# Carl Wilhelm Oseen

### Quick Info

Lund, Sweden

Engelbrekts, Stockholm County, Sweden

**Wilhelm Oseen**was a Swedish mathematician who worked in fluid dynamics.

### Biography

**C Wilhelm Oseen**was the son of Anders Theodor Oseen (1849-1907), a grammar school teacher and headmaster, and Elisabeth Ulrika Hyltén-Cavallius (1850-1944). Anders and Elisabeth (known as Betty) were married in Växjö in 1874. Anders and Betty Oseen had six children: Anna Gundborg Vilhelmina Oseen (1876-1939); Per Anders Arvid Oseen (1877-1912); Carl Wilhelm Oseen (1879-1944), the subject of this biography; Gertrud Severina Elisabeth Oseen (1881-1954); Wendela Signhilda Charlotta Oseen (1884-1954); and Knut Oskar Theodor Oseen (1885-1912).

Wilhelm Oseen attended school in Halmstad, where he showed he had many talents. He loved both mathematics and history but found it very hard to decide which of these subjects he wanted to pursue at university. While attending school he wanted to learn more than his teachers were giving him, so he studied both history and mathematics on his own, going well beyond the school syllabus. Not wanting to make a choice between these topics, after graduating from the secondary school in Halmstad on 5 June 1896, he enrolled as a student at Lund University still keeping his options open.

At Lund University, where he enrolled on 8 September 1896, Oseen was taught mathematics by, among others, Victor Bäcklund. In [5] Oseen describes Bäcklund's teaching:-

Bäcklund devoted himself to his teaching duties with ardour and delight and he often talked about the pleasure his lectures had given him. During the time that the author (Oseen) heard him (in the late 1890s) Bäcklund carried a double burden. Outside of the regular four lectures a week he gave a beginner's course in mechanics with exercises, also four hours a week. His interest in his audience was manifested by, among other things, invitations to a yearly party where lobster was a standing ingredient.Oseen graduated from Lund University with the degree Filosofie kandidat (equivalent to B.Sc.) on 14 December 1897. He continued his studies at Lund and was awarded the degree of Filosofie licentiat (perhaps between an M.Sc. and a Ph.D.) on 12 April 1900. His first publication appeared in 1900, namely

*On the general mapping of geodesic circles of a surface through contact transformations*(Swedish). He spent the winter semester of 1900-01 at the University of Göttingen in Germany where he attended David Hilbert's lectures on partial differential equations. Both Hilbert and Felix Klein were strong influences on Oseen who published two further papers in 1901 and also a dissertation. The paper

*Contribution to the theory of wave motion in currents*(Swedish) (1901) was reviewed by Emil Lampe (1840-1918) who wrote that the paper:-

... is a continuation of the investigations by H Hugoniot ... The paper only deals with the theories for perfect gases and makes repeated references to Helmholtz's lectures on the mathematical principles of acoustics, edited by A König and C Runge. The additions to Hugoniot's work refer to the expression for the propagation velocity of a wave when an adiabatic wave movement spreads over a slow current, and also to the propagation of a discontinuous wave in space. We also want to emphasise that an analytical derivation of the Doppler principle is given in the course of the investigation.H Hugoniot is Pierre-Henri Hugoniot (1851-1887) who is remembered today in the Rankine-Hugoniot conditions, the Rankine-Hugoniot relations, the Rankine-Hugoniot equation and several other concepts.

In his introduction to the paper

*Über einige irreduzible Gruppen von Berührungstransformationen im Raume*Ⓣ (1901), Oseen writes:-

As is well known, there are only three different types of finite continuous irreducible contact transformation groups on the plane. In contrast, the number of different types in 3-space is considerably larger. Of these groups in space, three were first discovered by Lie and are analogous to the groups on the plane ... Scheffers also identified all groups[of a certain type] ... Engel has also set up a strange 14-membered, primitive group. Finally Kowalewski has shown that the two primitive groups mentioned are the only primitive groups of contact transformations in space. This paper contains the determination of some other classes of finite, continuous, irreducible groups of contact transformations in space. The classes examined include the two imprimitive groups set up by Lie and also four, it appears, new groups. ... With four subgroups they are similar to Lie's groups.Oseen's 1901 dissertation is

*On the finite, continuous, irreducible contact transformation groups in space*(Swedish). He continued to publish with two papers appearing in 1902. He was awarded his Filosofie doktor (equivalent to a Ph.D.) on 29 May 1903. He was appointed as a substitute professor of mathematics at the University of Lund on 1 December 1904 and held this position until 1 October 1906. During this period, Oseen's publications were all in pure mathematics with the exception of three papers,

*Contribution to the theory of wave motion in currents*(Swedish) (1901),

*Contributions to the theory of wave motion in flows*(Swedish) (1902) and

*On a case of vortex motion in a fluid*(Swedish) (1902).

