# Børge Christian Jessen

### Born: 19 June 1907 in Copenhagen, Denmark

Died: 20 March 1993 in Copenhagen, Denmark

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**Børge Jessen**'s parents were Hans Jessen (1865-1935), a business manager, and Christine Vilhelmine Larsen (1875-1959). Børge was the youngest of his parents' five children, namely: Sten Jørgen Jessen (1900-1981); Inger Jessen (1902-1990) (who married Alfred Johannes Rosenkrantz); Bjørn Jessen (1903-1943); Gert Andreas Jessen (1905-1971); and Børge Christian Jessen (1907-1993), the subject of this biography.

Jessen became fascinated by mathematics while at school in Copenhagen. He had two excellent teachers, Mrs Teilman and Julius Pál. He was taught by Pál in his first year at the Sankt Jørgens Gymnasium in Frederiksberg, Copenhagen. This school, founded in 1858, had undergone a number of changes of name. It was called Henrik Madsens Skole from 1904 to 1919 when it became a state school called Sankt Jørgens Gymnasium. Julius Pál (1881-1946) was a Hungarian who was born into a Jewish family and originally named Gyula Perl. He modified his name to a more Hungarian version in 1909. He fled from the post-war problems of Hungary in 1919, coming to Copenhagen as a teacher at the Sankt Jørgens Gymnasium. He was a friend of Harald Bohr and later became his assistant. He did excellent work on Jordan curves and the Kakeya problem. Jessen writes in [6]:-

[Certainly Pal (he dropped the accent on the "a" when he moved to Denmark) was a demanding teacher who suggested to Jessen that he read the recently published four volume work on mathematical analysisI]feel a great debt of gratitude toward him.

*Laerebog i matematisk analyse*Ⓣ by Harald Bohr and Johannes Mollerup. This was a demanding task for a school pupil but Jessen had mastered large parts of this work before he graduated from the Sankt Jørgens Gymnasium in 1925. Later in 1925 he entered the University of Copenhagen where he aimed at specialising in mathematics but also took courses on physics, chemistry and astronomy.

Having studied *Laerebog i matematisk analyse* Ⓣ, Jessen knew most of the material offered for first year students, so he only took the mathematics courses by Johannes Hjelmslev (1873-1950) in geometry and by Jakob Nielsen in rational mechanics. He went on to take a course by Jakob Nielsen on topology and courses by Harald Bohr on number theory and complex analysis. By 1929, when he was in the fourth year of his university studies, he had already seven papers in print (five in Danish and two in German): *Løsning til Opgave 14. Aarg. 1926* Ⓣ (1926); *To Trekantsūtninger* Ⓣ (1926); *Bemaerkning om den Eulerske Polyedersaetning* Ⓣ (1928); *Om Delingslighed for maalelige Punktmūngder* Ⓣ (1929); *Om konvekse Kurvers Krumning* Ⓣ (1929); *Über konvexe Punktmengen konstanter Breite* Ⓣ (1929); and *Über monotone Funktionen* Ⓣ (1929). He had also read books by René-Louis Baire, Constantin Carathéodory, Henri Lebesgue, and Charles de la Vallée Poussin. His progress had been so outstanding that Harald Bohr asked him to collaborate on joint work on the Riemann zeta-function which led to their joint paper *Om Sandsynlighedsfordelinger ved Addition af konvekse Kurver* Ⓣ (1929). Jessen wrote a Master's thesis (equivalent to a Ph.D.) on the theory of almost periodic functions (a topic which Harald Bohr had initiated a few years earlier with three long papers) and graduated on 22 June 1929. Bernard Bru and Salah Eid write in [3]:-

A grant from the Carlsberg Foundation allowed Jessen to spend two months in Szeged, Hungary, later in 1929, where he had lengthy discussions with Frigyes Riesz, Alfréd Haar and Lipót Fejér. Moving to Göttingen for the academic year 1929-30, he attended courses by David Hilbert and Edmund Landau. He submitted his 3-part 76-page doctoral thesisHe was invited to make a presentation to the seventh Congress of Scandinavian Mathematicians, held in Oslo from19to22August1929. Jessen presented his theory of integration in German and in a particularly clear way, a very nice exposition with a reproduction of Hilbert's space-filling curve as it appeared in the original article of1891, which shows at first glance that measure is preserved, the curve preserving throughout construction a perfect symmetry between the two axes. Jessen did not state his two theorems which he undoubtedly considered marginal, but announced a Fourier theory for functions with a countable infinity of periods. The transactions of the congress were published in1930, so that at the proof stage Jessen could add a reference to Daniell of whom he had been informed meanwhile.

*Bidrag til Integralteorien for Funktioner af uendelig mange Variable*Ⓣ to the University of Copenhagen and returned there to defend his thesis on 1 May 1930. This thesis (equivalent to an habilitation thesis) was simply an improved version of the final chapter of his Master's thesis. An English version of the thesis, containing further developments of his results, was published in

*Acta Mathematica*in 1934 as a 75-page paper with the title

*The Theory of Integration in a Space of an Infinite Number of Dimensions*.

After a short trip to Paris, Jessen was appointed as a docent at the Royal Veterinary and Agricultural School in Copenhagen in the autumn of 1930. On 29 January 1931 he married Ellen Margrethe Charlotte Pedersen (21 May 1903-29 December 1979) in Solbjerg Church in the Frederiksberg district of Copenhagen. Ellen Pedersen had trained as a mathematician and was the daughter of Peder Oluf Pedersen (1874-1941) and Maria Theodora Lihme (1871-1930). P O Pedersen was an engineer and physicist who was rector of Den Polytekniske Lūreanstalt (now the Technical University of Denmark).

Jessen was able to spend from April 1933 to June 1934 on research leave funded by the Rockefeller Foundation. He went first to Cambridge, England, where he met G H Hardy, A S Besicovitch, L C Young, and Garrett Birkhoff (who was in Cambridge working with Philip Hall on group theory). On 23 September 1933 Jessen and his wife sailed from Southampton, England, to New York, USA, on the Cunard ship *Berengaria*. They arrived on 29 September and went to the Institute for Advanced Study in Princeton. While at the Institute for Advanced Study he collaborated with Salomon Bochner and Aurel Wintner leading to two joint papers (one with each) [3]:-

While based at Princeton, Jessen also visited Harvard University, Yale University and Brown University. On 4 June 1934 he visited the Niagara Falls, crossing into Canada at that time. On 23 July 1934, along with his wife, he sailed on the Cunard shipIn Princeton Jessen met Aurel Wintner. Two more different mathematicians can hardly be imagined. Jessen was elegant, reserved, rigorous, scrupulous, Wintner was impassioned, a compulsive eater, overflowing with projects and works in progress, all done with great noise. Wintner was always interested in celestial mechanics and accordingly in almost periodic functions. For some time he had been studying the limiting laws of series of independent random variables of the type considered by Steinhaus, Jessen and others, what was called at the time the problem of infinite convolutions, on the line or in a finite-dimensional space. Wintner had obtained interesting results on the subject, which was one that Jessen had also come near to either alone or with Harald Bohr. Sometime in1934, probably in the spring, Jessen and Wintner decided to pool their experience and write an article "Distribution functions and the Riemann zeta function" ...

*Georgic*back to England, arriving in Liverpool. They were back in Denmark in time for Jessen to attend the 8th Scandinavian Congress of Mathematicians in Stockholm 14-18 August 1934.

A happy event in 1934 became a tragedy; Christian Berg writes [2]:-

On 1 June 1935 Jessen was appointed as Professor of Geometry at the Technical University of Denmark in Copenhagen. This had been Den Polytekniske Lūreanstalt, but was known as Danmarks tekniske Højskole from 1933. It had been founded in 1829 and modelled on the École Polytechnique in Paris. Johannes Hjelmslev, the professor at the University of Copenhagen, was due to retire in 1940 and Jessen applied to be his successor. In fact Jessen was the only applicant for the professorship. On 9 April 1940, however, German forces entered Denmark despite the country having declared itself neutral. The Danish government quickly surrendered but Denmark was not occupied by German troops at that time and the government remained in office becoming a Protectorate Government. At this point Jessen withdrew his application for Hjelmslev's professorship and Hjelmslev was persuaded to remain in post until the end of August 1942. When Hjelmslev finally retired in 1942, Jessen again applied for the position once more being the only applicant. Berg suggests in [2] that the reason he was the only applicant was:-Børge and Ellen had a son, Lars in1934, but tragically the boy became ill of meningitis at the age of two and was disabled.

In 1948 Jessen became head of the Department of Mathematics, a position he continued to hold until 1967. During this time he played a major role in planning the H C Ørsted Institute which opened in 1963 to house mathematics, physics and chemistry.... probably because the other potential Danish applicants knew that they could not compete with him.

He became more involved in administration following his election to the board of the Carlsberg Foundation in 1950. He had already been elected to the Royal Danish Academy of Sciences and Letters as early as 1939. It was his role on the Carlsberg Foundation which gave him heavy duties, particularly from 1955 to 1963 when he served as chairman. This left him little time for research and indeed, between 1952 and 1967 his only research publication was *Some aspects of the theory of almost periodic functions*, a paper in the *Proceedings of the International Congress of Mathematicians, Amsterdam, 1954* which was published in 1957. Jessen also played a major role in the Danish Mathematical Society, being its secretary from 1930 to 1942, serving on the board from 1952 to 1958, the last four of these years as President of the Society. He also did editorial work, being editor of *Matematisk Tidsskrift B* Ⓣ from 1935 to 1949 and on the editorial board of *Acta Mathematica* from 1948 to 1988.

The International Congress of Mathematicians was held in Edinburgh, Scotland, in 1958. Jessen addressed the Closing Session of the Congress. See THIS LINK.

Christian Berg was a student at the University of Copenhagen in the 1960s. He tells us with first hand detail about Jessen as a teacher [2]:-

Jessen retired in 1977, giving the lecture [6] (From my years of learning) at a celebration in his honour held by the Department of Mathematics at the University of Copenhagen. His last years were tragic ones, for his wife Ellen died in 1979 and he became disabled due to Parkinson's. His eyesight and hearing both deteriorated and he suffered a further heavy blow when his son Lars died in 1990. He then left his apartment in central Copenhagen and spent his final years in a rest home. He asked Christian Berg to find a good home for his extensive mathematical library which was mainly donated to Aalborg University.In1960the curriculum in mathematics was changed, and Jessen taught the second year analysis course. It comprised the basic knowledge about Fourier series, Lebesgue integration and complex analysis, but Jessen also liked to include basic results like Weierstrass' approximation theorem, Peano's curve and Weierstrass' nowhere differentiable continuous function. The lectures were very well prepared, and the blackboard was used in an efficient way, from the upper left corner to the lower right corner. Complicated drawings were often made beforehand and hidden behind another blackboard, and already written formulas were modified with coloured chalk to save writing. It was an aesthetic experience to attend Jessen's lectures. The essential points were made clear, and after the lecture one had the impression that everything was easy and elegant. Jessen enjoyed including small anecdotes about the mathematicians behind a theorem, and he often circulated books from the library during the lectures, so we could look at a portrait of a famous mathematician or at a classical mathematical paper. When lecturing about Jensen's inequality in convexity, he said jokingly that there were two mathematicians with the name of Jensen - the famous telephone engineer behind the formula, and himself when his name was misspelled. About Wintner he told us that his name was used for a physical unit: "One Wintner meant100cigarettes a day". Due to the increased number of students in the1960s a new system involving teaching assistants was introduced with success. Two teaching assistants per class were chosen among the second year students and appointed as "fellow instructors". They had to learn the material at the same time as they helped their fellow students. On Saturday morning Jessen met with the fellow instructors and prepared them for the material to be covered in the lectures and exercises for the following week. I had the privilege of being such a fellow instructor and learned a lot because Jessen could not refrain from telling us many extra things. He also told us that he used to throw away the solutions of the exercises when the year was over, so that he had to rediscover the solutions every year. In this way, he was reminded about the difficulties of the exercises. At the final exam Jessen was always very favourable towards the students. He liked to cite Harald Bohr for having said that one should always give students a final grade that is a little higher than what they could expect. In that way they would always remember their years of study with joy. In addition to his teaching for the first or second year students, Jessen also gave courses for the students preparing for the Master's Degree. The lectures I followed were supported by handwritten notes of high quality distributed to the students. He liked to take up classical subjects such as conformal mapping, the Gamma function and the prime number theorem, where he could set a goal of obtaining a key result at the end.

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

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