure for the Teichmüller space.

Bers was a Guggenheim Fellow in 1959-60, and a Fulbright Fellow in the
same academic year. From 1959 until he left the Courant Institute in
1964, Bers was Chairman of the Graduate Department of Mathematics.

In 1964 Bers went to Columbia University where he was to remain until
he retired in 1984. He was chairman of the department from 1972 to
1975. He was appointed Davies Professor of Mathematics in 1972,
becoming Emeritus Davies Professor of Mathematics in 1982. During this
period Bers was Visiting Miller Research Professor at the University
of California at Berkeley in 1968.

Tilla Weinstein describes in [1] Bers as a lecturer:-

Lipa's courses were irresistible. He laced his lectures with humorous
asides and tasty tidbits of mathematical gossip. He presented
intricate proofs with impeccable clarity, pausing dramatically at the
few most critical steps, giving us a chance to think for ourselves and
to worry that he might not know what to do next. Then, just as the
silence got uncomfortable, he would describe the single most elegant
way to complete the argument.

Jane Gilman [1] describes Bers' character:-

Underneath the force of Bers' personality and vivacity was the force
of his mathematics. His mathematics had a clarity and beauty that went
beyond the actual results. He had a special gift for conceptualising
things and placing them in the larger context.

In [1] Bers life is summed up by Abikoff as follows:-

Lipa possessed a joy of life and an optimism that is difficult to find
at this time and that is sorely missed. Those of us who experienced it
directly have felt an obligation to pass it on. That, in addition to
the beauty of his own work, is Lipa's enduring gift to us.

We have yet to say something about Bers' great passion for human
rights. In fact this was anything but a sideline in his life and one
could consider that he devoted himself full-time to both his
mathematical work and to his work as a social reformer. Perhaps his
views are most clearly expressed by quoting from an address he gave in
1984 when awarded an honorary degree by the State University of New
York at Stony Brook:-

By becoming a human rights activist ... you do take upon yourself
certain difficult obligations. ... I believe that only a truly
even-handed approach can lead to an honest, morally convincing, and
effective human rights policy. A human rights activist who hates and
fears communism must also care about the human rights of Latin
American leftists. A human rights activist who sympathises with the
revolutionary movement in Latin America must also be concerned about
human rights abuses in Cuba and Nicaragua. A devout Muslim must also
care about human rights of the Bahai in Iran and of the small Jewish
community in Syria, while a Jew devoted to Israel must also worry
about the human rights of Palestinian Arabs. And we American citizens
must be particularly sensitive to human rights violations for which
our government is directly or indirectly responsible, as well as to
the human rights violations that occur in our own country, as they do.

Bers received many honours for his contributions in addition to those
we have mentioned above. He was elected to the American Academy of
Arts and Sciences, to the Finnish Academy of Sciences, and to the
American Philosophical Society. He served the American Mathematical
Society in several capacities, particularly as Vice-President
(1963-65) and as President (1975-77). The American Mathematical
Society awarded him their Steele Prize in 1975. He received the New
York Mayor's award in Science and Technology in 1985. He was an
honorary life member of the New York Academy of Sciences, and of the
London Mathematical Society.

Article by: J J O'Connor and E F Robertson