In Alfshög, Halland, Sweden, on 30 December 1904, Oseen married Klara Charlotta Strandmark (born 18 September 1879 in Alfshög, died 19 December 1943 in Stockholm). Klara was the daughter of Johan Edvard Strandmark, the headmaster of a High School, and Alida Vilhelmina Ewert. Wilhelm and Klara had four children, Birgitta Oseen, born 4 January 1906, Gunnel Oseen, born 25 July 1907, Gärd Oseen, born 9 July 1909, and Jurd Oseen, born 3 March 1914. Tragically, Gärd died at the age of nine on 14 October 1918.

Oseen's move to concentrate on applications of mathematics, particularly applications to fluids, after 1906 was probably influenced by Ludwig Prandtl with whom he kept up a fairly regular correspondence [4]:-

[Oseen], inspired by the work of the Dutch theoretical physicist H A Lorentz, posed an important problem regarding the movement of liquids. The new advance in Lorentz's research was that he took into account the viscosity of the liquid. This had usually been neglected in previous work, mainly because it considerably complicated the mathematical model. Oseen further developed Lorentz's study by considering, among other things, time-dependent fluid movements.He published

*On the theory of the movement of a viscous fluid*(Swedish) (1907) but also works on other applied topics such as

*On Dirichlet"s problem in the heat equation*(Swedish) (1907) and

*On the theory of the discontinuous movements of an electron*(Swedish) (1907). He began applying for a professorship in mechanics and mathematical physics at the University of Uppsala, using his most recent work on applications of mathematics to support his case. In the meantime, on 13 July 1907, he was appointed to a post as a substitute professor of physics at the University of Lund.

On 11 September 1909 he took up the appointment as professor of mechanics and mathematical physics at the University of Uppsala. It was a position he held for the rest of his career. His inaugural lecture in Uppsala was entitled 'The question of the will of freedom, viewed from a scientific point of view', showing his lifelong interest in philosophy. In 1911 he published

*Über die Stokes'sche formel, und über eine verwandte Aufgabe in der Hydrodynamik*Ⓣ. In this paper he addressed what is now known as Stokes' Paradox. Stokes had produced a formula for the resistance experienced by a sphere moving at a constant, infinitely low speed in a viscous, incompressible fluid. This formula worked in three dimensions but produced contradictions when applied to 2-dimensional flows.

We give some more information about Oseen's contributions to Stokes' Paradox and also a short extract from his 1911 paper at THIS LINK.

Oseen became one of the first Swedish scientists to accept Niels Bohr's atomic model. Bohr visited Oseen in Uppsala and, after he left, Oseen wrote to Bohr on 10 February 1912:-

Dear FriendWe note Oseen's comments about not having scientific colleagues at Uppsala.

I wish to thank you for your and your wife's visit here. You will understand what an inspiring it had on one who has not met a scientific colleague for over a year. Thanks also for both of your papers, which I read with great interest. If I pose a question concerning a-ray absorption, then please perceive this only as proof of my interest. Here is the question. Through your theory, a-ray absorption is brought into close connection with the question of ionisation by collision, for example the emission of secondary cathode rays. By your theory, how is it possible to explain hydrogen's exceptional status in this question? ... Weaker binding of the electrons?

Once again, thank you. My warmest greetings to your wife.

Your friend, C W Oseen.

In 1921 he was elected to the Royal Swedish Academy of Sciences and, in the same year, he proposed Albert Einstein for a Nobel prize. Every full professor in Sweden had the right to make nominations for Nobel prizes. Oseen became a member of the Royal Swedish Academy of Sciences' Nobel Committee for Physics in 1922 and he was able to argue strongly for the Nobel prize for physics being awarded to Einstein. Given Einstein's standing today it is difficult to understand the problem of convincing the committee that Einstein was worthy of the award. The theory of relativity, for which Einstein is best known today, was not considered well enough supported by experimental evidence by many scientists, both members of the committee and other scientists. Oseen presented the committee with a carefully, strongly, well-written document arguing that Einstein be awarded the 1921 reserve prize for his 1905 work on the photoelectric effect. Finally the committee was persuaded to make the award to Einstein in December 1922 (although in fact Einstein did not attend the presentation ceremony since he was on a voyage to Japan).

