**Børge Jessen** was a Danish mathematician best known for his work in analysis and in geometry.

- Jessen became fascinated by mathematics while at school in Copenhagen.
- 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 analysis Laerebog i matematisk analyse Ⓣ(Textbook of mathematical analysis) 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.
- Having studied Laerebog i matematisk analyse Ⓣ(Textbook of mathematical analysis), 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.
- 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.
- 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 of 1891, 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 in 1930, so that at the proof stage Jessen could add a reference to Daniell of whom he had been informed meanwhile.
- 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.
- 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.
- Jessen was able to spend from April 1933 to June 1934 on research leave funded by the Rockefeller Foundation.
- Jessen was elegant, reserved, rigorous, scrupulous, Wintner was impassioned, a compulsive eater, overflowing with projects and works in progress, all done with great noise.
- 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 in 1934, probably in the spring, Jessen and Wintner decided to pool their experience and write an article "Distribution functions and the Riemann zeta function" ...
- While based at Princeton, Jessen also visited Harvard University, Yale University and Brown University.
- They were back in Denmark in time for Jessen to attend the 8th Scandinavian Congress of Mathematicians in Stockholm 14-18 August 1934.
- On 1 June 1935 Jessen was appointed as Professor of Geometry at the Technical University of Denmark in Copenhagen.
- Johannes Hjelmslev, the professor at the University of Copenhagen, was due to retire in 1940 and Jessen applied to be his successor.
- Jessen was the only applicant for the professorship.
- 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.
- In 1948 Jessen became head of the Department of Mathematics, a position he continued to hold until 1967.
- 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.
- Jessen addressed the Closing Session of the Congress.
- 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.
- It was an aesthetic experience to attend Jessen's lectures.
- 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.
- 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.
- At the final exam Jessen was always very favourable towards the students.
- 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.

Born 19 June 1907, Copenhagen, Denmark. Died 20 March 1993, Copenhagen, Denmark.

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Origin Denmark

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive