Jacobus Hendricus van Lint

Born: 1 September 1932 in Bandoeng, Netherlands East Indies, now Indonesia
Died: 28 September 2004 in Eindhoven, The Netherlands

Jack van Lint's father was Hendrikus Jacobus van Lint who, at the time when Jack was born, was a mathematics teacher at a secondary school Bandoeng, Netherlands East Indies (now Indonesia). He was an excellent teacher and had a remarkable memory, two characteristics that his son Jack inherited. When Jack was five years old his father was given a year off and the family was able to return to the Netherlands. After a year the family returned to the Netherlands East Indies, but not to Bandoeng, rather they went to Batavia (now named Jakarta and the capital of Indonesia). The city was undergoing a period of modernisation and it was at the time that Jack began his education in an elementary school in Batavia.

After France and the Netherlands fell to the Germans in the summer of 1940 near the beginning of World War II, the Japanese decided to invade their colonies. By February 1942 only Java remained to complete the Japanese programme of conquest. Jack's father undertook military duties and was given the job of training pilots. The Allies attempted to prevent the Japanese invasion by attacking the fleet as it sailed towards Java. However the Allies were defeated at the Battle of the Java Sea on 27 February. The Japanese landed at three points on Java on 28 February and rapidly expanded their beachheads. Realising that defeat was inevitable, the military personnel were told to board one of ten ships which would take them to Australia. Jack's family, despite heavy bombing, were able to board one of these ships at Cilacap, a port on the southern coast of Java, which left shortly before the Allied troops in Java surrendered on 9 March. Of the ten ships, only three made Australia, the other seven being torpedoed. The van Lint family was lucky to be on one of the three.

The van Lint family were only in Australia for a few months before they were once again aboard a ship, this time sailing to the United States. They settled in Jackson, Mississippi, and Jack continued his education at an elementary school in Jackson. He attended this school for session 1942-43 and his ability at languages is nicely illustrated by the fact the by the end of the year he came top of the class in English. His father was sent to Chicago in 1943 and Jack attended elementary school there from 1943 until 1945. After World War II ended Jack's father, who had now trained as a meteorologist, was required to return to Indonesia to continue service in the Dutch army. However, it was not safe enough for women and children, so Jack, his brother Hans, and his mother spent a year in Bundaberg, Australia where Jack attended Intermediate school during session 1945-1946.

The Dutch had assumed that they would be able to return to the pre-war situation in Indonesia, but an Independence movement made this impossible and a series of risings marked the beginning of a revolution. It was not safe for the Dutch to remain and Jack's father, together with the rest of the van Lint family, sailed back to the Netherlands, arriving in November 1946. They went to live with family members in Arnhem and Jack began his secondary education in this city in 1946. By this time he was fourteen and during the many moves around the world he had lost a year so was old to be starting his secondary education. It was at this school that he showed his mathematical abilities but he was not to be able to complete his secondary education at Arnhem for in the middle of session 1948-49 the van Lint family moved to Zwolle where his father had been appointed as director of the Rijks HBS (hogere burgerschool) in Bagijnesingel. Jack's final year of secondary education was spent in the HBS in Zwolle and by the time he graduated in 1950 he was ranked as the best student in the Netherlands, a remarkable achievement for someone who had been forced to attend schools in four continents.

Van Lint entered Utrecht University in 1950 and there he was strongly influenced by Hans Freudenthal, Jan Popken and Frederik van der Blij. On 31 January 1955 he graduated M.Sc. with distinction) in mathematics and physics but he was already employed as an assistant to Hans Freudenthal in the Mathematical Institute of Utrecht University. He held this post from September 1952 to September 1956. Then he spent session 1956-1957 first at the University of Göttingen then at the University of Münster but during this period he was undertaking research for his doctorate with van der Blij as his thesis advisor. On 28 October 1957 he was awarded his doctorate (with distinction) from Utrecht University after submitting his thesis Hecke Operators and Euler Products on modular functions. In the thesis, he developed a theory of generalized Hecke operators, being automorphic forms of not necessarily integral dimension, as defined by Klaus Wohlfahrt in his 1955 dissertation at Münster University. This theory allowed him to derive, in a systematic way, many known results and some new ones. In the thesis van Lint also studied modular forms of non-integral dimensions that have an Euler product.

From September 1957 to June 1959 he was a research associate at the Netherlands Organisation for Pure Scientific Research. Then in June 1959 he was appointed as professor of mathematics at Eindhoven University of Technology. He continued to hold this chair until he retired in 1997 after being dean of the mathematics faculty from 1989 to 1991, then rector of the university from 1991 to 1996.

We will discuss his mathematical achievements below, but first let us note that van Lint was an excellent sportsman, particularly excelling as an outstanding swimmer. At the University he successfully campaigned for sports facilities for students, such as a private swimming pool. At Eindhoven the Van Lint Students Sports Week was instigated and also the International Professor van Lint Tournament. Let us also mention that van Lint married Elisabeth Barbara Janna Teunissen on 15 December 1961; they had two children Barbara (born 26 September 1962) and Jacobus Hendricus (born 15 November 1964).

