Rolf Nevanlinna
Early Life and Education
Rolf Herman Nevanlinna was born on October 22, 1895, in Joensuu, Finland. He was the son of Otto Nevanlinna, a professor of mathematics, and his wife, Margareta. From an early age, Rolf exhibited a profound interest in mathematics, likely influenced by his father's academic background. He attended the University of Helsinki, where he studied under the guidance of Ernst Lindelöf, a prominent Finnish mathematician. Nevanlinna completed his doctoral dissertation in 1922, focusing on the theory of meromorphic functions, a field that would become central to his later work.
Contributions to Mathematics
Nevanlinna Theory
Rolf Nevanlinna is best known for developing the Nevanlinna Theory, a branch of complex analysis that deals with the distribution of values of meromorphic functions. This theory provides a framework for understanding how often a meromorphic function takes on certain values. Nevanlinna's First and Second Main Theorems are cornerstones of this theory. The First Main Theorem relates the growth of a meromorphic function to the distribution of its values, while the Second Main Theorem provides a more detailed analysis involving the concept of deficiency.
Value Distribution Theory
Nevanlinna's work in value distribution theory extends beyond meromorphic functions to include entire functions. His contributions have provided deep insights into the behavior of these functions, particularly in understanding the frequency and distribution of their zeros and poles. This has significant implications for various fields, including number theory and differential equations.
Differential Equations
In addition to his work on meromorphic and entire functions, Nevanlinna made substantial contributions to the theory of differential equations. He explored the connections between differential equations and complex analysis, particularly in the context of linear differential equations with meromorphic coefficients. His work in this area has influenced subsequent research in both pure and applied mathematics.
Academic Career
University of Helsinki
After completing his doctoral studies, Nevanlinna joined the faculty at the University of Helsinki, where he quickly rose through the ranks. He became a full professor in 1936 and held this position until 1946. During his tenure, he mentored numerous students and contributed to the development of the university's mathematics department.
International Recognition
Nevanlinna's work gained international recognition, leading to numerous invitations to lecture and collaborate with mathematicians worldwide. He held visiting positions at several prestigious institutions, including the University of Zurich and the Institute for Advanced Study in Princeton. His contributions were acknowledged through various awards and honors, including membership in the Finnish Academy of Science and Letters and the Royal Swedish Academy of Sciences.
Later Years and Legacy
Nevanlinna Prize
In honor of his contributions to mathematics, the International Mathematical Union established the Nevanlinna Prize in 1981. This prize is awarded every four years to a mathematician under 40 who has made significant contributions to mathematical aspects of information science. The Nevanlinna Prize has since been renamed the IMU Abacus Medal.
Publications
Nevanlinna authored several influential books and papers throughout his career. His book "Eindeutige analytische Funktionen" (Unique Analytic Functions), published in 1936, remains a seminal work in the field of complex analysis. His collected works, published posthumously, continue to be a valuable resource for researchers in mathematics.
Death
Rolf Nevanlinna passed away on May 28, 1980, in Helsinki, Finland. His legacy endures through his groundbreaking contributions to mathematics and the ongoing influence of his work on subsequent generations of mathematicians.