Preface
This brochure gives a concise presentation of the past and the present of the
Alfréd Rényi Institute of Mathematics, birthplace of many important
scientific discoveries and venue of numerous high-level meetings of
mathematics. Besides an overview of the activities and the history of the
institute, you will find here information on our current members as well as
some former members and regular visitors whom we are proud of.
A first version of this text was compiled in 2000, on the occasion of the 50th
anniversary of the Institute. The present revised and updated version contains
a lot of additional information and we hope that it gives a faithful picture of
the Institute at the dawn of the third millenium.
1
A brief chronology of the Institute
1950 Founding of the Institute, under the name Institute for Applied
Mathematics of the Hungarian Academy of Sciences. Alfréd Rényi,
aged 29 at the time, is appointed as the first director.
1955 The name of the Institute is changed: it becomes the Mathematical
Institute of the Hungarian Academy of Sciences.
1958 The institute moves to its current premises.
1970 Death of Alfréd Rényi. László Fejes Tóth is the new director.
1983 László Fejes Tóth is followed by András Hajnal in the director’s chair.
1984 Paul Erdős, member of the Institute, receives the Wolf Prize in
Mathematics.
1992 Domokos Szász is appointed as the new director of the Institute.
1996 Gyula Katona becomes director of the Institute. Members of the
institute take an active part in the organization of the Second
European Congress of Mathematics, held in Budapest.
1999 The Institute takes up the name of its founder Alfréd Rényi.
2000 The Institute receives the grant “Centre of Excellence” from the
European Union.
2001 A new extension of the building of the institute is inaugurated, giving
rise to a great improvement in working conditions. A joint graduate
program is launched, in cooperation with Central European
University.
For a more detailed history, see the corresponding chapter in the second half
of this brochure.
2
Alfréd Rényi (1921-1970)
Born and educated in Budapest, he became a student of Lipót Fejér, and
wrote his dissertation in 1945 under the supervision of Frigyes Riesz. In 1946
he went to Leningrad (now Saint Petersburg) where Yu. V. Linnik and I. M.
Vinogradov were his advisors. His solution of
the so-called quasi-Goldbach conjecture in his
1947 thesis attracted considerable attention.
Partially due to this result, he became a
corresponding member of the Hungarian
Academy of Sciences in 1949. He received an
associate professorship at the Loránd Eötvös
University of Budapest in 1947, and a full
professorship in Debrecen in 1949. In 1950 he
was appointed as director of the Applied
Mathematical Institute of the Hungarian
Academy of Sciences. From 1952 on he was
also chair of the department of probability
Theory at Loránd Eötvös University. He kept
both positions until his death in 1970. He took
Alfréd Rényi
part in public life with amazing energy: he was
a member of the editorial board of several journals and secretary general of
the János Bolyai Mathematical Society. As director, he provided shelter at the
Institute for various prominent scientists who were persecuted after the 1956
revolution.
In his scientific work he made notable contributions to several branches of
mathematics. Some of his most important results concern probabilistic
methods in number theory (including a
breakthrough in Goldbach problems),
the development of the theory of
random graphs (jointly with Paul
Erdős), and the introduction of the socalled Rényi-entropy. The famous
Hungarian school in statistics grew out
from his work. His textbook on
probability theory, first published in
German and then translated into several
Alfréd Rényi
languages, has been in widespread use.
Aside of his theoretical work, he published regularly on popular mathematics,
and encouraged applications of mathematics. He was chair or co-chair of
3
numerous mathematical conferences, and was visiting professor at various
universities around the world. Through his students, his spirit is still alive
today.
For his contribution to the axiomatization and application of probability
theory he received the Kossuth Prize (the highest scientific prize awarded by
the government) twice: in 1949 and in 1954. In 1956 he became a full
member of the Hungarian Academy of Sciences. Two years after his untimely
death in 1970, the Institute founded a prize in his memory; since 1999 it also
bears his name.
Research at the Institute
Currently, researchers at the institute work in 10 research divisions, and some
of them also in smaller research groups focused on more special subjects. The
10 current research divisions are:
♦
♦
♦
♦
♦
♦
♦
♦
♦
♦
Algebra
Algebraic Geometry and Differential Topology
Algebraic Logic
Analysis
Combinatorics and Discrete Mathematics
Convex and Discrete Geometry
Information Theory
Number theory
Probability Theory and Mathematical Statistics
Set Theory and Set-theoretic Topology
In addition, research groups on cryptology, database theory, mathematical
immunology and statistical physics are also active at the Institute.
Let us now briefly review the history and activities of the various research
groups.
The school in combinatorics is the first to be mentioned. As the result of the
work of Paul Erdős, Tibor Gallai, András Hajnal, Alfréd Rényi, Pál Turán,
Vera T. Sós and their students, the Institute (in close collaboration with
Eötvös University) has become one of the world centers in combinatorics.
Here is the birthplace of the theory of random graphs, of the so-called
probabilistic method in combinatorics, of basic results about extremal graphs
and extremal set systems, or the regularity lemma describing the structure of
huge graphs. Our researchers have achieved breakthrough results concerning
discrepancy, combinatorial methods in group theory, and in combinatorial
applications of entropy and graph entropy. Among the combinatorial
4
applications of theoretical computer science, important results have been
achieved in search theory, in the complexity of combinatorial algorithms, in
cryptology and in the combinatorial theory of databases (in cooperation with
the Computer and Automation Research Institute of the Hungarian Academy
of Sciences).
From the very beginning, number theory has also been one of the most
ardently cultivated areas of research at the Institute. A significant analytic and
additive number theoretic school was formed under the leadership of Pál
Turán, in close collaboration with researchers from Loránd Eötvös
University. Basic results about the Riemann hypothesis, the distribution of
prime numbers, multiplicative functions, dense sequences and probabilistic
constructions of number theory have been achieved by Gábor Halász, András
Sárközy, Endre Szemerédi, Imre Ruzsa and their collaborators.
The analysis group was founded by Béla Szőkefalvi-Nagy, the famous
functional analyst. Following the footsteps of Lipót Fejér, Gábor Szegő, Pál
Erdős, Pál Turán and Géza Freud, research in approximation theory and the
theory of orthogonal polynomials has been the main focus of analysts at the
Institute. They initiated lacunary interpolation within interpolation theory, an
area still active today. More recently, rational approximation and weighted
approximation have also been the object of thorough study.
Research in set theory and in mathematical logic has also been successful and
highly acclaimed. Outstanding results have been achieved in combinatorial
set theory, culminating in a monograph about the theory of partitions coauthored by András Hajnal,
former director of the
Institute and later director of
DIMACS in New Jersey,
Paul Erdős, and Richard
Rado.
Presently,
settheoretic
topology and
mathematical logic also
have active groups at the
Institute. During the last
decades,
Budapest
has
Handwritten notes by Paul Erdős
become an important center
for algebraic logic as well. This school continues related work by Alfred
Tarski exploring a flourishing connection between cylindric algebras and
logic.
5
Discrete geometry has become an independent discipline in mathematics as a
consequence of the work of László Fejes Tóth, another former director of the
Institute. Hungarian researchers have played an essential role in this process.
The discrete geometry group of the Institute, together with researchers from
Loránd Eötvös University, achieved significant results in the field.
Being the main area of research cultivated by Alfréd Rényi, the founder of the
Institute, probability theory and mathematical statistics have always been
present, with particular emphasis on applications. It was also Rényi who
started to work on information theory in his last years. Later the Information
Theory Division became famous under the leadership of Imre Csiszár. One of
the most significant results here was the elaboration of multiuser information
theory. The group’s work opened up new directions in the application of
information theory, notably in statistics (maximal entropy), in probability
theory (measure concentration, theory of large discrepancies), and in
combinatorics (graph entropy, graph conductivity).
The Algebra Division was formed about forty years ago by László Rédei. Its
research profile initially focused on group and semigroup theory, lattices and
universal algebra. This spectrum has gradually expanded with the
introduction of category theory, linear algebra and ring theory. Presently a
group working on asymptotic properties of groups is also very active at the
Institute.
Biometrics, the branch of statistics connected with medicine, has always
played an important role in the life of the Institute. Outstanding advances
connected with genetics and recognition of cancer cells have resulted from
statistical investigations conducted by Gábor Tusnády.
The founder of the Hungarian school in statistical physics is Domokos Szász.
The Institute has been one of the centers of this field. The main areas
investigated are the dynamic theory of Brownian motion, infinite differential
equations, and the mathematical foundations of the Boltzmann hypothesis. In
the latter area of investigation, work of researchers of the Institute has
produced breakthrough results. The 1979 Kőszeg conference in this area was
of essential importance; here researchers from the Soviet Union and from
Western countries worked together on the topic for the first time.
The group in algebraic geometry and differential topology is the youngest of
the Institute. It came into existence in 1998 when young researchers having
obtained their PhD from prestigious foreign universities launched a weekly
seminar. Members of the group are working on a wide range of topics in the
6
forefront of current research but previously not cultivated in Hungary,
including classification of algebraic varieties, singularity theory, the theory of
motives or low-dimensional topology.
Contributions to applications of mathematics
The Institute was founded as a research centre for applied mathematics, and
applications determined its main profile during the 1950’s. This included
close collaboration with industrial partners. Over the decades, the Institute’s
main focus shifted towards theoretical research, especially after the
foundation of the Computer and Automation Research Institute of the
Academy which took over several fields of research in applied mathematics
from the Institute.
Nevertheless, applications still play an important part in the Institute’s life.
Results of our colleagues working in information theory and database theory
are implemented in cryptography and computer science. Within statistics, preestimation of population size and other problems related to living organisms
are among the most cultivated areas of application at the Institute. In the
1980’s the Institute’s help was essential for the revival of a profession
forgotten in Hungary for over forty years: that of insurance mathematics. The
Institute also took an active part in preparing the reform of the Hungarian
pension system.
In collaboration with the Hungarian Oncology Institute, our researchers have
developed a computer program for recognizing cancerous cells. Another joint
project, developed together with ASK Ltd., was a device for cutting curtains,
presented at the 2000 World Exhibition in Hannover. Among ongoing
collaborations, the most important one is a joint project in cryptography
together with Hewlett Packard Hungary, aiming at the elaboration of “digital
watermarking”.
With the evolution of industrial applications in Hungary, it is expected that
there will be a growing demand for theoretical mathematics and its
applications. The Institute is ready for the challenge.
Scientific meetings at the Institute
Most of our research divisions run a weekly seminar for specialists in the
field during the academic year. These have met at the same hour for decades
now and form part of the Institute’s tradition; for instance, everyone knows
that Thursday afternoon is for combinatorics, or Monday morning is for
algebra.
7
About once a month, always on a Monday afternoon, a colloquium lecture is
organized for all members of the Institute and for interested visitors. The aim
of these lectures is to present significant results of researchers of the Institute
to a wider audience, and also to give an opportunity for prominent researchers
from Hungary and abroad to speak about less specialized topics.
Every two years, the Institute organizes jointly with the János Bolyai
Mathematical Society the Pál Turán Memorial Lectures. This is usually a
series of three lectures given by a famous expert active in one of the research
areas of the late Pál Turán: number theory, analysis or combinatorics. Recent
Turán lecturers include Hugh Montgomery, Peter Lax and Peter Sarnak.
Since the 1960’s, the Institute has been hosting and organizing international
conferences ranging from 2-day workshops devoted to a specialized topic to
large conferences with hundreds of participants. During recent years, the
largest meetings organized by members of the Institute were the 2nd European
Congress of Mathematics in 1996, whose organizing committee was chaired
by the director of the Institute, the 1999 conference on ‘Paul Erdős and His
Mathematics’, which had 450 participants from all over the world, and the
2001 Euroconference on ‘Finite and Infinite Combinatorics’. In September
2001, the Institute hosted a 3-week summer school and workshop in algebraic
geometry devoted to ‘Higher Dimensional Varieties and Rational Points’
which received an important European subvention, and in 2003 the Von
Neumann Centennial Conference on linear operators and the foundation of
quantum mechanics, co-organized by the Bolyai Society and the American
Mathematical Society. In June 2004, a 3-week workshop in low-dimensional
topology will take place at the Institute, organized jointly with the Clay
Mathematical Institute.
Apart from these large events, the Institute regularly hosts a number of
international conferences and workshops for smaller groups of specialists,
which since 1998 are grouped in a Turán Workshop Series in mathematics.
The webpage http://www.renyi.hu/old-conferences.html contains a list of
meetings organized at the Institute since 1999.
Visitors at the Institute
A part of the Institute’s activity which has been receiving increasing
importance during recent years is the hosting of visitors from Hungary and
abroad.
8
Each year, the Institute offers visiting positions for mathematicians working
at Hungarian universities, usually for a duration of 6 or 12 months, providing
them ideal conditions for conducting undisturbed research. In such a way, the
Institute has had a part in the achievement of several breakthroughs: for
instance, Miklós Laczkovich of Eötvös University proved Tarski’s conjecture
on the ‘squaring of the circle’ while a visiting researcher at the Institute.
The Institute has been receiving foreign scientists for short stays for decades
now, many of them regular visitors and close collaborators of our researchers.
During recent years, the number of foreign visitors plummeted and the
Institute can now host visitors for longer stays as well. Instrumental in this
change was the Centre of Excellence grant of the European Union, allotted to
the Institute between 2001 and 2003, which made possible the invitation of
33 scholars and post-docs for visits ranging from one month to a whole year.
This grant also contributed to the funding of 13 international conferences
organized during this period.
Another institution enabling the invitation of visitors and the organization of
workshops is the Paul Erdős Mathematical Summer Institute, founded,
jointly with the János Bolyai Mathematical Society and several universities,
in 1997. It is co-financed by the Hungarian Ministry of Education, the
Hungarian Academy of Sciences, Rutgers University (US), Microsoft
Research (US), and Lucent Technologies (US).
During the coming years, the Institute wishes to develop its international
contacts further, with the aim of becoming not only an important European
centre but also a well-known meeting place for mathematical research.
Scientific and postgraduate education in the Institute
During the first decades of the Institute’s existence, most of its researchers
held part-time positions at various Hungarian universities and vice versa, a
number of distinguished university professors were also part-time members
of the Institute. This resulted in a close collaboration with the educational
system and enabled to draw many talented young students towards
mathematical research.
Nowadays our relation with undergraduate education is less tight. We do not
offer part-time positions any more for university teachers, but we regularly
host them as visiting researchers. Similarly, only a few members of the
Institute hold part-time university positions, though many of them still teach
undergraduate and graduate courses at various universities – mostly at Eötvös
University and at the Technical University of Budapest, but also in Debrecen.
9
On the other hand, the Institute takes a more and more active part in graduate
and post-graduate education. Our researchers usually serve as advisors to 1012 graduate students from universities in Budapest. From the academic year
2001/2002, a joint international graduate program has been launched
together with Central European University, open to all countries of the world.
The teaching language is English and the educational system is the one
currently adopted in the US; correspondingly, the PhD titles awarded will be
accepted in the US as well. Our researchers serve both as supervisors and
instructors in the program.
Within the framework of a program coordinated by the Hungarian Academy
of Sciences, the Institute hosts each year 10-15 young researchers with a oneyear contract, which is renewable twice. These are recent PhD’s or graduate
students about to finish their thesis, whose scientific work is supervised by a
researcher at the Institute. After the end of their contract, several young
researchers have received offers for a position at the Institute, some even
tenured ones.
The Institute also regularly hosts post-doctoral students from abroad whose
number is steadily increasing thanks to the availability of various intraEuropean and international fellowships. We have joined or are planning to
join various European research training networks which will help to develop
further the international training activities of the Institute.
Researchers currently working at the Institute
This section gives a brief presentation of our current members; it is followed
by lists of our honorary members and some prominent former members. All
researchers below have a PhD or equivalent title. The ‘Doctor of Science’
title is awarded by the Academy to researchers with a substantial research
experience and achievement; it roughly corresponds to that of a full professor.
Among the prizes mentioned, the Széchenyi Prize (formerly State Award, or
Kossuth Prize) is the highest distinction of the Hungarian Republic awarded
to scientists; the Academy Award and the Mathematical Award are awarded
by the Academy for outstanding research achievements. Several of our
researchers are members or corresponding members of the Hungarian
Academy of Sciences.
10
Hajnal Andréka (b. 1947, at the Institute since 1977)
Doctor of Science (1993).