Another of Oseen's very influential papers was published around the time that he was making the case for Einstein's Nobel prize. On 9 March 1921 he submitted his paper

*Eine Methode, die Zustandsgleichung der beliebigen Flüssigkeiten oder Gasen exakt zu berechnen*Ⓣ. The paper, which was communicated by Ivar Bendixson and Helge von Koch, begins as follows:-

Anyone familiar with modern Swedish mathematics knows the place in which it takes the problem of representing an analytic function by some unified mathematical expression in the widest possible part of its existence realm. If I had to describe the history of this problem here, I should have to remember how Mittag-Leffler devoted almost all his energy to the solution of this Weierstrassian problem. Of his successors in this field I would primarily have to recall Helge von Koch, whose extension of the Mittag-Leffler problem is of fundamental importance for what follows. However, I do not want to talk about the mathematical details here. The purpose of these lines is to show how a straightforward application of the results obtained by the colleagues mentioned should be sufficient to obtain a mathematically exact and, I believe, physically useful method of solving the problem that has for several decodes been subject to the most zealous efforts of a great number of scholars. Their actual task has been to infer the equation of state for a gas or a liquid, whose atoms interact with each other through known, but largely arbitrary forces.Although the 1920 International Congress of Mathematicians was called 'International', it was a limited definition of International. Mathematicians from Germany, Austro-Hungary, Bulgaria and Turkey were excluded. This decision, based on the countries 'blamed' for World War I being excluded, was supported by most people but it was strongly opposed by a small number, most notably G H Hardy and G Mittag-Leffler neither of whom attended. Oseen played a role in restoring truly international relations at this difficult time by initiating the International Congresses for Applied Mechanics. An informal gathering organised by Theodore von Kármán and Tullio Levi-Civita in Innsbruck in 1922 was followed by the First International Congress of Applied Mechanics held in Delft in 1924. Although this was a fully international meeting, the International Congress of Mathematicians in Toronto in 1924 did not allow mathematicians from Germany, Austro-Hungary, Bulgaria and Turkey to attend. Nevertheless, Oseen attended the International Congress of Mathematicians in Toronto in 1924 but did not lecture at the congress.

He published in German the important book

*Neuere Methoden Und Ergebnisse In Der Hydrodynamik*Ⓣ in 1927. We give a modified version of a short extract from the Preface to that book at THIS LINK.

We have mentioned above Oseen's membership of the Royal Swedish Academy of Sciences and, in particular, his membership of the Sciences' Nobel Committee for Physics. Let us note also that Oseen chaired the Nobel Committee for many years and also that he served as president of the Royal Swedish Academy of Sciences in 1934-35. He delivered the presidential address at the end of his term of office, giving the lecture

*Plato's idiom and mathematics*. Oseen told his audience of his interest in philosophy in general and that Plato was his favourite philosopher.

Oseen was a plenary speaker at the International Congress of Mathematicians in Oslo in 1936. He delivered his lecture,

*Probleme der geometrischen Optik*Ⓣ, on the morning of Thursday 16 July 1936 with Ernst Lindelöf as chair of the session. We give an English version of the beginning of his lecture at THIS LINK.

To gain a broader view of Oseen, we quote from [4]:-

Oseen's versatility was not limited to the field of physics. He successfully combined his early interest in history with his field of physics and adjacent fields through a number of biographical works. In addition to a large number of shorter life sketches of prominent Swedish scientists, including his teacher Victor Bäcklund, he wrote a larger biography of Johan Carl Wilcke. On an assignment from the Royal Swedish Academy of Sciences, he edited the edition of Scheeles' abandoned paper that was published in 1942 to celebrate the 200th anniversary of the chemist's birth. ...In 1982, the Royal Swedish Academy of Sciences inaugurated a medal, designed by the sculptor Léo Holmgren and dedicated to the memory of Oseen. The medal's inscription was

Literature and art were also among Oseen's interests. He lectured on both classical and modern literature and was also a performing artist with a number of oil paintings, watercolours and drawings as a result.

Pupils and friends have spoken of Oseen's characteristic features and, in addition to his intellectual capacity and sharpness, they emphasised his willpower and work ability, which, among other things, showed itself in the laborious and complicated calculations which he quickly perceived as challenges. He asserted strongly the demand for freedom of thought and expression. The truth must be sought unconditionally. As an academic teacher, Oseen was inspiring through his engaging and interesting lectures.

*Arcana umorum revelavit anisotropicorum*Ⓣ.

### References (show)

- E B Starikov,
*A Different Thermodynamics and its True Heroes*(Jenny Stanford Publishing, 2019). - G Broberg, Before 1932: Scientists writing their own history, in
*History of Science in Sweden: the Growth of a Discipline, 1932-1982*(Uppsala Studies in the History of Science, Uppsala), 9-24. - S Gieser, Philosophy and modern physics in Sweden: C W Oseen, Oskar Klein, and the intellectual traditions of Uppsala and Lund, 1920-1940, in
*Svante Lindquist (ed.), Center on the Periphery: Historical Aspects of 20th-century Swedish Physics*(Science History Publications, 1993), 24-41. - B Nagel, C Wilhelm Oseen,
*Swedish biographical lexicon***28**(1992-1994), 395. - C W Oseen, Albert Victor Bäcklund,
*KVA Arsbok***22**(1922).

### Additional Resources (show)

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Written by J J O'Connor and E F Robertson

Last Update April 2020

Last Update April 2020