**Johan Jacob Seidel**was known to almost everyone as Jaap Seidel. His parents were both school teachers [5]:-

He attended Galvanistraat primary school then in 1930-31 participated in the Masterclass which took pupils from a number of schools and prepared them for attending the best quality secondary schools [5]:-At birthday parties the young boy saw teachers all the time.

He entered the Municipal Gymnasium in The Hague in 1931 and graduated from this high school in 1937. Later that year he entered the University of Leiden to study mathematics and physics. De Bruijn writes [5]:-I remember the hard problems in applied arithmetic, about rowing boats in a flowing river.

In his first year he took Kloosterman's Linear Algebra course; it had a major impact and throughout his research career the influence of this course was evident. He passed his Candidates Examination in 1940. This was a difficult period since the German forces quickly overwhelmed the Dutch armies in the spring of 1940. Attempts were made to continue to run the country despite the German occupation but the University of Leiden was closed by the German occupational authorities in 1941, because students protested against the dismissal of their Jewish professors. When it became clear that the closure was not going to be a short one, Seidel, who had continued his studies there up to that point, now transferred to the Free University of Amsterdam where he was strongly influenced by Johannes Haantjes. However, his studies were disrupted again when the German occupiers forced him to go to Berlin as a labourer in a factory. Soon Seidel found an opportunity to escape from the Germans and was able to return to the Netherlands where he remained in hiding for the rest of the war.Jaap at once became a member of the little club of Leiden mathematics students living in The Hague, gathering weekly, usually at my home. ... Jaap was much more social than the others, certainly much more social than I was, and it always remained like that. At an early age already, Jaap had experience in what is now called Networking.

From March to July 1946, Seidel taught engineering at a secondary training school in Amsterdam, then from September 1946 to September 1950 he taught at the prestigious Vossius Gymnasium in Amsterdam. While undertaking his duties as a teacher, he was also working on his doctoral dissertation. Haantjes had moved from Amsterdam to Leiden, so it was natural for Seidel to submit his doctoral studied there. He was awarded his doctorate by the University of Leiden in 1948 for his thesis *De congruentie-orde van het elliptische vlak* Ⓣ written with Johannes Haantjes as his advisor. Haantjes and Seidel announced the results in the paper *The congruence order of the elliptic plane* (1947). Seidel published full proof in his 71 page thesis published in 1948. L M Blumenthal writes in a review:-

He was appointed as an instructor at the University of Delft in 1950 and promoted in 1955. Seidel had been put in charge of the Entertainment Committee for the International Congresses of Mathematicians held in Amsterdam in September 1954. He had the [5]:-This thesis contains the proofs promised in a recent note that the congruence order of the elliptic plane, with respect to the class of metric spaces, is seven(that is, seven is the smallest number with the property that an arbitrary metric space is congruent with a subset of the elliptic plane whenever each seven of its points are). Though the algebraic-geometric methods by which this result is established occasionally lead to proofs involving the examination of many cases and subcases(the longest proof covers more than seven pages)and they could hardly be carried through in elliptic three-space, the arguments(elementary in character)are presented in a clear and orderly manner. The reader must be referred to this painstaking work itself for details.

*... idea to attach an Escher exhibition to the congress. It was a great success. A great thing for Escher too: having it in the prestigious Stedelijk Museum, it gave him a recognition that he did not have before. And it brought him into contact with scientists from all over the world. In particular with Coxeter and young* Penrose.

In the spring of 1955 Seidel was given leave to study with Van der Ven in Rome, an unusual privilege for someone in his position. Johannes Haantjes became ill in 1955 (he died in the following year) and Seidel was asked to give some of his courses at Leiden. This proved excellent experience for him.

The Technical University Eindhoven was established in 1956 as a Technische Hogeschool (Technical College) and Seidel was appointed to run the mathematics department at the new university [5]:-

Van Lint writes about a new, and far more vigorous, period in Seidel's research career which started when he stopped being Head of Mathematics at Eindhoven [6]:-Jaap organized the mathematical department and the mathematical curricula all by himself. It was really a one-man-show. He was a wonderful organizer, knew to attract quite a good group of professors and instructors, and he let them do it the way he wanted it to do.

