Herbert Federer
Brown University
July 23, 1920 - April 21, 2010
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Scientific Discipline: Mathematics Membership Type:
Emeritus
(elected 1975)
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Herbert Federer made deep and original contributions primarily to two fields of mathematics: surface area theory and geometric measure theory. Research on surface area theory had been flourishing since the 1930s, but beginning with two papers he published in 1944 Federer became one the field’s leaders. He developed techniques, based on new methods in algebraic topology, that were applicable to area theory for surfaces of any dimension. Federer will best be remembered, however, as a pioneer in geometric measure theory—as one who made fundamental and profound advances in many different ways, thus helping new ideas to develop. It is difficult to imagine that the field’s rapid growth, as well as its subsequent influence on other areas of mathematics, could have happened without his contributions. Federer’s seminal 1960 paper “Normal and integral currents” (coauthored with Wendell Fleming) is generally considered to mark the birth of geometric measure theory.
Federer himself was born in Vienna, Austria, and immigrated to the United States in 1938, at the age of 18. He attended college and graduate school at the University of California, Berkeley, receiving a BA in mathematics and physics in 1942 and his PhD in mathematics in 1944. During 1944 and 1945 Federer served in the U.S. Army at the Ballistics Research Laboratory in Aberdeen, MD. Immediately after receiving an Army discharge, he joined the Department of Mathematics at Brown University, where he remained until his retirement in 1985.
Federer was an Alfred Sloan Research Fellow (1957–1960), a National Science Foundation Senior Postdoctoral Fellow (1964–1965), and a John Guggenheim Memorial Fellow (1975–1976). He became a fellow of the American Academy of Arts and Sciences in 1962 and a member of the National Academy of Sciences in 1975.
Federer’s authoritative book "Geometric Measure Theory" appeared in 1969. To quote his former PhD student Robert Hardt: “Forty years after the book’s publication, the richness of its ideas continue to make it both a profound and indispensable work. Federer once told me that, despite more than a decade of his work, the book was destined to become obsolete in the next 20 years. He was wrong. The book was just like his car, a Plymouth Fury wagon purchased in the early 1970s that he somehow managed to keep going for almost the rest of his life. Today [May 2012] "Geometric Measure Theory" is still running fine and continues to provide thrilling rides for the youngest generation of geometric measure theorists.”