Her main areas of interest include logic, algebraic logic,
theoretical computer science, and relativity theory. She
proved (jointly with Hodkinson and Németi) that every
finite relativized relation algebra is representable over a
finite base. She is a member of the Council of the
Association of Symbolic Logic.
Pham Ngoc Ánh (b. 1956, at the Institute since 1988)
Doctor of Science (1988).
His main area of interest is ring and module theory.
Probably his most famous result states that a commutative
rings admits Morita duality if and only if it is linearly
compact.
András Ádám (b. 1934, at the Institute since 1957) Doctor
of Science (1986)
He is interested in Boolean functions, graph theory and
algebraic automata theory. He has written two books.
László Babai (b. 1950, at the Institute since 1997) Member
of the Academy, Mathematical Award (1983)
Plenary lecturer of the 1992 European Congress of
Mathematics. He contributed to the theory of graph
automorphisms and of permutation groups, in particular
concerning the number of elements in primitive
permutation groups. His other important field is complexity
theory, where his theorem about transparent proofs is of
basic importance. Currently on leave from the Institute, he
is a professor at the University of Chicago.
Antal Balog (b. 1956, at the Institute since 1983) Doctor of
Science (2000), Mathematical Award (1992), Academy
Award (1995)
His field is number theory, especially the distribution of
prime numbers. A well-known expert in sieve methods and
exponential sums, his most striking result is that there are
infinitely many "magic" triangles, tetrahedrons, etc. in
primes.
11
Imre Bárány (b. 1947, at the Institute since 1978) Doctor
of Science (1993), Erdős Prize (1995), Academy Award
(1998)
Invited speaker at the International Congress of
Mathematicians, Beijing, 2002. His main areas of interest
are discrete and convex geometry, with applications in
operation research and computer science. He has obtained
fundamental results about the asymptotic shape of certain
random objects.
István Berkes (b. 1947, at the Institute since 1971) Doctor
of Science (1996), Academy Award (2003).
His main field of interest is probability theory and its
applications in analysis, in particular for orthogonal and
lacunary series.
András Bezdek (b. 1956, at the Institute since 1983)
His fields of interest are discrete and combinatorial geometry and convexity.
Many of his results concern packing and covering problems in 2- and 3dimensional Euclidean space.
András Biró (b. 1971, at the Institute since 1997)
He works in various areas on number theory, including the analytic theory of
automorphic functions, Turán’s theory of power sums and diophantine
approximation. He recently solved
problems of Yokoi and Chowla
concerning quadratic fields of class number one.
Péter Bod (b. 1924, at the Institute since 1959; deputy
director, 1985–1995; retired in 2003). Doctor of Science
(1973).
His main fields of interest are operation research and actuarial
problems in social security. He has achieved results in
multiobjective linear programming, in the characterization of
convex sets having a least element, in the non-linear
generalization of input-output models and in the mathematical
modeling of large-scale systems. He currently serves as
Advisor to the Director.
12
János Bognár (b. 1932, at the Institute from 1960, retired in 1995)
A specialist in functional analysis, he has written a monograph on Indefinite
inner product spaces (volume 78 of the prestigious Ergebnisse series of
Springer-Verlag).
Károly Böröczky, Jr. (b. 1964, at the Institute since 1992;
scientific secretary, 1996–2000)
His main fields of interest are discrete and combinatorial
geometry as well as the theory of toric varieties. His
monograph on Finite packing and covering will be published
soon by Cambridge University Press. Organizer of several
important international meetings in algebraic geometry and
topology.
Endre Csáki (b. 1935, at the Institute since 1959) Doctor of
Science (1989).
He is interested in limit theorems of probability and
statistics and in combinatorial methods for random walk
problems. He gave rates of convergence in Strassen’s
theorem, thereby establishing a connection between Chung’s
and Strassen’s laws of the iterated logarithm.
Imre Csiszár (b. 1938, at the Institute since 1961) Member of
the Academy, IEEE Shannon Award (1997), Academy Award
(1988).
He is the leader of the Hungarian school in information
theory. His main work is the book “Information Theory”
written jointly with János Körner. The book was the first
overview of multiuser information theory.
Ervin Deák (b. 1929, at the Institute from 1964; retired in 1995)
At first his area of research was general topology, regarding in particular
various notions of dimension, later his interest switched to questions of
mathematical education.
Mátyás Domokos (b. 1968, at the Institute since 1995)
A specialist in ring theory, he first worked on polynomial
identities, then his research shifted to invariant theory and its
connections with representations and quantum groups.
13
Gábor Elek (b. 1963, at the Institute since 1996)
His work concentrates on the interface between functional analysis on
manifolds, algebra and combinatorics; his main interest is in amenable groups,
topological entropy and l_p-cohomologies.
Miklós Erdélyi Szabó (b. 1962, at the Institute since 2002)
He is interested in set theory, topological models as well as in artificial
intelligence; he is also the head of our Computer Department.
Péter L. Erdős (b. 1956, at the Institute since 19??)
He works in extremal graph theory and the application of graphs to problems
in mathematical biology.
Gábor Fejes Tóth (b. 1947, at the Institute since 1974),
Doctor of Science (1996).
Working in discrete geometry, he is a worldwide
recognized authority on packing and covering problems.
His survey papers are the standard references about the
field. Organizer of prestigious international meetings in
discrete geometry (including Oberwolfach seminars).
Zoltán Füredi (b. 1954, at the Institute since 1978) Doctor
of Science (1989), Academy Award (1989).
Invited lecturer at the 1994 International Congress of
Mathematicians. He has achieved ourstanding results in
extremal set theory, graph theory and discrete geometry,
including the solution (together with P. Frankl) of a famous
problem of Littlewood and Offord.
János Gerlits (b. 1945, at the Institute since 1968)
His field of research is general and set-theoretic topology. In particular, he has
important results on function spaces and on cardinal functions of dyadic
spaces.
Ervin Győri (b. 1954, at the Institute since 1977; deputy
director since 1997) Doctor of Science (1994).
His main fields of interest are combinatorics and graph
theory. His major results are a minimax theorem on
intervals, a partition characterization of k-connected graphs
(proved independently by L. Lovász as well) and solutions to
several problems of Erdős in extremal graph theory.
14
István Juhász (b. 1943, at the Institute since 1975) Doctor
of Science (1977), Mathematical Award (1977), Academy
Award (1997)
His main areas of interest are set theory and general
topology. Together with A. Hajnal he has created an
internationally recognized school in set-theoretic topology.
He is the author of two monographs: Cardinal functions in
topology and Cardinal functions - ten years later.
Gyula Katona (b. 1941, at the Institute since 1966; Director
since 1996) Member of the Academy, Academy Award
(1989).
An internationally recognized expert in combinatorics, he
has achieved important results in extremal set theory and
concerning the combinatorial structure of databases. He also
pays great attention to educating future scientists: several of
his students are leading mathematicians today. His
organizing work is also of great importance.
András Kroó (b. 1954, at the Institute since 1976) Doctor
of Science (1988), Academy Award (2002).
His main area of interest is Approximation Theory. His
best known result concerns the differentiability of the
operator of best approximation in the space of continuous
functions.
Antónia L. Földes (b. 1945, at the Institute since 1969)
An expert in probability theory, she is mainly interested in questions of local
time, random walks and Wiener processes. Currently on leave from the
Institute.
Anna Lee (b. 1928, at the Institute from 1971; retired since
1993)
A researcher in algebra, her field of interest is matrix
theory. She has investigated involutions of the complete
matrix ring over the complex numbers.
Judit Madarász (b. 19??, at the Institute since 2001)
She works in algebraic logic and the logical foundations of relativity theory.
15
Zoltán Magyar (b. 1959, at the Institute since 1987)
His main field of research is the analytic theory of Lie
groups and their representations. Author of two
monographs: one on Continuous Linear Representations,
the other on The Lebesgue Integral.
Péter Major (b. 1947, at the Institute since 1971) Doctor of
Science (1989), Academy Award (1984)
He is interested in probability theory and statistical physics.
His best known result is a joint work with János Komlós and
Gábor Tusnády about the approximation of identically
distributed random variables by a Wiener process. This
construction is often called the KMT theory or the
Hungarian method in the literature.
Endre Makai, Jr. (b. 1947, at the Institute since 1970)
Doctor of Science (1996), Academy Award (1998).
He has a double research interest: he works in convex and
discrete geometry and also in general topology. He has
obtained important results by combining geometrical and
purely topological methods.
László Márki (b. 1947, at the Institute since 1970) Doctor
of Science (1996)
His main area of interest is algebra: semigroups, rings,
universal algebra, categories. He has recently introduced the
notion of semi-abelian categories (with Janelidze and
Tholen) which answers an old question of MacLane. He
served as Vice-President of the European Mathematical
Society from 1993-1996.
Katalin Marton (b. 1941, at the Institute since 1974)
Doctor of Science (1999).
After working on problems in information theory and some
related problems in combinatorics and ergodic theory, her
current recent interest is mainly in measure concentration.
16
József Merza (b. 1932, at the Institute from 1967, retired since 1993)
His research interest was in classical differential geometry. He served as
managing editor of the Institute’s proceedings Studia Scientiarium
Mathematicarum Hungarica for decades and also as head of the library, where
he is still active today.
Dezső Miklós (1957, at the Institute since 1982, deputy
director since 1996).
His main areas of research are combinatorics (extremal set
theory, algebraic combinatorics) and the combinatorial
structure of databases. A very active organizer, editor of
several volumes.
Zsigmond Nagy (b. 1950, at the Institute since 1975)
He has achieved significant results in general and settheoretic topology, in particular concerning the theory of
function spaces.
Tibor Nemetz (b. 1941, at the Institute since 1969)
Doctor of Science (1996)
His research interests include combinatorics, information
theory, statistics as well as didactics. He is one of the
initiators in Hungary of research in cryptology and its
practical applications. He is especially interested in the
estimation of the entropy of written languages.
András Némethi (b. 1959, at the Institute since 2004) Doctor of Science
(2001)
A well-known expert on singularities of complex algebraic varieties.
Continuing the program initiated by M. Artin and Laufer, he has obtained
deep results in the classification of normal surface singularities by studying
both algebro-geometric and topological invariants.
17
István Németi (b. 1942, at the Institute since 1976)
Doctor of Science (1987)
His main areas of interest are logic, algebraic logic,
theoretical computer science, and relativity theory. He has
obtained fundamental results about cylindric algebras and
relation algebras, solved several famous problems raised
by Tarski and created a school in algebraic logic at the
Institute. Author of the monograph Cylindic set algebras
(jointly with Andréka, Henkin, Monk and Tarski).
János Pach (b. 1954, at the Institute since 1977) Doctor of
Science (1996), Academy Award (1998)
His main fields of interest are discrete and computational
geometry, convexity and combinatorics. He is a recognized
expert in geometric graph theory and author of the
influential book Combinatorial Geometry (jointly with
Pankaj Agarwal). Besides being a prolific researcher, he has
a number of students around the world. Apart from his
position at the Institute, he is also a professor at the Courant
Institute, New York.
Dénes Petz (b. 1953, at the Institute between 1982 and 1992
and from 2004) Doctor of Science (1989)
His fields of research are functional analysis and the
mathematical foundations of quantum theory. Author of two
monographs: Quantum Entropy and its Use (with M. Ohya,
Springer, 1993) and The Semicircle Law, Free Random
Variables and Entropy (with F. Hiai, AMS, 2000).
János Pintz (b. 1950, at the Institute since 1977) Doctor of
Science (1984).
An internationally recognized expert in analytic number
theory, he has achieved important results concerning the
distribution of prime numbers and the Goldbach
conjectures.
László Pyber (b. 1960, at the Institute since 1987) Doctor of
Science (1998), Erdős Prize (1996).
Invited speaker of the 1996
Mathematics. His main interest
theory. He has determined the
number of n-element groups.
European Congress of
lies in asymptotic group
asymptotic value of the
Recently, he has been
18
successful in studying residual properties of groups and the
subgroup growth problem (jointly with Lubotzky, Shalev and
others).
Lídia Rejtő (b. 1946, at the Institute since 1969)
Her research interest is in mathematical statistics and limit theorems in
probability theory. Currently on leave from the Institute.
Szilárd Révész (b. 1958, at the Institute since 1990)
He began his mathematical research by investigating
problems related to the distribution of prime numbers. Later,
his interest shifted to approximation theory, in particular
inequalities and extremal problems.
Imre Z. Ruzsa (b. 1953, at the Institute since 1976)
Corresponding member of the Academy, Academy Award
(1995), Erdős Prize (1989).
He is a leading expert in additive number theory and has
basic results in applying probabilistic methods in number
theory. Together with Gábor Székely, he has also developed
a semigroup theoretic method in proving limit theorems for
probability distributions.
Ildikó Sain (b. 1951, at the Institute since 1982)
Her main research interest lies in model theory, algebraic
logic and universal algebra. Recently, she has been
interested in finitizable algebraization of first-order logic.
Attila Sali (b. 1959, at the Institute since 1984)
He has been working in several areas of combinatorics, including extremal
and algebraic combinatorics, database theory and graph theory.
Miklós Simonovits (b. 1943, at the Institute since 1986)
Corresponding member of the Academy, Academy Award
(1993).
His main areas of interest are combinatorics and graph
theory. He is one of the pioneers of extremal graph theory,
an area where he is still very active today. Together with L.
Lovász, he has obtained fundamental results concerning the
algorithmic complexity of computing the volume of a
convex body in Euclidean space.
19
Gábor Simonyi (b. 1963, at the Institute since 1989)
His main research activity blends information theory and
graph theory; in particular, he is an expert on graph
entropy.
Lajos Soukup (b. 1958, at the Institute since 1986)
His main field of interest is set theory, in particular independence results in
set-theoretic topology. His work with S. Shelah in set theory and the theory of
Boolean algebras is also widely known.
András Stipsicz (b. 1966, at the Institute since 2002)
He is a well-known expert in symplectic topology, with a main focus on 4manifolds. Together with R. Gompf, he wrote the important advanced
textbook 4-Manifolds and Kirby Calculus (AMS, 2000).
József Szabados (b. 1938, at the Institute since 1968)
Doctor of Science, Academy Award (1982).
His field of interest is approximation theory; in particular
interpolation and weighted polynomial approximation in
various spaces. He wrote the monograph Interpolation of
Functions (jointly with P. Vértesi). He has been managing
and editing the journal Acta Mathematica Hungarica since
1962.
Endre Szabó (b. 1964, at the Institute since 1996)
His main interest is in algebraic geometry, where he has
achieved significant results concerning rationally connected
varieties and automorphism groups of varieties.
Tamás Szamuely (b. 1971, at the Institute since 1998; scientific secretary,
2001–2004)
He is interested in wide-ranging topics in algebraic and arithmetic geometry,
including algebraic cycles, motives, fundamental groups and geometric
aspects of class field theory. Speaker at the Bourbaki Seminar in June 2003.
20
Domokos Szász (b. 1941, at the Institute since 1971;
Director, 1993–1995), Member of the Academy, Academy
Award (1984).
Though he began his career as a probability theorist, he is
best known as the founder of the internationally renowned
Hungarian statistical physics school. Starting from
equilibrium statistical physics, he turned to the theory of
billiards, and in particular the Boltzmann ergodic
hypothesis. Together with Ya. G. Sinai, he achieved the
first breakthrough in the mathematical foundation of the
hypothesis.
Endre Szemerédi (b. 1940, at the Institute since 1965)
Member of the Academy, Academy Award (1979), Erdős
Prize (1977).
His profound results in number theory and combinatorics are
widely used and have a significant impact on research. He
showed that any sequence of integers with positive density
contains arithmetical progressions of arbitrary length,
thereby solving a famous problem of Erdős and Turán. His
most influential result in combinatorics is the so-called
regularity lemma.
Gábor Székely J. (b. 1947, at the Institute since ???)
Doctor of Science (1986)
His main areas of interest are algebraic probability theory
and nonparametric statistical tests. He is the author of
Paradoxes in probability theory and mathematical
statistics (1986) as well as Algebraic probability theory
(with Imre Z. Ruzsa, 1988). He is currently on leave from
the Institute.
Ágnes Szilárd (b. 19??, at the Institute since 2003; scientific secretary from
2004)
She is interested in computing invariants for singularities of complex
algebraic varieties.
21
Gábor Tardos (b. 1964, at the Institute since ???) Prize of
the First European Congress of Mathematics, Erdős Prize
(1999).
Invited speaker at the Second European Congress of
Mathematics. His main areas are complexity theory and
combinatorics. He has achieved profound results about
first-order statements on random graphs and an important
breakthrough towards the Hanna Neumann conjecture
concerning subgroups of free groups.
Vera T. Sós (b. 1930, at the Institute since 1987) Member of
the Academy, Academy Award (1983), Foreign member of
the Austrian Academy of Sciences, Széchenyi Award (1997)
She is one of the founders of the Hungarian school in
combinatorics. Her other main research area is number
theory, especially diophantine approximation and uniform
distribution. In combinatorics, she has achieved important
results on pseudorandom structures and extremal problems.
Géza Tóth (b. 1968, at the Institute since 2001)
He has obtained significant results in discrete and combinatorial geometry,
with a main focus on geometric aspects of Ramsey theory.
Gábor Tusnády (b. 1941, at the Institute since 1965)
Member of the Academy, Erdős Prize (1981).
The basic goal of his work is building and investigating
stochastic models. He has achieved significant results in
statistical problems connected with genetics and cancer
research and has created interdisciplinary research groups
around his projects.
Péter Vértesi (b. 1941, at the Institute since 1975) Doctor
of Science (1982), Academy Award (2002)
He works in approximation theory, especially interpolation
theory. His most significant result is the almost
everywhere divergence theorem of Lagrange interpolation
(joint work with P. Erdős). Together with J. Szabados, he
wrote the book Interpolation of Functions.
22
Richárd Wiegandt (b. 1932, at the Institute since 1964)
Doctor of Science (1975).
He works in algebra with a main interest in rings and
radicals. He is one of the founders of general radical theory
going beyond algebraic structures.
23
Honorary members of the Institute
Miklós Ajtai (1946-) External member of the Academy
His main fields of interest are theoretical computer science, mathematical
logic and combinatorics. He has achieved several breakthroughs in the
theory of randomized algorithms, mostly jointly with J. Komlós and E.
Szemerédi. At the Institute between 1970 and 1985, he presently works at
IBM Almaden Research Center.
József Beck (1952-) Doctor of Science (1993)
Invited speaker at the International Congress of Mathematicians (Berkeley,
1986). A leading expert on uniform distribution and discrepancy theory, he
is the author of Irregularities of Distribution (with W. L. Chen, Cambridge
University Press, 1987). Probably his best known result is his 1993 solution
of an old conjecture on uniform distribution on the k-dimensional torus. He
has also done important work in game theory. At the Institute between 1977
and 1984, he is currently Harold Martin Chair Professor at Rutgers
University.
Béla Bollobás (1943-) External member of the Academy
A worldwide recognized expert in combinatorics. He is the author and editor
of numerous books, including authoritative texts on Combinatorics, Modern
Graph Theory and Random Graphs. A regular visitor to the Institute, he is
currently a professor at the University of Memphis, Tennessee.
László Csirmaz (1951-)
His research interest is in logic and computer science. After a period at the
Institute between 1975 and 1996, he is now head of the Computer and
Statistics Center at Central European University.
Miklós Csörgő (1932-) External member of the Academy
He is interested in fine analytic path properties of
stochastic processes, Wiener, empirical, local time and
released processes. He is author and co-author of five
books, among which Strong Approximations in
Probability and Statistics, written jointly with Pál Révész,
is a frequently cited fundamental work in the subject. He
is currently a professor at Carleton University, Ottawa,
Canada.
24
Péter Frankl (1953-) External member of the Academy
His main field of interest is combinatorics. He has proven fundamental
results in the theory of extremal hypergraphs. Excellent juggler, a TV
personality in Japan. He worked at the Institute between 1976 and 1980 and
is now at the University of Tokyo.
József Fritz (1943-) Corresponding member of the
Academy, Academy Award (1984)
His main field of interest is mathematical physics. He has
obtained fundamental results on differential equations with
infinite degree of freedom (jointly with R. L. Robinson), and
for infinite dimensional stochastic differential equations. He
has students at various places around the world. After
working at the Institute between 1967 and 1993, he is now a
professor at the Technical University of Budapest.
Kálmán Győry (1940-) Member of the Academy, Academy Award (1992),
Széchenyi Prize (2002)
He is the initiator in Hungary of the study of diophantine equations and the
leader of the Debrecen number theory school. He has achieved important
results in applying Baker’s method in transcendental number theory to
finding effective bounds on the solutions of diophantine equations. He is a
professor at the University of Debrecen, where he also served as Dean and
Rector.
András Hajnal (1931-) Member of the Academy, State
Award (1970), Academy Award (1967); Director of the
Institute (1983–1992).
Invited speaker at the 1974 International Congress of
Mathematicians. With Paul Erdős, Attila Máté and Richard
Rado, he is the founder of combinatorial set theory and
with P. Hamburger the author of a standard textbook on set
theory. The Hungarian set theory school gained world fame
under his leadership. He worked at the Institute between
1970 and 1992 and is currently a professor at Rutgers
University where he also served as director of DIMACS.
25
Gábor Halász (1941-) Member of the Academy, Erdős
Prize (1976)
A prominent expert in analytic number theory, he has
obtained fundamental results concerning mean values of
multiplicative arithmetic functions. He has also worked in
approximation theory and complex analysis and has an
impressive list of students. After spending the period 19641986 at the Institute, he is now a professor at Eötvös
University.
János Horváth (1924-) External member of the Academy
An expert in functional analysis and operator theory, he is the author of an
influential 2-volume monograph on Topological Vector Spaces and
Distributions. He is currently professor emeritus at the University of
Maryland.
Jerry L. Kazdan (19??-)
Working on the interface of the theory of partial differential equations and
differential geometry, he has obtained fundamental results (jointly with F.
Warner) on the characterisation of curvature functions on 2-manifolds. He is
a professor at the University of Pennsylvania and at Central European
University.
János Kollár (1956-) External member of the Academy
Invited speaker at the 1990 International Congress of Mathematicians.
Working mainly in algebraic geometry, he is a leading authority on the
classification of higher dimensional varieties. Together with Miyaoka and
Mori, he initiated the study of rationally connected varieties. He is the author
of the important monographs Shafarevich Maps and Automorphic Forms
(Princeton, 1995), Rational Curves on Algebraic Varieties (Springer, 1996)
and Birational Geometry of Algebraic Varieties (with. S. Mori, Cambridge,
1998) and is editor of Inventiones Mathematicae. Currently he is a professor
at Princeton University and a regular visitor to the Institute.
János Komlós (1942-) External member of the Academy
His areas of interest include probability theory, the theory
of algorithms and graph theory. He is well known among
others, for the "KMT embedding" in probability theory
(joint work with Major and Tusnády), or for the AKS
sorting network. At the Institute between 1967 and 2001,
he is now a professor at Rutgers University.
26
János Körner (1946-)
His main fields of interest are information theory and combinatorics. His
book Information Theory written jointly with Imre Csiszár was the first
overview of multiuser information theory. He has strongly contributed to
combinatorical applications of information theory, in particular he
introduced the concept of graph entropy. After a period at the Institute
between 1970 and 1996, he is now a professor in Rome.
Miklós Laczkovich (1948-) Member of the Academy,
Academy Award (1991), Széchenyi Award (1998)
His main research area is real analysis. Among other
fundamental results, he has verified A. Tarski’s conjecture
about "squaring the circle". He is a professor at Eötvös
University and has been a visiting researcher at the Institute
several times.
László Lovász (1948-) Member of the Academy, State
Award (1985), Wolf Prize (1999)
He is one of the leading experts of the world in his major
areas of research: combinatorics, graph theory and
theoretical computer science. He has settled several
famous questions in combinatorics like the Shannon
capacity problem, the perfect graph conjecture, or the
Kneser conjecture. His book Combinatorial Problems
and Exercises is a standard text and reference in the field.
Beyond his theoretical work he is a very active and
productive organizer of the Hungarian and international
mathematical community. He is a professor at Eötvös
University and at Microsoft Research.
Mihály Makkai (1939-) External member of the
Academy
A worldwide recognized, leading researcher in logic and
the foundations of mathematics. He has made
fundamental contributions to model theory and is one of
the founders of categorical logic. He is a professor at
McGill University, Montreal, Canada.
27
Péter Pál Pálfy (1955-; Deputy Director, 1991–1996)
Doctor of Science (1997), Mathematical Award (1993)
His research interests are in group theory and universal
algebra. His most cited results include the classification of
minimal algebras and the determination of finite groups
with the general Cayley isomorphism property. After
twenty years spent at the Institute from 1980, he is now a
professor at Eötvös University.
Pál Révész (1934-) Member of the Academy, State Prize
(1978)
He has obtained important results for local time, random
walks and empirical processes in probability theory.
Recently, he has also been interested in Wiener processes.
Jointly with Miklós Csörgő, he wrote the fundamental
book Strong Approximations in Probability and Statistics.
After a period at the Institute between 1964 and 1985, he
is now a professor emeritus at the Technical University of
Vienna.
András Sárközy (1941-) Corresponding member of the
Academy, Academy Award (1992).
His main areas of interest are additive and combinatorial
number theory. Probably his most famous result is that
the difference set of a dense sequence of integers always
contains a perfect square. A researcher at the Institute
between 1971 and 1994, he is now a professor at Eötvös
University.
Tamás Schmidt (1936-; Deputy director, 1971–1990)
Doctor of Science (1969),
His main area of research is lattice theory and universal
algebra. His most celebrated result is a joint theorem with
G. Grätzer stating that every algebraic lattice is
isomorphic to the congruence lattice of an algebra. After a
long stay at the Institute between 1958 and 1990, he is
now a professor at the Technical University of Budapest.
28
Bálint Tóth (1955-) Doctor of Science (1999),
Mathematical Award (1995), Academy Award (2003).
Invited speaker at the third European Congress of
Mathematics, 2000. His main areas of research are
probability theory and stochastic processes. His major
results are limit theorems for random walks with long
memory exhibiting anomalous diffusion and the
construction of the so-called `true self-repelling motion’,
a stochastic process with striking analytic and
phenomenological properties. After a period at the
Institute between 1983 and 1998, he is now a professor at
the Technical University of Budapest.
29
Some prominent former members of the Institute
György Alexits (1899–1978) Member of the Academy,
Kossuth Prize (1951), State Award (1970)
He was mainly interested in real functions. His most
important results are in the field of Fourier analysis and
approximation theory. He was at the Institute between
1971 and 1974.
László Alpár (1914–1991) Doctor of Science (1978)
He worked in analysis. His main results deal with the
behaviour of analytic functions on the circle of convergence.
At the Institute between 1956 and 1984, he also served as
Deputy Director.
András Békéssy (1925-) Doctor of Science, Deputy
director (1964–1971), Academy Award (1984)
He is interested in applications of complex analysis, in
combinatorics and in probability theory. He has worked
for WHO, and has written a book about databases
(together with János Demetrovics). He worked at the
Institute between 1964 and 1971.
Imre Bihari (1915–1999) Doctor of Science (1979)
His main field of interest was differential equations. At the
Institute between 1962 and 1985, he initiated the study of
semi-linear differential equations.
Ákos Császár (1924-) Member of the Academy, Kossuth
Prize (1963)
His main interests are in real analysis and in general
topology; he is the author of comprehensive textbooks on
both subjects. His most important result is the unification
of different topological structures by introducing
syntopogenous structures. Though never a full-time
member, he has been actively taking part of the Institute’s
life for decades now.
30
Jenő Egerváry (1891–1958) Member of the Academy,
Kossuth Prize (1949, 1953)
He was the leader of the research group at the Technical
University of Budapest, the predecessor of the Institute. He
has obtained outstanding results in numerical optimization.
He has also worked on the three-body problem, but his most
significant result is the Egerváry-Kőnig theorem about 0-1
matrices.
Árpád Elbert (1939–2001) Doctor of Science (1989)
His main interest was in differential equations, where he
managed, among other things, to relax the conditions
needed for solving semi-linear differential equations. He
worked at the Institute from 1963 until his untimely
death.
Paul Erdős (1913–1996) Member of the Academy, member
of six foreign Academies, Wolf Prize (1984), Kossuth Prize
(1958), State Award (1983), Gold medal of the Academy
(1991)
With over 1500 papers he is, after Euler, the most prolific
mathematician of all times. He worked intensively in
number theory, and gave, together with Atle Selberg, the
first elementary proof for the prime number theorem. In
approximation theory, he proved the almost everywhere
divergence of Langrange interpolation (jointly with P.
Vértesi). He opened new fields in set theory, as, for
example, partition theory (jointly with Richard Rado). His
ideas and results also had an essential impact on discrete
geometry. During the second half of his life he turned to
combinatorics, where, among other things, he developed the
probabilistic method. In his whole life he wandered from
conference to conference and research center to research
center. He was invited to lecture all over the world from
Princeton to Beijing. He raised numerous famous open
problems, by means of which he created entire schools in
several branches of mathematics. He was officially a
member of the Institute from 1972 until his death.
31
László Fejes Tóth (1915-) Member of the Academy,
foreign member of four foreign Academies, Director of the
Institute (1970-1982), Kossuth Prize (1957), State Award
(1973), Gauss memorial medal (1974), Gold Medal of the
Academy (2001).
During the 1940s and 1950s, his results created a new
branch of mathematics: discrete geometry. Within this
field, he obtained significant results concerning extremal
properties of polyhedra. He solved the 2-dimensional case
of the sphere packing problem (part of Hilbert’s Problem
18). The influence of his books as well as his ability to
pose interesting problems created a school around him
reaching as far as the US. He was a regular organizer of
Oberwolfach conferences. He worked at the Institute from
1965 until his retirement in 1983.
Géza Freud (1922–1979) Doctor of Science, Kossuth Prize
(1959).
He was a worldwide recognized expert on orthogonal
polynomials and wrote a monograph on the subject. Several
of his theorems are starting points for present-day research.
He developed the theory of one-sided polynomial
approximation. A founder of weighted approximation, he
introduced a class of weights which now bears his name. He
emigrated in 1974, after 20 years spent at the Institute.
Tibor Gallai (1912–1992) Corresponding member of the
Academy, Kossuth Prize (1956), Academy Award (1972)
He achieved his most important results in elementary
combinatorial problems and graph theory. He played a
key role in creating the Hungarian school in
combinatorics. He worked at the Institute between 1958
and 1968.
György Grätzer (1936-) External member of the Academy
He is an authority in lattice theory and universal algebra. His 200 papers and
books (among them Universal Algebra and General Lattice Theory) have
had a great impact on the developments of these topics. He was a member of
the Institute between 1958 and 1964.
32
Endre Makai (1915–1987) Doctor of Science (1955), State
Award (1973), Academy Award (1970).
He worked in analysis, mostly on Fourier series and
differential equations. His research in applications to
engineering,
especially
the
description
of
the
eigenoscillation of membranes, is also important. He was at
the Institute between 1962 and 1980.
András Prékopa (1929-) Member of the Academy,
Széchenyi Award (1996)
He has not only founded the Hungarian operation research
school, but has also developed it to acquire international
fame. The Prékopa inequality for real functions is the
starting point of several profound inequalities. Though a
full-time member of the Institute only in 1957/58, he
conducted a group of operation research here for many
years
László Rédei (1900–1980) Member of the Academy,
Kossuth Prize (1950, 1955)
After obtaining significant results in algebraic number
theory, he switched to group theory, where his research
culminated in important results on factorizability of groups.
He developed the theory of lacunary polynomials that later
became important in combinatorics. Author of an important
textbook on Algebra and several research monographs, on
finite p-groups, semigroups and the foundations of
geometry. Though he was very active at the Institute from
the 1960’s, he was a full-time member only towards the end
of his life (1971–74).
Károly Sarkadi (1914–1985) Doctor of Science, State
Award (1966)
One of the pioneers of Hungarian statistics. He developed
an exact statistical method for checking Gaussian
distribution which, apart form its theoretical significance,
can also be successfully applied in practice. He worked at
the Institute between 1952 and 1984.
