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Helge Tverberg delivers a memorial for Ernst Sejersted Selmer
On 7 June 2007 Professor Emeritus Helge Tverberg delivered a memorial speech for Professor Ernst Sejersted Selmer in a joint meeting of the Norwegian Academy of Science and Letters. The speech was delivered in Norwegian but we give an English translation below.
Memorial speech for Professor Ernst Sejersted Selmer, by Helge Tverberg.
Ernst S Selmer was born on 20 February 1920 as the first child of (later) Professor Ernst Westerlund Selmer, who was also a member of the Norwegian Academy of Sciences and Letters, and Mrs Ella Selmer. The Selmer family came to Norway from Schleswig-Holstein in the early 18th century and has left many traces here. Its best-known member is probably Selmer's great-grandfather's cousin, Christian August Selmer, Prime Minister in 1884.
A few words about Selmer's parents may be in order to shed light on his energetic nature. Not everyone knows that the philologists' infamous 12-hour exam was due to Ernst W Selmer, who once sat for over 20 hours, so it was felt necessary to introduce a limit. Ella Selmer was active in the parents work at Stabekk gymnasium where Ernst and his two brothers, Knut (also an Academy member) and Nicolay attended. She was later the driving force behind the construction of a nine-storey apartment block at Kringsjå for university pensioners.
Selmer's mathematical talent was already evident during his school days. In 1937 he received a prize at school, and he was also a contributor to Tall og Tanker (Numbers and Thoughts), a separate mathematics magazine at Stabekk Gymnasium. In 1938 he won the Crown Prince Olav's Mathematics Prize for high school students. His brother Nicolay was also awarded Crown Prince Olav's Mathematics Prize, so if he had not died in 1943, while training to be a bomber pilot, the family might have had two mathematicians. Ernst also showed a sporting side as an outstanding shot putter and discus thrower in intergymnasium competitions, also in a Nordic context.
Selmer's study period at the University of Oslo began in a special way. At the same time as he studied mechanics, physics and chemistry, he worked with mathematics. In 1942 and 1943 he published a total of eight articles on prime numbers. In his main thesis from 1945, which is based on these, he mentions that the work on the thesis involved 600-700 hours of calculation work; this was a foreshadowing.
The continuation was also special. In 1943, the Germans closed the University and arrested all the students they could lay their hands on. Selmer fled to Sweden and in 1944 he was sent on to England, where he "arrived with the first V1 bombs", as he said. His technical talent had been discovered in Sweden, so in addition to the more mathematically focused work with codes that he had already started there, he was now given complete technical responsibility for all Norwegian military and civilian cipher machines in London.
In 1945 he was able to complete his cand.real. studies, with the brilliant main grade 1.15. He was also able to marry Signe Randi Johanne (better known as Lillemor) Faanes who had been waiting for him at home. She was his great support throughout his life and his great efforts in many fields would probably not have been possible without her.
In 1946 he became a university lecturer in Oslo, and his great pedagogical abilities immediately became apparent (I have heard that he was the Pedagogical Seminar's best student in practical teaching skills). Throughout the years he gave very good lectures, richly illustrated with concrete examples, and at all levels. In 1948 he published a textbook on differential and integral calculus that became a long-lasting success. It was characterised by his practical sense and was very suitable for students who needed certain knowledge without going into too much of the theoretical background.
Selmer now began mathematical research in earnest. In 1951, his major doctoral thesis was published on Diophantine equations of the type . Here are given integers and one asks for solutions in integers (the trivial solution does not count). He solved many equations and showed that many others had no solution. The case is particularly interesting. The corresponding equation has no solution despite passing certain tests. This shows that the so-called Hasse-Minkowski principle, which applies to quadratic equations, does not apply to cubic equations. The example will forever link Selmer's name to the triple 3, 4, 5, just as Pythagoras's is linked to the same triple.
Selmer spent the spring semester of 1949 in Cambridge, where he became acquainted with the number theorist J W S Cassels who later became famous. This was useful to both of them, because Cassels could use Selmer's extensive calculations, and could also continue to develop the theory. He also discovered a group that was implicit in Selmer's results and named it the Selmer group. Previously, the great Norwegian mathematicians Abel, Sylow and Lie had had groups named after them, so this must have felt good!
The next stay abroad in Princeton and Los Angeles in 1951-52 was of particular importance to Selmer. Now he could use electronic computers, the revolutionary new tool, to continue his calculations from his doctoral thesis. His combination of practical and theoretical talent came into its own here: he later proudly said that he was the first to write a program for the Princeton computer that worked on the first attempt. It should also be mentioned that at this time he actually constructed, alone, a computer that, under the name Burroughs 205, was the only serious competitor to the IBM 650 in the late 1950s.
By the way, it must have been an adventure for a young university lecturer to come to Princeton and meet, and associate with, people like von Neumann, Einstein, Oppenheimer and our own Norwegian star Atle Selberg.
In 1956, Selmer studied polynomials of the form with a view to factoring into polynomials with integer coefficients. This material was further developed by Wihelm Ljunggren and a number of his students, and also by the famous Polish mathematician Andrzej Schinzel. The polynomials have recently been named Selmer polynomials.
