Lars Valerian Ahlfors

1907-1996

Finnish-American Mathematician

Finnish-born mathematician Lars V. Ahlfors became one of the first two people to receive the Fields Medal in 1936. In awarding the medal, the International Congress of Mathematicians (ICM) cited Ahlfors's complex analysis work, and in particular his investigations of Riemann surfaces, schematic devices for mapping the relation between complex numbers according to an analytic function. Ahlfors's studies in this area led to developments in meromorphic functions—functions that are analytic everywhere except in a finite number of poles—which in turn spawned a new field of analysis.

Ahlfors's father, Axel, was a mechanical engineering professor at the polytechnical institute in Helsingfors, Finland, where Ahlfors was born on April 8, 1907. Ahlfors's mother, Sievä Helander Ahlfors, died giving birth to him, and the boy grew up close to his father. From an early age, the young Ahlfors took an interest in mathematics, teaching himself calculus from his father's engineering books.

In 1924, 17-year-old Ahlfors entered the mathematics program at the University of Helsingfors, where he came under the tutelage of two outstanding mathematicians, Ernst Lindelöf and Rolf Nevanlinna. Lindelöf, who taught all the significant Finnish mathematicians of Ahlfors's generation, took a paternal role with his students. Ahlfors's most intensive contact with Lindelöf was during his undergraduate years; after graduating in 1928, he followed Nevanlinna to the University of Zürich, where the professor was replacing the distinguished Hermann Weyl (1885-1955).

As a student of Nevanlinna, Ahlfors attracted notice when he proved Denjoy's conjecture on the number of asymptotic values of an entire function. He did this by using conformal mapping, a function involving the angle of intersection between two curves. This was a formative period intellectually for Ahlfors, who had never before been out of Finland or had any exposure to what he later called "live mathematics." Aside from Nevanlinna, number theorist George Pólya (1887-1985) had a strong influence on Ahlfors during this time.

After leaving Zürich, Ahlfors spent three months in Paris, where he developed a geometric interpretation of Nevanlinna's theory of meromorphic functions. He then took a job at Abo Akademi, a Swedish-language university in Finland, and began work on his thesis, which concerned conformal mapping and entire functions. After finishing his thesis in 1930, he earned his Ph.D. in 1932. Also in that year, he was named a fellow of the Rockefeller Institute, and as a result had an opportunity to study in Paris.

A much greater award was to follow, but in the meantime Ahlfors returned to his hometown of Helsingfors to take a job as an adjunct professor at the university there in 1933. Also in 1933, he married Austrian-born Emma Lehnert, and the couple eventually had three daughters. Ahlfors began a three-year assignment as an assistant professor at Harvard University in 1935, and in the following year he attended the International Congress of Mathematicians (ICM) at Oslo, Norway.

The ICM announced that it would begin awarding a new prize, the Fields Medal—equivalent to a Nobel in mathematics—to recognize mathematicians under the age of 40 who had produced outstanding work. Much to the surprise of the 29-year-old Ahlfors, the ICM presented him one of its first two Fields medals, citing his "research on covering surfaces related to Riemann surfaces of inverse functions of entire and meromorphic functions."

Ahlfors returned to Finland in 1938, taking a position as a professor at the University of Helsinki. At the latter part of World War II—which had forced the closing of the university, during which time Ahlfors continued his studies of meromorphic curves—Ahlfors accepted a position at the University of Zürich. This took him away from the fighting, and returned him to the place where his most fruitful work had begun; but after the war, Ahlfors returned to Harvard, where he began teaching in 1946.

He spent the remainder of his career at Harvard, during which time he published his influential Complex Analysis in 1953. Ahlfors retired in 1977, and five years later won the Steele Prize for his three editions of Complex Analysis. He died of pneumonia on October 11, 1996, near his home in Boston.

JUDSON KNIGHT