As an indication of his work we look the titles of conference presentations by Seidel:It is remarkable, for a mathematician, that Seidel's third period, as a prominent scientist, started when he was already47years old. The joint paper with Van Lint in1966(still cited)started a long sequence of important contributions to the theory of strongly regular graphs and design theory. He never ceased being a geometer, but algebraic methods and tools from algebra influenced his work increasingly. This algebraic trend and the fact that he is not a soloist, but the epitome of a collaborator, led to numerous joint papers with P J Cameron, Ph Delsarte, and J-M Goethals. A continued interest in very many other parts of mathematics was rewarded: a number of papers linked his own research to other areas such as group theory and the theory of integration.

Strongly regular graphs, *Third Waterloo Conf. on Combinatorics, *1968;

Quasisymmetric block designs, *Calgary Internat. Conf., Calgary, *1969;

Configurations, *Colloquium on Discrete Mathematics, Amsterdam, *1970;

Eutactic stars, *Fifth Hungarian Colloq., Keszthely, *1976;

Graphs related to exceptional root systems, *Fifth Hungarian Colloq., Keszthely, *1976;

The pentagon, *Bicentennial Congress Wiskundig Genootschap, Amsterdam, *1978;

The pentagon, *Second International Conference on Combinatorial Mathematics, New York, *1978;

Spherical designs, *Relations between combinatorics and other parts of mathematics, Ohio State Univ., Columbus, Ohio, *1978;

Two-graphs, a second survey, *Algebraic methods in graph theory, Szeged, *1978;

Strongly regular graphs, *Seventh British Combinatorial Conf., Cambridge, *1979;

Cubature formulae, polytopes, and spherical designs, *The geometric vein, Toronto, *1979;

Graphs and two-distance sets, *Combinatorial mathematics, VIII, Geelong, *1980;

Tables of two-graphs. *Combinatorics and graph theory, Calcutta, *1980;

Delsarte's theory of association schemes. *Graphs and other combinatorial topics, Prague, *1982;

Harmonics and combinatorics, *Combinatorics and applications, Calcutta, *1982;

Few-distance sets in *R*_{p,q}. *Symposia Mathematica, Rome, *1983;

Integral lattices, in particular those of Witt and of Leech. *Mathematical Structures in Field Theories, Amsterdam, *1986-1987;

Graphs and their spectra. *Combinatorics and graph theory, Warsaw, *1987;

Designs and approximation. *Finite geometries and combinatorial designs, Lincoln, NE, *1987;

Introduction to association schemes. *Séminaire Lotharingien de Combinatoire, Thurnau, *1991;

More about two-graphs. *Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity, Prachatice, *1990;

Spherical designs and tensors. *Progress in algebraic combinatorics, Fukuoka, *1993.

All these conferences published proceedings and Seidel's contribution was published in each. However he also spoke at many conferences where no proceedings were published, for example the 1976 British Mathematical Colloquium held in Aberystwyth in Wales in April of that year. His plenary lecture was *Spherical codes and designs*.

We end this biography with two tributes to Seidel. The authors of [2] write:-

The authors of [1] write:-Jaap Seidel loved Mathematics. He wanted to learn it, to understand it, and most of all to teach it. In his courses and personal contacts he was very inspiring. Many mathematicians, especially young ones, were influenced by Jaap. Besides being a teacher, he was also very interested in what other researchers were doing. He always tried to find links to subjects he had been working on. Jaap's work makes connections with several branches in mathematics, and he had struck friendships with mathematicians all over the world. He has been called an ambassador of mathematics.

Professor Seidel's love of mathematics and his enthusiasm as an expositor of mathematics have led to an international reputation as an ambassador of mathematics. He has been especially active in Eastern Europe and in Asia where he has contacted many mathematicians and introduced their work to the Western world. His encouragement and enthusiasm have been especially valuable to young mathematicians. Many of us have been warmly welcomed by Jaap and Ada into their home and into their family. Very quickly, mutual mathematical interests grew into a close personal friendship.

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

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