Lars Valerian Ahlfors (18 April 1907 – 11 October 1996) was a Finnish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, remembered for his work in the field of

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed ver ...

s and his text on

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

Background

Ahlfors was born in

Helsinki, Finland Helsinki ( or ; ; sv, Helsingfors, ) is the capital, primate, and most populous city of Finland. Located on the shore of the Gulf of Finland, it is the seat of the region of Uusimaa in southern Finland, and has a population of . The city ...

. His mother, Sievä Helander, died at his birth. His father, Axel Ahlfors, was a professor of engineering at the

Helsinki University of Technology Helsinki University of Technology (TKK; fi, Teknillinen korkeakoulu; sv, Tekniska högskolan) was a technical university in Finland. It was located in Otaniemi, Espoo in the metropolitan area of Greater Helsinki. The university was founded in ...

. The Ahlfors family was Swedish-speaking, so he first attended the private school

Nya svenska samskolan (also known as '','' ), was a Swedish-language, co-educational private educational institution in Helsinki, Finland, from 1888 to 1977. History was founded in the spring of 1888 as an educational institution with nine levels. The founders were ...

where all classes were taught in Swedish. Ahlfors studied at

University of Helsinki The University of Helsinki ( fi, Helsingin yliopisto, sv, Helsingfors universitet, abbreviated UH) is a public research university located in Helsinki, Finland since 1829, but founded in the city of Turku (in Swedish ''Åbo'') in 1640 as the R ...

from 1924, graduating in 1928 having studied under

Ernst Lindelöf Ernst is both a surname and a given name, the German, Dutch, and Scandinavian form of Ernest. Notable people with the name include: Surname * Adolf Ernst (1832–1899) German botanist known by the author abbreviation "Ernst" * Anton Ernst (1975- ...

and

Rolf Nevanlinna Rolf Herman Nevanlinna (né Neovius; 22 October 1895 – 28 May 1980) was a Finnish mathematician who made significant contributions to complex analysis. Background Nevanlinna was born Rolf Herman Neovius, becoming Nevanlinna in 1906 when his ...

. He assisted Nevanlinna in 1929 with his work on Denjoy's conjecture on the number of asymptotic values of an

entire function In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane. Typical examples of entire functions are polynomials and the exponential function, and any fin ...

. In 1929 Ahlfors published the first proof of this conjecture, now known as the Denjoy–Carleman–Ahlfors theorem. It states that the number of asymptotic values approached by an entire function of order ρ along curves in the

complex plane In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the -axis, called the real axis, is formed by the real numbers, and the -axis, called the imaginary axis, is formed by the ...

going toward infinity is less than or equal to 2ρ. He completed his doctorate from the University of Helsinki in 1930.

Career

Ahlfors worked as an associate professor at the

from 1933 to 1936. In 1936 he was one of the first two people to be awarded the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award h ...

(the other was

Jesse Douglas Jesse Douglas (3 July 1897 – 7 September 1965) was an American mathematician and Fields Medalist known for his general solution to Plateau's problem. Life and career He was born to a Jewish family in New York City, the son of Sarah (née ...

). In 1935 Ahlfors visited

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of highe ...

. He returned to

Finland Finland ( fi, Suomi ; sv, Finland ), officially the Republic of Finland (; ), is a Nordic country in Northern Europe. It shares land borders with Sweden to the northwest, Norway to the north, and Russia to the east, with the Gulf of Bot ...

in 1938 to take up a professorship at the University of Helsinki. The outbreak of war in 1939 led to problems although Ahlfors was unfit for military service. He was offered a position at the Swiss Federal Institute of Technology at Zurich in 1944 and finally managed to travel there in March 1945. He did not enjoy his time in

Switzerland ). Swiss law does not designate a ''capital'' as such, but the federal parliament and government are installed in Bern, while other federal institutions, such as the federal courts, are in other cities (Bellinzona, Lausanne, Luzern, Neuchâtel ...

, so in 1946 he jumped at a chance to leave, returning to work at Harvard, where he remained until his retirement in 1977; he was William Caspar Graustein Professor of Mathematics from 1964. Ahlfors was a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

in 1962 and again in 1966. He was awarded the Wihuri Prize in 1968 and the

Wolf Prize in Mathematics The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts ...

in 1981. He served as the Honorary President of the International Congress of Mathematicians in 1986 at

Berkeley, California Berkeley ( ) is a city on the eastern shore of San Francisco Bay in northern Alameda County, California, United States. It is named after the 18th-century Irish bishop and philosopher George Berkeley. It borders the cities of Oakland and E ...

, in celebration of his 50th year of the award of his Fields Medal His book ''Complex Analysis'' (1953) is the classic text on the subject and is almost certainly referenced in any more recent text which makes heavy use of complex analysis. Ahlfors wrote several other significant books, including ''Riemann surfaces'' (1960) and ''Conformal invariants'' (1973). He made decisive contributions to

meromorphic In the mathematical field of complex analysis, a meromorphic function on an open subset ''D'' of the complex plane is a function that is holomorphic on all of ''D'' ''except'' for a set of isolated points, which are poles of the function. The ...

curves, value distribution theory,

conformal geometry In mathematics, conformal geometry is the study of the set of angle-preserving ( conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two di ...

quasiconformal mapping In mathematical complex analysis, a quasiconformal mapping, introduced by and named by , is a homeomorphism between plane domains which to first order takes small circles to small ellipses of bounded eccentricity. Intuitively, let ''f'' : ''D' ...

s and other areas during his career.

Personal life

In 1933, he married Erna Lehnert, an

Austrian Austrian may refer to: * Austrians, someone from Austria or of Austrian descent ** Someone who is considered an Austrian citizen, see Austrian nationality law * Austrian German dialect * Something associated with the country Austria, for example: ...

who with her parents had first settled in

Sweden Sweden, formally the Kingdom of Sweden,The United Nations Group of Experts on Geographical Names states that the country's formal name is the Kingdom of SwedenUNGEGN World Geographical Names, Sweden./ref> is a Nordic countries, Nordic c ...

and then in

. The couple had three daughters. Ahlfors died of pneumonia at the Willowwood nursing home in

Pittsfield, Massachusetts Pittsfield is the largest city and the county seat of Berkshire County, Massachusetts, United States. It is the principal city of the Pittsfield, Massachusetts Metropolitan Statistical Area which encompasses all of Berkshire County. Pittsfield� ...

in 1996.

Bibliography

Articles * Ahlfors, Lars V. ''An extension of Schwarz's lemma.'' Trans. Amer. Math. Soc. 43 (1938), no. 3, 359–364. doi:10.2307/1990065 * Ahlfors, Lars; Beurling, Arne. ''Conformal invariants and function-theoretic null-sets.'' Acta Math. 83 (1950), 101–129. doi:10.1007/BF02392634 * Beurling, A.; Ahlfors, L. ''The boundary correspondence under quasiconformal mappings.'' Acta Math. 96 (1956), 125–142. doi:10.1007/BF02392360 * Ahlfors, Lars; Bers, Lipman. ''Riemann's mapping theorem for variable metrics.'' Ann. of Math. (2) 72 (1960), 385–404. doi:10.2307/1970141 * Ahlfors, Lars Valerian. ''Collected papers. Vol. 1. 1929–1955.'' Edited with the assistance of Rae Michael Shortt. Contemporary Mathematicians. Birkhäuser, Boston, Mass., 1982. xix+520 pp. * Ahlfors, Lars Valerian. ''Collected papers. Vol. 2. 1954–1979.'' Edited with the assistance of Rae Michael Shortt. Contemporary Mathematicians. Birkhäuser, Boston, Mass., 1982. xix+515 pp. Books * Ahlfors, Lars V. ''Complex analysis. An introduction to the theory of analytic functions of one complex variable.'' Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York, 1978. xi+331 pp. * Ahlfors, Lars V. ''Conformal invariants. Topics in geometric function theory.'' Reprint of the 1973 original. With a foreword by Peter Duren, F. W. Gehring and Brad Osgood. AMS Chelsea Publishing, Providence, RI, 2010. xii+162 pp. * Ahlfors, Lars V. ''Lectures on quasiconformal mappings.'' Second edition. With supplemental chapters by C. J. Earle, I. Kra, M. Shishikura and J. H. Hubbard. University Lecture Series, 38. American Mathematical Society, Providence, RI, 2006. viii+162 pp. * Ahlfors, Lars V. ''Möbius transformations in several dimensions.'' Ordway Professorship Lectures in Mathematics. University of Minnesota, School of Mathematics, Minneapolis, Minn., 1981. ii+150 pp. * Ahlfors, Lars V.; Sario, Leo. ''Riemann surfaces.'' Princeton Mathematical Series, No. 26 Princeton University Press, Princeton, N.J. 1960 xi+382 pp.

References

External links

* *
Ahlfors
entry on Harvard University Mathematics department web site.
Papers of Lars Valerian Ahlfors : an inventory
(Harvard University Archives)

The MacTutor History of Mathematics page about Ahlfors
The Mathematics of Lars Valerian Ahlfors
''Notices of the American Mathematical Society''; vol. 45, no. 2 (February 1998).
Lars Valerian Ahlfors (1907–1996)
''Notices of the American Mathematical Society''; vol. 45, no. 2 (February 1998). *
National Academy of Sciences Biographical MemoirAuthor profile
in the database

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastruct ...

{{DEFAULTSORT:Ahlfors, Lars 1907 births 1996 deaths 20th-century Finnish mathematicians Academic staff of the Helsinki University of Technology Finnish emigrants to the United States Complex analysts Fields Medalists Foreign Members of the Russian Academy of Sciences Foreign Members of the USSR Academy of Sciences Harvard University faculty Institute for Advanced Study visiting scholars Mathematical analysts Members of the United States National Academy of Sciences People from Uusimaa Province (Grand Duchy of Finland) People from Winchester, Massachusetts Swedish-speaking Finns Wolf Prize in Mathematics laureates Members of the Royal Swedish Academy of Sciences