A conference was held recently at the
University of New South Wales to celebrate the ninetieth birthday of well-known
local mathematician George Szekeres (pronounced roughly ‘sack-er-ash’).

The conference took place over two
days in late May; the first day concentrated on combinatorics, the second
day on number theory. These have always been favourite areas of research
for George. Eminent mathematicians from around the world were invited to
speak about recent developments, and

about the problems in each area that George contributed to in such a formative
way. The speakers included Vera Sos, Bela Bollobas, Ronald Graham, Alf van
der Poorten, and John Coates, all of whom have been colleagues or students
of George through the years. Each speaker also shared warm recollections
of their experiences with George, and of their knowledge of him as a person.

George Szekeres was born in Budapest,
Hungary, in 1911, and his gifts in science and mathematics were soon apparent.
An important influence during his high school career was the journal ‘Középiskolai
Matematikai és Fizikai Lapok’, which provided mathematical problems
and enrichment. (George was much later instrumental in establishing a similar
high school mathematics journal ‘Parabola’ in Australia.) George
went on to study chemical engineering at the Technological University of
Budapest, to contribute to the family’s leather business. During his
time at university, he often met with a small group of enthusiastic students,
drawn from the ranks of the ‘Lapok’ problem-solvers, to pose mathematical
problems and discuss solutions. The group was simmering with talent, including
Paul Erdös and Paul Turán, both outstanding mathematicians of
this century. Also attending was Esther Klein, who has lectured on geometry
at NMSS on two occasions, and whom George would marry in 1937.

Towards the end of the 1930s, life
was becoming increasingly difficult for Jews in Hungary. George and Esther
eventually found it necessary to leave, and moved to Shanghai, where their
son Peter was born in 1940. George worked as a leather chemist there, and
later as a clerk in an American air force base. In 1948 George accepted
an offer of a lectureship at the University of Adelaide. He remained there
for fifteen years, during which time their daughter Judith was born in 1954.
In 1963, the family moved to Sydney (except for Peter who was studying physics
in London), where George had accepted a position at the University of New
South Wales as the Chair

of Pure Mathematics on the condition that he would not have to be an administrator.
Also in 1963, he was elected to the Australian Academy of Science, and awarded
the Academy’s Lyle Medal in 1968. George retired in 1976, but as Emeritus
Professor, his friendly face can still be found in his office in the mathematics
department at UNSW, several days a week. In Sydney, George has also been
a valued member of the amateur classical musical scene, playing violin and
viola in the North Sydney Symphony Orchestra and the Ku-ring-gai Philharmonic
Orchestra.

George’s original mathematical
output has continued through most of his adult life, beginning even during
his undergraduate days, and sustained right up until the present. His mathematical
interests are incredibly diverse, but there are several recurring themes.
One prominent topic is combinatorics, and there is at least one combinatorial
problem which has been a thread running through George’s whole life.
It was first posed by Esther in the early 1930’s, and was the subject
of a collaborative paper with Paul Erdös (‘A combinatorial problem
in geometry’, 1935). Erdös referred to this problem as the ‘Happy
Ending Problem’, because it had a happy ending namely George and Esther’s
marriage! The problem has yet to be fully solved, and George is currently
working on a computer search that

will test a particular special case. Besides combinatorial geometry, he
has also made contributions in the theory of partitions, graph theory, and
other areas of combinatorics. Another prominent topic in George’s career
is general relativity; George is perhaps best known for his role in developing
the mathematical theory underlying the study of black holes. He embraced
the computer age with enthusiasm, making early contributions to techniques
of numerical analysis, especially in the theory of computing high dimensional
integrals. More recently, his research interests include combinatorial geometry,
Hadamard determinants, and chaos theory.

I first met George Szekeres about two
years ago, when a lecturer at UNSW suggested that George might be able
to help me with a problem about random walks. He was indeed very helpful;
he showed me a general method of attacking such problems, and provided
much additional information. There were several things I learnt about
George from that first encounter. He enjoys discussing and working on
mathematics with people, no matter what their level of mathematical
development or formal attainment. The techniques he used to solve the
problem displayed a fantastic depth of

mathematical experience, which only such a long and dedicated career
can bring. Most importantly, George and Esther provide living proof
that old age is certainly no barrier for a sparkling, active intellect.
It is this last aspect of George’s life that inspires admiration
and optimism in everybody who knows him.

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