## Lars V. Ahlfors

### Lars V. Ahlfors, 89, Pioneer in the Outer Reaches of Higher Math

Lars Valerian Ahlfors, a mathematician whose mind plumbed the theoretical outer reaches of higher mathematics, died on Oct. 11 at the Willowood nursing home in Pittsfield, Mass. He was 89 and lived in Boston.Dr. Ahlfors retired from Harvard University in 1977 as the William Caspar Graustein Professor of Mathematics, a chair to which he was named in 1964. He first went to Harvard as an assistant professor in the late 1930's and returned in 1946 as a full professor.

In 1936, he was awarded the first Fields Medal, the mathematics equivalent of the Nobel Prize, by the International Mathematics Society.

Like many mathematicians and physicists of world rank, Dr. Ahlfors laid the foundations of a life's work in his 20's. Unlike some of his peers, he remained at the forefront for decades as a theoretician and teacher.

Dr. Ahlfors was best known for his contributions to complex analysis, a fundamental subject that has applications ranging from number theory to modern physics.

He whetted his appetite in his native Helsinki, Finland, when his mentors at Helsinki University interested him in the analysis of mathematical and algebraic complexes. His research in Helsinki and at the Polytechnic Institute in Zurich resulted in his innovative approach to conformal mapping and a noted study of the asymptotic values of an entire function.

His textbook ''Complex Analysis,'' appeared in 1953, had new editions in 1966 and 1979, and remains a standard text, with the publisher McGraw-Hill. He published almost 100 papers and three other mathematical books, including his proof of the ''Ahlfors finiteness theorem'' in 1964.

He received his doctorate at Helsinki University in 1930. After his early turn at Harvard, homesickness drew him back to Finland. He taught at Helsinki University until 1944 and spent a year in Zurich before returning to Harvard.

Dr. Ahlfors is survived by his wife of 63 years, Erna Lehnert Ahlfors, of Nassau, N.Y.; three daughters, Cynthia Edwards, of Jumeauville, France, Vanessa Gruen, of Darien, Conn., and Caroline Mouris, of Nassau; a brother, Axel, of Torup, Sweden; a sister, Unga Appelqvist, of Helsinki, and several grandchildren and great-grandchildren.

By WOLFGANG SAXON, October 20, 1996 © The New York Times Company