**Werner Romberg**'s father, Julius Romberg, was a geologist. Werner was brought up in Berlin where he attended school. He entered the University of Heidelberg in 1928 where he studied mathematics and physical science. His science lecturers included the chemist Karl Johann Freudenberg (1886-1983), and the physicist Philipp Lénárd (1862-1947) whose main contributions were on cathode rays. Lénárd was a Nazi whose political views were abhorrent to Romberg. His mathematics professors at Heidelberg included the geometer Heinrich Liebmann (1874-1939) and Arthur Rosenthal (1887-1959). Both Liebmann and Rosenthal were Jewish and both lost their positions when the Nazis came to power. It was standard practice for German students at this time to study at several different universities and, after two years at Heidelberg, Romberg moved to Munich in 1930 where he continued his studies. His physics teachers in Munich included Arnold Sommerfeld and Walther Gerlach who was the ordinary professor being a successor to Wilhelm Wein. Gerlach discovered the spin quantisation in a magnetic field. Romberg's mathematics lecturers at Munich included Constantin Carathéodory and Oskar Perron.

While he was at Heidelberg, he had to make a choice between mathematics and physics. He said:-

He began undertaking research in Munich advised by Sommerfeld who was particularly pleased to have a young student who was showing such expertise both in mathematics and physics. However, in the early 1930s the Nazi party was gaining ground and Romberg, who had staunch left-wing views, was bitterly opposed to them. He had seen the dangers which the Nazis posed very early in their campaign for power and was very public in his opposition to them. He joined the Socialist Workers Party which had split off from the Social Democratic Party in the autumn of 1932. The left-wing of the Social Democratic Party had been unhappy with the way the leaders were running the party and formed their own organisation which was joined by some disaffected members of the German Communist Party. Romberg wrote [3]:-Despite the recommendation of Professor Liebmann, that I should stay with the mathematics, I chose physics as my major. I wanted not only to know that the theoretical considerations were consistent, but also to investigate their relation to the real world.

Let us note that Romberg's doctoral thesis wasI was close to the Socialist Workers Party as it supported the joint fight of the Social Democratic Party and the German Communist Party against the Nazis. We were about10to20students and therefore known to the Nazis. In1932Sommerfeld formulated a prize competition for the University of Munich and suggested that I should participate. I submitted the solution and received the following response: "The assignment was completely solved by the sender. However, since the sender lacks the necessary maturity of mind, the prize cannot be awarded." Sommerfeld suggested I submit it as a Ph.D. thesis and urged me to hurry. Accordingly I was able to pass the examination with magna cum laude in the summer of1933. Sommerfeld had heard about requests for theoretical physicists from the USSR. By was of curing me of my leftist illusions, he recommended me.

*Polarisation des Kanalstrahllichtes*Ⓣ. The position in the USSR referred to in the above quote was in Dnipropetrovsk in the Ukraine. The Soviet regime had made a small change to the spelling of the city and, at the time that Romberg went there, it was known as Dnepropetrovsk. It is a large industrial city in south central Ukraine on the Dnieper river. Romberg took up his appointment as a theoretical physicist in the Department of Physics and Technology there in 1934. Joseph Stalin, the Russian dictator, began his purges in 1935. Although mainly aimed at eliminating rivals, these purges also applied to foreigners who were distrusted. Romberg, as a German citizen, had his right to stay in the Soviet Union ended in 1937 and so he had to leave his position in Dnepropetrovsk. He travelled through Warsaw to Prague, where he had relatives who he could live with and, in order to make enough money to live, he worked as a private tutor. He also made contact with staff at the Institute of Astrophysics of the Charles University of Prague. With hindsight, however, it is clear that Prague was not a good choice for Romberg.

In March 1938 Adolf Hitler absorbed Austria which became a part of Germany. He then turned his attention towards Czechoslovakia and, by May 1938, he was known to have plans to invade that country. The Munich Agreement signed on 30 September 1938 allowed Hitler to annex the western part of Czechoslovakia. Romberg knew he had to escape and he was fortunate to have the necessary contacts in Prague to help him get in touch with Egil Andersen Hylleraas (1898-1965) in Oslo. Hylleraas had worked in Bergen before being appointed as Professor of Theoretical Physics in Oslo in 1937. Romberg offered to work as Hylleraas's assistant and Hylleraas managed to obtain money from the Brogger Committee to enable Romberg to leave Prague and travel to Olso. However, getting out of Czechoslovakia was not easy at this stage as the German military were checking everyone leaving at the border posts. His only solution was to fly from Prague and so avoid the German checks. He flew from Prague to Oslo on 20 November 1938 and indeed worked as Hylleraas's assistant. Together they wrote *Über die Schwingungen eines stabil geschichteten, durch Meridiane begrenzten Meeres. II. Berechnung der Eigenfrequenzen* Ⓣ which continued a study already begun by Hylleraas. In this work they investigated the hydrodynamical equations for an ideal incompressible fluid on a rotating sphere which is subjected to the influence of tidal forces. The paper was published in 1941.

Hylleraas was not the only person in Oslo with whom Romberg worked. The authors of [1] write:-

However, Romberg was not safe in Oslo for, on 9 April 1940, German troops invaded Norway and soon occupied Oslo. Romberg, always one step ahead of the German advance, had already left Oslo and crossed the border into Sweden.He also worked for a short period with Johan Holtsmark(1894-1975), who built a Van de Graaff generator(the second one in Europe and the first particle accelerator in Scandinavia)for nuclear disintegration between1933and1937at the Norwegian Institute of Technology in Trondheim.

Romberg lived in Uppsala from 1940 to 1944. Of course, the Nazis were not too pleased that Romberg was managing to keep out of their clutches. In 1941 the German Reich stripped Romberg of his German citizenship and in 1943 they revoked his doctorate. Late in 1944, when Oslo had been liberated from the Germans, Romberg was able to return there and once again take up his former position as Hylleraas's assistant. He became a Norwegian citizen in 1947. While in Oslo, he worked on the differential analyser. He also studied numerical methods, publishing *Approximation eines Kurvenstückes durch wenige sin-Funktionen* Ⓣ in 1949. In this paper he gives an algorithm to determine an approximation to an experimentally determined function. The method involves successive approximations based on a least square technique.

Harald Wergeland (1912-1987) had been appointed as professor of physics at the Norwegian Institute of Technology in Trondheim in 1946. He was a friend of Romberg's and well acquainted with his abilities. He encouraged Romberg to apply for the position of dosent in physics at the Norwegian Institute of Technology in Trondheim. This national technology college had been established in 1900 although it had taken several years before the decision to site it at Trondheim rather than Oslo was accepted. Romberg was appointed as a dosent, which was essentially an assistant lectureship, and left Oslo in 1949. It was while he was in this post at Trondheim that Romberg made his most important contribution when he published the paper *Vereinfachte Numerische Integration * Ⓣ in 1955. This paper contains what today is known as Romberg integration and we now look briefly at this method.

Romberg's aim with this paper was to increase the speed of convergence of the trapezium rule, a standard numerical integration method. He was not the first to have this aim for Lewis Fry Richardson, in 1927, had introduced a special case of what today is called Richardson extrapolation. However, the basic ideas involved here go back much further than this, for Colin Maclaurin had used similar ideas in 1742 and even before this Christiaan Huygens had already basically used Richardson extrapolation in his methods to calculate π in *De Circuli Magnitudine Inventa* Ⓣ in 1654. In fact, rather remarkably, Huygens' approximations are better than what would be achieved by Richardson extrapolation. However, in [12] Ole Osterby suggests that although Richardson gave what:-

But the ideas involved here go back much further than this, for Archimedes was employing similar techniques in his calculations of π and square roots such as √3 (see [11] and [12]). What Romberg achieved was a systematic approach to applying extrapolation to the trapezium rule, by successively halving the step size in order to attain higher and higher accuracy. He claimed that similar accuracy could be obtained as other methods with less computational work and illustrated this with numerical examples. Claude Brezinski and Luc Wuytack write in [4]:-... is exactly the same operation which Huygens performs but he does it out of a different motivation, namely that of summing a geometric series. I therefore think it is fair to say that Huygens did not invent Richardson extrapolation although one could easily be led to believe so from looking at the calculations.

In 1963 Jean-Pierre Laurent published a rigorous analysis of Romberg integration and after that the method became widely known and widely used.This method can now be found in every textbook on numerical analysis without any reference to Romberg's original paper, a proof of true fame. Besides its usefulness, Romberg's method also showed to non-specialists that convergence acceleration methods can be quite powerful. Thus, it had an important impact on the development of this domain of numerical analysis.

Let us return to give some further details of Romberg's career. Loa Nordal writes in [10]:-

In 1960 the Norwegian Institute of Technology established a chair in applied mathematics with the idea that this would boost their position with computers. Romberg was offered the chair which he was happy to accept [13]:-For some time Romberg was a candidate for the position as director of the Norwegian Computing Centre. He also knew Konrad Zuse and his machines, and he had written vividly about them in the popular science journal 'Fra fysikkens verden'. Nevertheless, Romberg lacked the political strength and skills needed to realise a pioneering project in Trondheim, and none of his attempts got any support from the funding authorities.

The first course in the Norwegian Institute of Technology curriculum that was devoted to digital computing was Romberg's 'Numerical Methods I and II' from 1962-63. The course had, from 1957, been a part of the auxiliary education in mathematics. Romberg had then given a short introduction to mechanical and electrical computers, without going into detail on how to program or use them. As an example of his research at this time we mention the paperIn his new position, Romberg gave courses in many areas of applied mathematics, and he established the field of numerical analysis at the Norwegian Institute of Technology.

*Eine Lösungsmethode für Eigenwertprobleme*Ⓣ (1965) written jointly with Jan Ole Aasen. The authors give the following summary of this paper:-

In 1968, Romberg returned to Germany when he was appointed to the chair of Mathematical Methods in Science and Numerical Analysis at the University of Heidelberg. He was also the scientific head of the Computer Centre at Heidelberg from its founding in 1969 to 1975. Peter Sandner wrote:-Analytical eigenvalue problems are usually replaced by finite-dimensional algebraic eigenvalue problems. An iteration scheme related to Sturm sequences for solving such problems is presented. It is also indicated how the method may reduce the labour for obtaining solutions of the analytical eigenvalue problem.

Romberg retired in 1978 when he was 69 years old. He was to enjoy a long retirement. In December 1988, when he was nearly eighty years old, theHe was an open and straightforward man ... and above all a kind and humble person. ... It is because of these characteristics that Werner Romberg was my role model and always will be. This view I share with all the Computer Centre staff who had the opportunity to get to know him personally in the early years of the Computer Centre on the Friedrich-Ebert-Platz.

*Romberg Seminar on Quadrature, Interpolation, Extrapolation and Rational Approximations*was held at the University of Trondheim in his honour [6]:-

After his death in February 2003, Willi Jäger wrote:-... this seminar was given his name to honour him for his services to our country[Norway]and our institution in the fields of applied mathematics, numerical analysis and digital computations. The seminar was, a small one with11participants, based on invitations, each invited person was asked to give a lecture. In particular, Professor Romberg was asked to give an informal talk on the introduction of digital computers in Norway.

On20February Professor Dr Werner Romberg's family, his colleagues and friends, the University of Heidelberg and the Faculty of Mathematics and Computer Science bade farewell to Romberg, who died at the age of almost94years after a full life. Werner Romberg was an outstanding scientist with a high international reputation. His life was shaped by science and his work as a university teacher, but also by his resistance against Nazism and his commitment to peace and democracy.

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