33
János Surányi (1918-) Doctor of Science (1957)
His main areas of interest are logic, number theory and
didactics. Together with P. Erdős, he wrote the much-cited
textbook Topics in Number Theory. He is also widely
known as editor of the Hungarian Problem Book, based on
the problems of mathematical competitions for secondary
schools. Though never a formal member, he conducted a
seminar on didactics at the Institute for a long time.
Árpád Szabó (1913–2002), Member of the Academy
His original field of interest was ancient Greek culture.
Persecuted for political reasons, he found shelter at the
Institute in 1958, where he remained until his retirement
in 1983. It is while working here that he became a
worldwide respected authority on Greek mathematics.
Author of a great number of books, many of which have
been translated into various foreign languages.
Károly Szilárd (1901–1980) Doctor of Science
His main areas of interest were differential equations and
their applications. He has obtained fundamental results
about ballistics. He was awarded the Stalin Prize for work
done in this area while he was a prisoner of war in the
Soviet Union.
Béla Szőkefalvi-Nagy (1913–1998) Member of the
Academy, Kossuth Prize (1950, 1953), State Award
(1978), Gold medal of the Academy (1987)
As the worthy heir of Frigyes Riesz, he was the leader of
the Hungarian functional analysis and operator theory
school. Author of several monographs, among which the
most famous one is his Leçons d’analyse fonctionnelle
written jointly with his master F. Riesz, a fundamental
textbook translated into six languages. Though never a
full-time member of the Institute, he is the founder of the
research group in analysis.
34
Lajos Takács (1924-)
He initiated a new line of applying combinatorial enumeration in the theory
of stochastic processes and was one of the pioneers of queuing theory.
Author of several research monographs, among which the influential
Combinatorial methods in the theory of stochastic processes. He entered the
Institute in 1955 and worked here until his emigration in 1958.
Pál Turán (1910–1976) Member of the Academy,
Kossuth Prize (1949, 1952)
Founder of the Hungarian analytic number theory school,
he also achieved far-reaching results in approximation
theory, in complex analysis and in graph theory. His
famous method of power sums by which he obtained
results related to the Riemann Hypothesis is exposed in
his book On a new method in analysis and its applications, published in German and English. He had a number
of students around the world. Though active at the
Institute for decades, he became a full-time member only
in 1975, a year before his untimely death.
Ottó Varga (1909–1969) Member of the Academy,
Kossuth Prize (1952)
He obtained important results in differential geometry,
especially concerning the foundations and the
characterization of Finsler spaces. He spent the two last
years of his life at the Institute.
István Vincze (1912–1999) Doctor of Science (1972),
State Award (1966), Deputy director (1950-1964)
He obtained basic results in mathematical statistics and
its applications and wrote a monograph on the subject. He
worked at the Institute from its foundation until 1982.
35
The Rényi Prize
In 1972 the Institute founded the Rényi Prize in the memory of its founder.
The prize is awarded yearly (from 2001 every two years) to one or two
members of the Institute having recently achieved a major result.
So far the following researchers have been awarded the prize:
1972: Gábor Halász
1973: Endre Szemerédi
1974: József Szabados
1975: János Komlós
1976: Gyula Katona
1977: András Sárközy; Gábor Tusnády (refused the prize)
1984: József Beck; Péter Vértesi
1985: Zoltán Füredi; János Pintz
1986: Emil Kiss; Imre Ruzsa
1987: Hajnal Andréka; János Körner
1988: Imre Bárány; József Fritz
1989: István Berkes; Péter Major
1990: Pham Ngoc Ánh
1991: Antal Balog; Ervin Győri
1992: János Pach
1993: László Pyber; Lajos Soukup
1994: Nándor Simányi; Gábor Simonyi
1996: Endre Makai; Katalin Marton
1997: Gábor Fejes Tóth
1998: András Kroó
1999: Gábor Tardos
2000: Péter Pál Pálfy
2001: Mátyás Domokos
2003: László Márki
36
History of the Institute
Hungarian mathematics acquired international fame by the end of the 19th
century, as is testified by the work of such great scholars as Gyula Kőnig,
József Kürschák, Lipót Fejér, Alfréd Haar or Frigyes and Marcel Riesz. At
the time, research in theoretical mathematics was conducted by talented
Resolution of the foundation of the Institute
37
teachers at universities, colleges, and secondary schools, as everywhere else
in the world. In fact, the first independent mathematical institutes only came
into being towards the middle of the 20th century, and their founding was
prompted by nonscientific reasons: in the US by the flux of European
immigrant scholars, and in the Soviet Union by the necessity of employing
scientists whose research was valued by the regime but who could not teach
for political reasons.
Thus, after 1949, research institutes of the Hungarian Academy of Sciences
came into being following this Soviet model, but in many fields, especially in
exact sciences, the ‘condition’ for entering them was not really political
(un)reliability, but rather scientific excellence. This was the case of our
Institute, officially founded in 1950, but which was, however, not without a
predecessor.
In fact, in the second half of the 1940’s a research group in mathematics was
already functioning under the auspices of the Technical University of
Budapest, created following an initiative of the Ministry of Culture. Its leader
was Jenő Egerváry, a significant theoretical mathematician who, having spent
considerable time in Germany, was also familiar with modern applied
mathematics. It is on the basis of this group that the Institute for Applied
Mathematics of the Hungarian Academy of Sciences was created on August
1, 1950, following successful lobbying by György Alexits, at the time deputy
secretary of state. 29-year-old young talent Alfréd Rényi was appointed as the
first director, and for many years Jenő Egerváry served as President of the
Scientific Board.
The Institute consisted of five research divisions at first. The Division of
Mechanics and Tension Analysis, under the leadership of Jenő Egerváry, was
the follower of the research group at the Technical University mentioned
above. The other four units were the Division of Probability and Mathematical Statistics led by Alfréd Rényi; the Division of Actuaries and Economics
led by István Vincze; the Division of Numerical and Graphical Methods led
by György Hajós of Eötvös University (with an exterior branch in Miskolc);
and the Division of Chemical Engineering led by István Fenyő.
At the beginning of the 1950’s, the main task of members of the Institute was
to put their special mathematical knowledge at the disposal of industrial
companies. For example, at the Division of Numerical and Graphical
Methods it was possible to order calculations which could not be performed
elsewhere. The statistics group, being familiar with the theory of sampling as
well as with the corresponding procedures, could be helpful to quality control
38
organizations. The biometry group gave advice on performing reliable
statistical analyses in theoretical medicine, or on the planning of biological
and agricultural experiments.
Gradually, the scope of research conducted at the institute began to widen. In
the foreword of The 2nd Proceedings of the Applied Mathematical Institute,
published in 1954, Rényi already mentions seven divisions: Mechanics and
Tension Analysis; Probability; Mathematical Statistics; Numerical and
Graphical Methods; Differential Equations; Electromechanics; and Real
Analysis. As can be seen from this list, theoretical research has now gained
territory besides the applied fields, prompting the necessity of restructuring
and renaming the institute. This took place in 1955. As Rényi wrote in 1960,
on the occasion of the 10th anniversary of the Institute’s foundation, “the
manifold problems and tasks faced by the staff of the Institute... can be solved
only if mathematicians’ efforts in applying results are supported by
theoretical research. The Institute can now realize more efficiently the
connecting of applied work to theoretical research, having been restructured
under the name Mathematical Institute of the Hungarian Academy of
Sciences as of August 1, 1955.”
According to Rényi, “the change of name expresses that the Institute should
be a home not only to applied research, but to pure mathematics as well,
leading to a closer connection between theory and application. In the process
of restructuring the Institute, new theoretical divisions will be established
soon [...]” One of the newly
established units was the Division
of Complex Analysis led by Pál
Turán (the predecessor of the
current number theory group);
another one the research group in
functional analysis. Based in
Szeged under the leadership of
Béla Szőkefalvi-Nagy, this group is
the ancestor of today’s Division of
Analysis. It also furnishes a good
example of a practice followed at
György Grätzer, Paul Erdős,
the time but abandoned later:
Pál Turán and Alfréd Rényi
research
groups
performing
significant scientific work somewhere in the country became, in a way or
another, attached to the institute. The 1960’s also saw the birth of a research
group in abstract algebra, led by László Rédei – this was a subject already
quite remote from practical applications. As Rényi writes in a spirit typical
39
for an era still suspicious about purely theoretical research: “No single
division of the Institute can be considered as exclusively theoretical or
exclusively application-oriented; the differences that emerge are only due to
the relative importance attributed to theoretical research versus application.”
Since then, the research profile of the Institute has evolved in function of
scientific trends and the availability of researchers specializing in a given
field. Following the influence of Pál Erdős, Pál Turán, András Hajnal,
László Fejes Tóth and others, research conducted in various areas of discrete
mathematics (graph theory, combinatorial set theory, discrete geometry, to
name but a few) has become one of the main forces of the Institute, leading to
the creation of several new divisions. In the 1990’s, young researchers having
studied abroad introduced subjects that have been previously missing from
the palette of the Institute, such as algebraic geometry and differential
topology. The future will certainly see the emergence of new research topics;
the Institute, however, does not aim at covering all fields of mathematics,
only those where it can set up a strong research group.
Thus it can be seen that over the years theoretical research has gradually
become the dominant activity at the Institute. Applications, however, have
not been forgotten. A research group directed towards economic applications
started its work in 1959 under the leadership of András Prékopa. This group,
later transferred to the newly founded Computer and Automation Research
Institute, was the precursor of the Hungarian school in operation research that
attained international fame. From the 1960’s, researchers at the institute
became involved in industrial applications through individual contracts. For
example, Alfréd Rényi and János Szentágothai worked together on a
mathematical model of the brain. At the end of the 1970’s GANZ Equipment
Works developed programs using combinatorial ideas. Differential equations
describing the subterranean burning of oil fields of Zala county were also
investigated. Colleagues from the Institute developed computer programs of
long-range forecasting for the Hungarian Aluminum Trust, and created an
algorithm for designing chips for the Company of Microelectronics. In recent
years, the Institute has been successful in applying its expertise in databases
and cryptography.
40
Resolution of altering the name of the Institute
Thus during the past decades,
the Institute underwent quite a
number of transformations, but
in its spirit it remains close to
that of its founding director.
From July 1, 1999, the Institute
bears the name of Alfréd Rényi,
in honour of his achievements
in mathematics and scientific
organization.
The building of the Institute
The Institute is located in a four-story historical building in the heart of
downtown Budapest; see the next section for the building’s history.
On the ground floor you find in particular the Director’s office, the
secretaries’ room (look at the painted ceilings!) and the library of the
institute. From the entrance hall you can also enter the Institute’s inner
courtyard. Equipped with round tables, chairs and even a whiteboard, it is a
calm and pleasant place for a mathematical discussion or just a chat when the
weather is fine. It is from there that you may access the computer managers’
room.
On the first floor you find mostly offices, but also the Finance Department
and the main lecture room. This impressive room is suitable for seminars
with up to a hundred participants. Though it still retains its original shape of a
century ago (look at the cameos representing symbols of sciences and
engineering!), it is also equipped with audiovisual facilities meeting the needs
of the 21st century. Its excellent acoustics permit the organization of concerts
(there is indeed a Christmas concert here each year); it can be also
transformed into a ballroom during the Mathematicians’ Ball. The lecture
room opens from a pleasant lounge suitable for discussions as well as smaller
receptions.
The second floor is again mostly occupied by offices, but you also find here
two smaller seminar rooms called the dogs’ room and the cats’ room,
respectively (ask a local colleague for the origin of these names) and another
lounge. The recently created third floor is exclusively devoted to offices.
41
History of the building
After its foundation, the Institute – with eleven full-time and a few part-time
researchers – was housed in four offices on the second level of the main
building of the Technical University. Later the Institute moved into rented
rooms, among others in 31 Stalin (now Andrássy) avenue and 4 Zichy Jenő
street. In 1958, it moved to its present day premises at 13–15 Reáltanoda
street.
Until 1887, there were two separate lots and houses on the site of the
Reáltanoda building. In 1868 baron Béla Rédl bought the lot at 13 Reáltanoda
street. He received permission to build a one-story palace during the same
year, which is documented as an existing building by 1873. In 1886 baron
Rédl bought the neighboring lot at 15 Reáltanoda street from its former
owner and enlarged his palace. The present arrangement, a building enclosing
a relatively large courtyard, was formed after several modifications. It was
built in stages, which can be seen not only from the plans of the building but
also from its facade. It is conceivable that the plans for the original palace at
13 Reáltanoda street were designed by Theofil Hansen of Vienna; those of the
1886-87 extension are by János Wagner.
Baron Richard Hammerstein inherited the palace in 1907, and applied for a
permission to enlarge it to a three-story building. Before the construction
could have been started, he sold the building to the Hungarian Engineering
and Architecture Association (HEAA) and Alajos Hauszmann, then president
of HEAA, made designs for the residence. Hauszmann was one of the most
sought-after Hungarian architects of his time; his most famous building is
that of the Curia (Supreme Court), today Museum of Ethnography, on
Kossuth square, just opposite the Parliament. His design for the Institute
consisted of the addition of a third story and a representative lecture room,
resulting in a beautiful and harmonious building. It served as the seat of the
HEAA until 1946. Afterwards it became a ‘People’s College’ for several
years, then the seat of the Confederation of Societies in Engineering and
Exact Sciences. The Mathematical Institute has been the occupant of the
building since 1958.
The next major restructuring of the institute’s building was carried out
between 2000 and 2003, approximately a century after Hauszmann’s work.
Its main aim was to provide more office space for a continuously expanding
institution, but also to improve general working conditions and, from the
point of view of architecture, to eliminate later modifications of the building
42
and restore Hauszmann’s design as closely as is possible without confronting
practical needs of the institute.
The most spectacular part of this transformation was the creation of 12 new
air-conditioned offices in the northern part of the institute’s attic which also
gave way to the elimination of some anomalous conditions on the second
floor, giving rise to the new lounge and the two small seminar rooms. On the
first floor a flat from the neighbouring building was attached to the institute,
thereby enlarging the office space, and the entrance hall was restored to its
original shape, close to Hauszmann’s design. Finally, a fifty-year-old dream
came true by the construction of an elevator in the inner courtyard.
The library
The library of the Institute is the most important mathematical library in
Hungary, with a stock of almost 40,000 titles and over 300 periodicals
arriving regularly via exchange or subscription. The basis for exchange is the
Institute’s journal (see the next section). The number of library visitors is
constantly increasing: while in 1977 it had 611 readers and 2044 visitors, in
1999 these figures climbed up to 1640 and 14,500, respectively.
The library received computer equipment in the second half of the 1980’s; it
currently uses the Corvina system for handling library procedures and for
exchanging information with other libraries in Hungary. Today the catalogue
of the institute’s library can also be consulted via the Internet. For local users
many journals are available online and they have access to all major
mathematical databases such as Mathematical Reviews and Zentralblatt
MATH.
The journal of the Institute
The first issue of the forerunner of our current journal,
the Proceedings of the Applied Mathematical Institute,
was published in 1953, followed by the second and the
third issues in 1954 and 1955, respectively. The next
issue, published in 1956, had a modified title,
corresponding to the change in the name of the Institute.
These proceedings were published yearly until 1964.
Our
current
journal,
Studia
Scientiarum
Mathematicarum Hungarica, a scientific periodical
established in 1966 and published by the Hungarian Academic Publishing
House (today a branch of Kluwer Academic Publishers) is, in a certain sense,
A cover of Studia
43
a continuation of these proceedings. The editor-in-chief has always been the
director of the institute and the editorial board includes the heads of the
research divisions. Currently, there are four issues a year, among which
occasionally special issues in the honour of distinguished Hungarian
mathematicians.
The homepage of the Institute
As any significant institution nowadays, the Institute has a homepage on the
Internet, accessible at http://www.renyi.hu. Its main features include:
♦ latest news from the Institute on front page, together with a list of
upcoming events;
♦ information about the Institute’s activities, open positions, training
programs;
♦ a regularly updated list of mathematical seminars in Budapest and
Hungary, e-mailed weekly to those who join an open subscription
list;
♦ a directory of the Institute, with links to homepages of researchers
and research groups;
♦ homepages of conferences organized at the Institute as well as
archives for past conferences and seminars;
♦ the library’s page, with electronic access to the catalogue and (for
local users) online journals and databases;
♦ practical information for visitors.
Please visit this page for further information concerning the Institute. We are
grateful for any comment or criticism.
44