In 1957, Selmer became a professor at the University of Bergen, where he remained until his retirement in 1990. Here he became a resource person. Not only did he put a lot of effort into developing the teaching of pure mathematics, he was also the main architect of the Faculty of Mathematics and Natural Sciences' curriculum of 1959. In the years 1960-68 he was vice-dean and dean of the faculty, interrupted only by a year off in Cambridge in 1964-65.
At Cambridge he entered another mathematical area: linear recursion and periodic sequences. This was related to his work with codes during the war. Unknown to most people, he had continued this afterwards. He had close contact with intelligence services both inside and outside NATO, and he developed, among other things, codes that were used by the whole of NATO. The interesting mathematics he came across here provided the basis for a number of major projects, including those of Dan Laksov and Tor Helleseth, both now members of the Academy. Helleseth is now head of the Selmer Centre at the University of Bergen. It was established in 2003, but its roots go back over 60 years.
Despite his many tasks, Selmer was a very thorough and inspiring graduate supervisor. He sometimes did research in parallel with the student (without the latter losing credit) and one student told me that he sometimes stayed up at night to be able to arrive at a result first and thus beat his supervisor.
Selmer's relationship with computers was multifaceted. In 1968 he arranged for our department to have an administrative assistant who would perform calculations on a computer for the pure mathematicians (instead of teaching). This administrative assistant was of great benefit, not only to Selmer and his group, but also to the rest of us; I myself really benefited from it on several occasions. At the University of Bergen, Selmer was a key figure in the introduction of teaching in and use of electronic data processing. At the national level, he was, among other things, a member of the State Council for Data Processing for many years, and a board member of the Norwegian Central Computing Centre. He was also involved in matters of great social importance: the introduction of personal identification numbers, where he could use his special mathematical insight, and the question of teaching university subjects at district university colleges. In the latter case, the Selmer Committee's recommendation (1972) had a strong influence on further developments. All this, together with his scientific efforts, meant that he was made a Knight of St Olav, 1st class, in 1983. Before that, he was already a member of the Norwegian Academy of Sciences and Letters and of the Trondheim Society of Sciences.
From the mid-1970s, Selmer was given the opportunity to concentrate on the subject fully again, now in yet another new field: combinatorial additive number theory. It can be said, somewhat frivolously, that this concerns certain problems that arise, for example, when exchanging amounts of money for coins of given values. The collaboration with students and institute employees, and with Gerd Hofmeister in Mainz, meant that Mainz and Bergen were for a number of years the leading centres in this special field. Selmer himself was proud that after turning sixty he had written "two doctorates". The problems in this field may seem quite simple, but they are not at all. They are also very well suited to the use of computers, which may have influenced Selmer's choice.
On the mathematical side, it should also be mentioned that Selmer was very heavily involved when the Norwegian Mathematics Council was formed in 1971, and that he took the initiative for the first Nordic Combinatorics Meeting in 1981. Both projects have proven important and viable.
All of this would have been a big enough effort for most people. But not for Selmer: for 25 years, from 1954 to 1978, he was the editorial secretary of the semi-popular science journal Nordisk Matematisk Tidskrift. Here he did everything, from meticulous proofreading to writing assistance. When he was relieved in 1979, a group of eight mathematicians in Kristiansand shared the job among themselves. This work gave him many friends and acquaintances in the Nordic countries, and was probably partly a stimulus during periods of less mathematical activity.
We colleagues could never notice that Selmer was too busy or stressed. He had a constant good mood, a fine sense of humour and a sober but pleasant nature. Through his versatile activities, he came into contact with countless people outside the Institute, but I have never heard an unfavourable word about him. There was a palpable loss when the Selmers retired to Ski in 1990. But we understood well that they wanted to be closer to their country house in Hvitsten and to their only child, the microbiologist Johanne-Sophie Selmer at Karlstad University. Selmer prioritised home and family; as a young man, it made a strong impression on me when he would not break an agreement with his daughter in favour of a meeting with Fields Medalist Alan Baker. Work was his life, but he had one hobby, gardening, carried out with characteristic zeal and diligence, so that sometimes the botanist Knut Faegri would make excursions to Selmer's garden.
The retirement years at Ski were good for the Selmers. One mathematical event particularly pleased them. In 1994, the Englishman Andrew Wiles proved the so-called Fermat's Last Theorem on certain Diophantine equations. This can perhaps be considered the greatest mathematical event of the twentieth century. The Selmer group played an important role in this proof, and it was of course both interesting and pleasant for Selmer to participate in the presentation of the Rolf Schock Prize to Wiles in Stockholm.
Selmer was in good physical and mental shape until he suffered a stroke in the autumn of 2004. After that, he was never the same, but he kept his good humour, so it was always a pleasure to visit him. On 8 November 2006, he quietly fell asleep. On 16 February 2007, a memorial seminar was held in his honour at our department. It was perhaps only then that the extent and versatility of his contributions to the profession, the university, and society became fully apparent to us. I gratefully salute his memory.
Last Updated December 2025