Van Lint's research following the award of his doctorate continued on a number of distinct paths, one of which was a direct outcome of the work of his thesis. His papers included Über einige Dirichletsche Reihen (1958), On some special theta functions (1958), On the multiplier system of the Riemann-Dedekind function eta (1958), Linear relations for certain modular forms (1959), On the hermitean product of ordered point sets on the unit circle (1960), and A problem in Hilbert space (1960). He then became interested in number theory publishing papers in that topic such as (jointly with N G de Bruijn) On the number of integers ≥ x whose prime factors divide n (1962), (jointly with H E Richert) On primes in arithmetic progressions (1965), and (with P Erdős) On the number of positive integers ≤ x and free of prime factors > y (1966). However, around this time, Jaap Seidel encouraged him to take an interest in combinatorics and discrete mathematics. This was a significant move and resulted in works for which he is most famed.

In 1971 he published the book Coding theory. G Solomon wrote in a review:-

For the student with a background in algebra, the author has written an elegant set of notes on algebraic coding. Written from the viewpoint of the mathematician, and with no intent to be all-inclusive, he has managed to give the reader some deep insights and directions into the major problems of the subject.
In 1975 he published Graph theory, coding theory and block designs written jointly with Peter Cameron. Norman Biggs writes:-
This book is based on lectures given by the authors during 1973 at Westfield College, University of London. The material has been well adapted to the chosen format, and the result is a brisk and entertaining introduction to some areas of common ground between graph theory, coding theory and design theory. In several places the treatment compares favourably, in clarity and elegance, with previous accounts available in the literature.
A revised edition appeared in 1980 which Vera Pless reviewed:-
The predecessor of this book was a welcome volume which gave the relevant concepts and theorems in these three areas and showed their interrelationships. ... The high level of presentation of the previous volume has been maintained. The present volume should be very useful in the fruitful areas of research which the relationships between these areas present.
In 1982 van Lint published Introduction to coding theory. Giuseppe Longo writes:-
This is a concise, self-contained and neat introduction to the subject of coding theory suitable for students of mathematics. To some extent, it is an updated version of 'Coding theory', by the same author, but the scope is wider.
Van Lint himself explained several years later that:-
... this book was conceived in 1981 as an alternative to outdated, oversized, or overly specialized textbooks in this area of discrete mathematics.
Van Lint continued to publish outstanding texts. The next, written jointly with Gerard van der Geer, was Introduction to coding theory and algebraic geometry. The book was based on lectures given in the seminar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Düsseldorf, 16-21 November 1987. It is described as 'elegant and useful'. Another book written jointly with Peter Cameron was Designs, graphs, codes and their links which in many ways is a third revised edition of their earlier text:-
The format is very much the same: short, tightly reasoned chapters with an emphasis on the concrete and special rather than on general theories.
In 1992 van Lint published his final text (although he went on to produce several later revised editions of his earlier books). The 1992 book, written with R M Wilson, was A course in combinatorics. The authors boldly suggest that:-
... after a course like this, students who subsequently attend a conference on 'combinatorics' would hear no talks where they are completely lost because of unfamiliarity with the topic.
It may be a bold claim but most would agree that in the 530 pages of the book they succeed admirably. The authors also explain in the Preface:-
Of course, none of the chapters could possibly give a complete treatment of the subject indicated in their titles. Instead we cover some highlights - but we insist on doing something substantial or nontrivial with each topic. ... The material in every chapter has been presented in class, but we have never managed to do all the chapters in one year.
It was not only as a researcher and expositor that van Lint excelled. He made an outstanding contribution in many other areas. He acted as an editor for nine international journals:
Nieuw Archief voor Wiskunde, Managing editor (1983-1987);
Journal of Combinatorial Theory A (1976-2004); Discrete Mathematics (1972-2004);
SIAM Journal of Applied Mathematics (1976-1979);
International Journal of Mathematical Education (1978-1988);
Annals of Discrete Mathematics (1972-1980); Geometriae Dedicata (1983-2004);
IEEE Transactions Information Theory (1986-1989);
Codes, Designs and Cryptography (1990-2004).
He was an active member of various international committees:
European Science Foundation (1977-1978), European Mathematical Council (1978-1990),
International Council of Scientific Unions / CTS (1986-1994),
International Committee on Mathematical Instruction (1986-1994),
National Fund for Scientific Research (Belgium, 1990-1997),
Scientific Committee ECM 2000 (1997-1999).
A particular honour which few have matched is that he was invited to address the International Congress of Mathematicians on four separate occasions, in Warsaw in 1983, in Berkeley in 1986, in Kyoto in 1990, and in Berlin in 1998. He was also an invited speaker at the International Congress on Mathematical Education on three separate occasions, in Karlsruhe in 1976, in Berkeley in 1980, and in Adelaide in 1984.

Among the other honours which van Lint received we mention: elected member of the Royal Netherlands Academy of Arts and Sciences (1972); appointed Knight in the Order of the Lion of the Netherlands (1993); honorary professor Technical University of Bucharest, Romania (1995); honorary doctorate from the University of Bergen, Norway (1996); honorary doctorate from the Technical Unversity of Bucharest (1996); honorary professor Xi'an Jiaotong University, China (1996); Neways Award from Eindhoven (1997); Euler Medal of the Institute of Combinatorics and Applications, Canada (1997); honorary doctorate from the University of Gent, Belgium (2000); and elected honorary member of the Koninklijk Wiskundig Genootschap (Dutch Mathematical Society) (2004).

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

July 2008
MacTutor History of Mathematics