Sigurdur Helgason, Professor Emeritus of Mathematics, Dies at 96

Published: December 6, 2023

Sigurdur Helgason
Sigurdur Helgason

Sigurdur Helgason, emeritus professor of mathematics at MIT, passed away on Sunday, December 3, 2023, at the age of 96. Helgason for many decades led the study of group actions on manifolds. Generations of mathematicians entered the field through his classic 1962 text Differential Geometry and Symmetric Spaces, and its greatly expanded 1978 second edition Differential Geometry, Lie Groups, and Symmetric Spaces. His own research contributions included the Plancherel and Paley-Wiener theorems for Riemannian symmetric spaces. He was a superb lecturer, a well-regarded graduate advisor, and a cherished colleague.

Helgason came to MIT as a CLE Moore Instructor in 1954. Following postdoctoral appointments at Princeton University, the University of Chicago and Columbia University, he joined the MIT mathematics faculty in 1959. He officially retired from the faculty after 55 years in 2014.

As a part of his geometric work, Helgason helped to create the modern theory of Radon transforms: seeking to reconstruct a function from its integrals along various subspaces. (This is the mathematical basis of many kinds of medical imaging.) Helgason understood that a zoo of special results could be understood as instances of a very general “double fibration”:

math diagram of double fibration

This insight became part of the foundation of his work on the Fourier transform on symmetric spaces, his existence results for solutions of group-invariant differential equations, and his contributions to infinite-dimensional representation theory. Helgason advised 17 doctoral dissertations (13 at MIT), and was a vital resource for many more.

He served as the graduate faculty chair for seven years, from 1986 to 1993. He received MIT’s first Graduate Teaching Award in 1975. He gave over 200 invited lectures in the U.S., Canada, Europe, Japan and China. Among these was an Invited Lecture at the International Mathematics Congress, 1970, four lectures at the American Mathematical Society (1962-1982), three lectures at the Scandinavian Mathematical Congress (1968-1984), and the Langvad Cultural Exchange lectures at the University of Copenhagen in 1982.

In 1988, Helgason received the Leroy P. Steele Prize of the American Mathematics Society, for his two books Differential Geometry, Lie Groups, and Symmetric Spaces (1978), and its successor, Groups and Geometric Analysis (1984). The 1978 book was a fundamental revision and expansion of his 1962 classic text, Differential Geometry and Symmetric Spaces.

He received a Fulbright Grant in 1952, a Proctor Fellowship at Princeton, 1953-1954, and a Guggenheim Fellowship, 1964-1965. He was made a Member of the Icelandic Academy of Sciences in 1960, Fellow of the American Academy of Arts and Sciences in 1970, and Member of the Royal Danish Academy of Sciences and Letters in 1972. He received the Børge Jessen Diploma Award from the Danish Mathematical Society in 1982. He was awarded a Doctor Honoris Causa from the University of Iceland in 1986, from the University of Copenhagen in 1988, and from the University of Uppsala in Sweden in 1996. In 1991, Helgason was awarded the Major Knights Cross of the Icelandic Falcon. Since 2012, he has been a Fellow of the American Mathematical Society.

Helgason was born September 30, 1927 in Akureyri, Iceland. He completed the bachelor’s in mathematics at the University of Copenhagen in 1952, receiving the University’s Gold Medal in 1951 (for solving a mathematical prize problem). He received his PhD from Princeton University in 1954 studying under Salomon Bochner. His first postdoctoral appointment was at MIT as a CLE Moore Instructor, 1954-1956, followed by a lecturer appointment at Princeton, 1956-1957, and a Louis Block Research Lecturership at the University of Chicago, 1957-1959. He joined the MIT mathematics faculty as Assistant Professor in 1959, (appointed Visiting Assistant Professor at the University of Chicago 1959-1960, while on leave from MIT). He was promoted to Associate Professor in 1961, and to Full Professor in 1965. During this period he had visiting appointments at the Institute for Advanced Study (1964-1966, 1974-1975, and Fall 1983), and at the Institut Mittag-Leffler (1970-1971).

Helgason married Artie Gianopulos on June 9, 1957. She survives him, along with their children Thor Helgi Helgason and Dr. Anna Loa Helgason. He was predeceased by his parents Helgi Skúlason (1892-1983) and Kara Briem (1900-1982); a brother Skúli Helgason (1926-1973); and a sister Sigriður Helgadóttir (1933-2003).