Search Results for Arne Beurling


  1. Arne Beurling biography
    • Arne Carl-August Beurling .
    • Arne Beurling's father was Konrad Gustaf Verner Beurling (18 September 1872 - 19 February 1959).
    • Konrad and Elsa Beurling had two sons, Ake Gustaf Beurling, born on 16 May 1902, and Arne, the subject of this biography, born in February 1905.
    • Arne was brought up by his mother and her lady companion called Titti.
    • Although Beurling was brought up by his mother, he spent time with his father and they would go hunting together.
    • Beurling, like his father, had a fiery temper and could suddenly fly off into a rage.
    • Although Beurling got on well with his father, nevertheless, given they both had a temper it is not surprising that they often had arguments and, it is said, sometimes physical fights.
    • His father Konrad was so confident at this stage that his son would become a professor that he told all his friends "He is going to be a professor." In the year he graduated from high school, Beurling began studying at Uppsala University.
    • Beurling was certainly not reluctant to take this break in his studies.
    • Neither could I have known that Arne Beurling had found a different proof in 1929 while hunting alligators in Panama.
    • At this stage, however, Beurling did not complete his doctorate but undertook compulsory military service in 1930-31.
    • The fact that Ahlfors had published the proof of the Denjoy conjecture delayed the submission of Beurling's thesis which had already been delayed by the year in Panama and the year of military service.
    • Beurling's thesis is described by Ahlfors and Carleson as follows [',' L Ahlfors and L Carleson, Arne Beurling in memoriam, Acta Math.
    • Beurling's leading idea was to find new estimates for the harmonic measure by introducing concepts, and problems, which are inherently invariant under conformal mapping.
    • Arne and Britta Beurling had two children, Pher-Henrik Konrad Beurling born 11 December 1936 (died 26 April 1962) and Christina born in 1938.
    • During World War II, Beurling worked on cracking the German codes.
    • Kjellberg writes in [',' B Kjellberg, Memories of Arne Beurling, February 3, 1905 - November 20, 1986, The Mathematical Intelligencer 15 (3) (1993), 28-31.','8]:- .
    • Beurling was one of the most charming persons you could meet.
    • Ulfving writes [',' L Ulfving, The Geheimschreiber Secret : Arne Beurling and the success of Swedish signals intelligence.','10]:- .
    • It is now known that Professor Arne Beurling was the man behind the breaking of the German Geheimschreiber.
    • Quite possibly the finest feat of cryptoanalysis performed during the Second World War was Arne Beurling's solution of the secret of the Geheimschreiber.
    • Arne Beurling's greatness is given by the fact he had at his disposal only the teleprinter tapes with the cipher text.
    • That secret Arne Beurling took with him to the grave.
    • We have explained above that Beurling had a quick temper but we must not give the impression that he was not a kind human being.
    • In 1944 Beurling, as soon as he heard that Ahlfors had come to Sweden, invited him to Uppsala.
    • The discussions he engaged in there with Beurling laid the foundations for their future mathematical collaboration.
    • Lars was then on a lecture visit to Uppsala and heard the traumatic news first from Beurling.
    • It seemed to me that Arne's extraordinary sensitivity had raised our friendship to a level that I had not experienced before, and from that moment on, I have come to regard Arne as the personification of what true friendship can be." When Beurling died forty years later, Ahlfors began his eulogy at Princeton with the words: "Arne Beurling was the best friend I ever had." .
    • During the session 1948-49 Beurling was a visiting professor at Harvard in the United States.
    • John Wermer writes [',' J Wermer, Recollections of Arne Beurling, The Mathematical Intelligencer 15 (3) (1993), 32-33.','11]:- .
    • Beurling's lectures were like nothing else.
    • We had to work hard, and we must have seemed amusingly naive to Beurling.
    • Beurling worked on the theory of generalized functions, differential equation, harmonic analysis, Dirichlet series and potential theory.
    • The concepts of energy and the Dirichlet integral took Beurling to a global axiomatic theory called the theory of Dirichlet spaces for complex functions.
    • Describing their work on this last mentioned paper, Malliavin writes [',' Jubileumsskrift Arne Beurling 100 ar, U.U.D.M.
    • We devoted half of the academic year 1960-1961 to this problem; very often I stayed at Beurling's house for a full night of cooperative work.
    • I was made welcome there by Mrs Beurling, a former distinguished PhD student at Uppsala University, where she had been president of the association of graduate students.
    • Mrs Beurling worked in a Chemistry lab at Princeton University.
    • Nevertheless Beurling was not "aesthetically" satisfied with these proofs.
    • Lennart Carleson was a research student of Beurling and completed his doctoral thesis in 1950.
    • He explained the way that Beurling worked [',' Jubileumsskrift Arne Beurling 100 ar, U.U.D.M.
    • We learned much on mathematical research through Beurling's seminars.
    • They took place every second Tuesday, 6-8 pm, when Beurling invariably would talk about his own work (he did not read much).
    • Beurling received many honours for his outstanding contributions.
    • In 1976-77 the Mittag-Leffler Institute in Stockholm held a "Beurling Year".
    • It is interesting to note that Beurling had been offered the directorship of the Mittag-Leffler Institute before emigrating to the United States but had turned the offer down.
    • The authors of [',' L Ahlfors and L Carleson, Arne Beurling in memoriam, Acta Math.
    • Arne Beurling was a highly creative mathematician whose legacy will influence future mathematicians for many years to come, maybe even for generations.
    • Beurling's personal friends and students will never forget his unquestioning loyalty and boundless generosity.
    • Paul Malliavin was strongly influenced by Beurling and his work.
    • He gave a lecture Arne Beurling - a visionary mathematician (in [',' Jubileumsskrift Arne Beurling 100 ar, U.U.D.M.
    • In my youth Beurling appeared to me more as a mathematician working on hard concrete problems than an abstract theory builder.
    • Sixty years later Beurling appears now to me more as the key initiator of important theories than a problem solver.
    • How can we explain this paradox? After having got sharp results, Beurling waited for their publication until he reached a proof which quoting his own words must be "elementary and transparent".
    • This, sometimes strenuous, search for beauty in the proofs explains why, starting from concrete problems, Beurling reached basic general principles of universal applicability.
    • The far reaching consequences of this Beurling's quest for Beauty illustrate magnificently the Unity of Mathematics and, by consequence, its transcendental Truth.
    • Yngve Domar, one of Beurling's students in the 1940s, is quoted in [',' B Beckman, Codebreakers: Arne Beurling and the Swedish Crypto Program During World War II (American Mathematical Society, Providence R.I., 2002).','1] as follows:- .
    • if the label [of genius] is to be put on anybody, then the right thing is to put it on Beurling.
    • Beurling was a pioneer.
    • When Beurling wrote a mathematical paper, even a short one, other mathematicians took up the thread and developed new theories based on his work.
    • Lennart Carleson wrote (see for example [',' B Beckman, Codebreakers: Arne Beurling and the Swedish Crypto Program During World War II (American Mathematical Society, Providence R.I., 2002).','1]):- .
    • Beurling had a complicated and passionate relationship to mathematics.
    • I think that was the way Beurling thought of mathematics.
    • It seems appropriate to end this short biography with words written by Ahlfors about Beurling in The collected works of Arne Beurling (Birkhauser, Boston, 1989):- .
    • Honours awarded to Arne Beurling .
    • .

