**Arne Beurling** was a Swedish mathematician who worked in harmonic analysis, complex analysis and potential theory.

- Beurling was certainly not reluctant to take this break in his studies.
- 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 leading idea was to find new estimates for the harmonic measure by introducing concepts, and problems, which are inherently invariant under conformal mapping.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Sixty years later Beurling appears now to me more as the key initiator of important theories than a problem solver.
- 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.
- 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.

Born 3 February 1905, Gothenburg, Sweden. Died 20 November 1986, Princeton, New Jersey, USA.

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Origin Sweden

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive