# Ahlfors, Lars V. (Lars Valerian), 1907-1996

Alternative names## Biographical notes:

Lars Varlerian Ahlfors (1907-1996), Professor of Mathematics at Harvard University (1935-1938, 1946-1977) was an internationally known theoretician and teacher. In a career that spanned sixty years, he made decisive contributions in mathematics through his studies of complex functions, meromorphic curves, the value distribution theory, Reimann surfaces, conformal geometry, extremal length, quasiconformal mappings, and Kleinian groups. Over his lifetime he published almost 100 papers and several books.

From the description of Papers of Lars Valerian Ahlfors, 1929-1987. (Harvard University). WorldCat record id: 77067966

Lars Valerian Ahlfors (1907-1996), Professor of Mathematics at Harvard University (1935-1938, 1946-1977) was an internationally known theoretician and teacher. In a career that spanned sixty years he made decisive contributions in mathematics through his studies of complex functions, meromorphic curves, the value distribution theory, Reimann surfaces, conformal geometry, extremal length, quasiconformal mappings, and Kleinian groups . Over his lifetime he published almost 100 papers and several books.

Ahlfors was born on April 18, 1907, in Helsingfors, Finland, Russian Empire (now Helsinki, Finland ). His father, Axel Ahlfors, was a professor of mechanical engineering at the Institute of Technology in Helsinki . Ahlfors mother Sievä died at Lar's birth. Ahlfors interest in mathematics began at a very young age. He could read and perform simple mathematical calculations at the age of four. As a schoolboy he studied calculus using the books he found in his father's engineering library. At age 17, he graduated from Nya Svenska Samskolan high school.

After receiving his master's degree from the University of Helsinki (1928), Ahlfors became a math celebrity. Under the direction of his mentors Rolf Nevanlinna and Ernst Lindelof, he presented a new theory of asymptotic values of an entire function, based on a new approach to conformal mapping . Ahlfors work was recognized as a breakthrough in mathematical analysis and his approach became a standard in the field.

Ahlfors' academic career began in 1929 as a lecturer at Abo Adademi, a small Swedish-language university. He became an associate professor at the University of Helsinki in 1933. In the same year, he married Erna Lehnert of Vienna . Ahlfors' mathematical studies were recognized across the Atlantic, and in 1935 he took a leave of absence from the University of Helsinki to accept a lecturer's position at Harvard University. In 1936 he was appointed to an assistant professorship . His initial stay at Harvard University was short. Homesickness and a new position at the University of Helsinki lead to his departure in 1938.

During the 1930's Ahlfors pioneered the development of quasiconformal mapping. He also began the study of a new field of analysis called metric topology . This involved the mathematical study of spatial objects such as curves and surfaces. He achieved significant results in the development of complex analysis, a field that has applications in both physics and number theory. In 1936 Ahlfors was recognized by his peers when the International Congress of Mathematics presented him with the first Fields Medal.

Ahlfors was a full professor at the University of Helsinki during the war years (1938-1945). It was at this time that he began his work on meromorphic curves and their relationship to topology . Although his work went unnoticed at the time, it was rediscovered after the war and other mathematicians followed Ahlfors line of research in the 1970s. In March 1945, Ahlfors and his family moved to the University of Zürich after he accepted a professorship in applied mathematics . Ahlfors found himself unhappy in Switzerland and when Harvard University offered him another position (1946) he left Europe and came to Cambridge to stay.

Ahlfors' years at Harvard (1946-1971) were devoted to research and teaching. Continuing his mathematical investigations, he developed efficient tools to study various problems associated with complex analysis. In 1953 he wrote the textbook Complex Analysis . This book grew in part from his experiences in the classroom and became the standard text for students of pure mathematics for many years. New editions were published in 1966 and 1979. Ahlfors' studies of quasiconformal mappings demonstrated their intrinsic role in the theory of analytical functions and shed new light on Reimann surfaces. His pioneering efforts in the study of Kleinian groups, möbius transformations, and Teichmüller spaces led to important developments in mathematical physics and were used by others to expand the boundaries of mathematics.

Ahlfors acted as a role model, advisor and mentor to his students. He taught courses in advanced calculus, complex function theory, geometric function theory, and Reimann surfaces. Some of these courses were taught before any textbooks had been published about their subjects. Moreover, Ahlfors routinely made his detailed notes available to his students to read in the library after class. Ahlfors held a weekly seminar for graduate students, many of whom became leaders in the field, and invited noted mathematicians to his class to lecture about advanced mathematical topics. From 1948 to 1950, Ahlfors was the Chairman of the Mathematics Department. In 1964 he was appointed the William Caspar Graustein Professor of Mathematics.

After his retirement from full-time teaching in 1977, Ahlfors accepted a number of visiting appointments from other institutions. He found himself traveling to Columbia University (1978), the University of Michigan (1979), the University of Minnesota (1980), and the University of California/San Diego (1983). In addition, he received several awards and honors from mathematical organizations. In 1978 he had the distinction of giving the plenary lecture to the International Congress of Mathematics for the third time. In 1981 he was presented with the Wolf Prize, by the Wolf Foundation, an Israeli-based organization dedicated to the promotion of science and art. Finally, in 1986 he was made honorary President of the International Congress of Mathematics when the congress held its annual meeting in the United States.

Most mathematicians make their impact early in their careers and then fade away. Unlike many of his peers, however, Ahlfors remained in the forefront of mathematical development for several decades. Moreover, his new ideas, innovative approaches, and techniques helped advance the work of other mathematicians. Lars Valerian Ahlfors died on October 11, 1996 .

- Ahlfors, Lars Valerian, ed. Lars Valerian Ahlfors: Collected Papers. Boston: Birkäuser, 1982.
- Bott, Raoul, Clifford Earle, Dennis Hejhal, James Jenkins, Troels Jorgensen, Steven G. Krantz, Albert Marden, Robert Osserman Lars Valerian Ahlfors. Notices of the American Mathematical Society 45, no. 2 (1998) : 248-255.
- Gehring, Frederick, Irwin Kra, Steven G. Krantz, Robert Osserman. The Mathematics of Lars Valerian Ahlfors. Notices of the American Mathematical Society 45, no 2 (1998) : 233-242.
- Gleason, Andrew, George Mackey, Raoul Bott. Faculty of Arts and Sciences-Memorial Minute: Lars Valerian Ahlfors. Harvard University Gazette, 25 January 2001, 16.
- Lehto, Olli.On the Life and Works of Lars Ahlfors. The Mathematical Intelligencer 20, no. 3 (1998) : 4-8.
- Mathematician Lars Ahlfors Dies at Age 89. Harvard University Gazette, 17 October 1996, 2.

From the guide to the Papers of Lars Valerian Ahlfors, 1929-1987, (Harvard University Archives)

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#### Subjects:

- Mathematicians
- Mathematics--Research
- Mathematics--Study and teaching (Higher)

#### Occupations:

#### Places:

- Massachusetts--Cambridge
*(as recorded)*