  2. Lennart Carleson biography
    • Carleson's research thesis was supervised by Arne Beurling and he was awarded his doctorate in 1950 for On a Class of Meromorphic Functions and Its Exceptional Sets.
    • It was my great fortune to have been introduced to mathematics by Arne Beurling; the tradition he, T Carleman and Marcel Riesz initiated is very obviously responsible for the good standard of mathematics in our country.
    • Personally I am very happy for this opportunity to express to Arne Beurling my gratitude for having guided me into a fruitful area of mathematics and for having given an example that only hard problems count.
    • Besides his papers Carleson has published an influential book on potential theory 'Selected problems in the theory of exceptional sets' and helped make accessible the unpublished work of Arne Beurling (i.e., as co-editor with P Malliavin, J Neuberger, and J Wermer of 'The collected works of Arne Beurling' 2 Vols 1989) ..

  3. Lars Ahlfors biography
    • At this stage Ahlfors' health was poor and he had an irregular heartbeat so he was allowed to go with his family in Sweden, where Arne Beurling gave them a great deal of help and friendship [',' D J Albers and L V Ahlfors, An interview with Lars V Ahlfors, College Math.
    • His achievements include the proof of the Denjoy conjecture, the geometric derivation of the Nevanlinna theory, an important generalization of the Schwarz lemma, the development (with Beurling) of the method of extremal length, and numerous decisive results in the theories of Riemann surfaces, quasi-conformal mappings and Teichmuller spaces.

  4. Anders Wiman biography
    • Wiman also taught Arne Beurling and influenced him greatly, but had retired before Beurling submitted his thesis.

  5. Gustav Elfving biography
    • The committee set up to make recommendation regarding the appointment to the chair of mathematics at the University of Helsinki consisted of Lars Ahlfors, Arne Beurling and Harald Bohr.

History Topics

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Societies etc

  1. Swedish Mathematical Society
    • The first President of the Society was Arne Beurling.
    • Discussions about producing a publication were held in a meeting of the new Society which took place in November 1950 when Beurling explained to members that there was a proposal to produce two new international mathematics journals published jointly by the Scandinavian mathematical societies, one a high level research journal, the other an elementary journal concerned with the teaching of mathematics [',' K Markstrom, The Swedish Mathematical Society, London Mathematical Society Newsletter 474 (2018), 41.','2]:- .


  1. International Congress Speaker
    • Arne Beurling, On Null-Sets in Harmonic Analysis and Function Theory.


  1. References for Arne Beurling
    • References for Arne Beurling .
    • B Beckman, Codebreakers: Arne Beurling and the Swedish Crypto Program During World War II (American Mathematical Society, Providence R.I., 2002).
    • K O Eriksson, Karlekens kod och krigets: berattelsen om Britta Ostberg, lakare och Arne Beurling, matematiker och kryptoforcerare.
    • L Ahlfors, The story of a friendship: Recollections of Arne Beurling, The Mathematical Intelligencer 15 (3) (1993), 25-27.
    • L Ahlfors and L Carleson, Arne Beurling in memoriam, Acta Math.
    • Jubileumsskrift Arne Beurling 100 ar, U.U.D.M.
    • .
    • B Kjellberg, Memories of Arne Beurling, February 3, 1905 - November 20, 1986, The Mathematical Intelligencer 15 (3) (1993), 28-31.
    • J W Neuberger, Beurling's analyticity theorem, The Mathematical Intelligencer 15 (3) (1993), 34-38.
    • L Ulfving, The Geheimschreiber Secret : Arne Beurling and the success of Swedish signals intelligence.
    • J Wermer, Recollections of Arne Beurling, The Mathematical Intelligencer 15 (3) (1993), 32-33.

Additional material

  1. Markstrom SMS
    • The first President of the society was Arne Beurling, who served from 1950 to 1952.


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Famous Curves

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EMS Archive

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BMC Archive

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Gazetteer of the British Isles

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Astronomy section

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JOC/BS August 2001