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Andreas Floer died on May 15th, 1991 in Bochum, Germany, at the age of 34. He was on leave at the Ruhr-Universität Bochum. Andreas was born on August 23, 1956 in Duisburg, Germany. He received the degree Diplom-Mathematiker from the Ruhr-Universität in 1982, having specialized in algebraic topology. In the fall of that year he came to Berkeley as a doctoral student, working with Clifford Taubes on gauge theory and with Alan Weinstein on symplectic geometry. After two years at Berkeley he returned to Germany to fulfill a military-service obligation. While there, he resumed his work at Bochum, rapidly completing a dissertation on V.I. Arnold's fixed-point conjecture for symplectic maps to earn the degree Dr. rer. nat. in December 1984. His Berkeley dissertation with Taubes, which was to be on the subject of monopoles on 3-manifolds, was not completed but appeared later as a research paper.
In spring 1985 he returned to Berkeley as a research associate. Participation in a seminar led to the beginning of his work on the fundamental theory now called Floer homology. Andreas obtained a postdoctoral fellowship in mathematical physics at the State University of New York at Stony Brook on the strength of his German doctorate. After a year at Stony Brook he spent two years as a Courant Instructor at New York University and completed there some of his seminal work. In 1988 he returned to Berkeley as an Assistant Professor.
During the last two years of his life Andreas received honors at a rapid pace: invitations as visiting lecturer from all over the world (Moscow, Oxford, Paris, Zurich), a Sloan Fellowship (1989), and an invitation as a plenary speaker at the International Congress of Mathematicians in Kyoto (1990). The latter invitation, one of only 15 at a meeting held every four years, was quite exceptional for someone so young. By 1990 he was promoted to Professor at Berkeley while considering several offers from universities in the U.S. and Europe, among them Bochum, where he returned in the fall of 1990 as a full professor.
In his research Andreas Floer developed a new method for "counting" the solutions of maximum-minimum problems arising in geometry. A certain quantity called the "index" traditionally used to classify solutions was infinite, and therefore unhelpful, in many important but apparently intractable problems. Andreas realized that the difference between the indices of any two solutions could still be defined and could be used where the index itself was useless. Combining this observation with detailed, careful analysis, and using work of many other mathematicians as well as his own, Andreas developed a theory that led to the solution of a number of outstanding problems. The value of his work was grasped immediately by specialists in differential geometry, topology, and mathematical physics, for whom "Floer homology" has become an essential part of their problem-solving toolkit.
Although Andreas' fame came from his research, he had an intense personal concern with questions of teaching. Thanks in part to his German education, he was dissatisfied with the traditional American "by the book" approach to undergraduate courses. While teaching a course in real analysis, he had taken the material apart from top to bottom, reanalyzing standard concepts and theorems in order to prepare his students for mathematics as it is done today.
Andreas is survived by his mother, Marlies Floer, and his brothers, Detlef and Rainer Floer. To them we extend our heartfelt sympathy. The death of such a brilliant young mathematician at the height of his creative powers is a special tragedy: we rejoice and marvel at the deep and seminal insights he had already had, but mourn the loss to science and mankind of the further beautiful and important discoveries he would have made.
John Addison
Andrew Casson
Alan Weinstein
In spring 1985 he returned to Berkeley as a research associate. Participation in a seminar led to the beginning of his work on the fundamental theory now called Floer homology. Andreas obtained a postdoctoral fellowship in mathematical physics at the State University of New York at Stony Brook on the strength of his German doctorate. After a year at Stony Brook he spent two years as a Courant Instructor at New York University and completed there some of his seminal work. In 1988 he returned to Berkeley as an Assistant Professor.
During the last two years of his life Andreas received honors at a rapid pace: invitations as visiting lecturer from all over the world (Moscow, Oxford, Paris, Zurich), a Sloan Fellowship (1989), and an invitation as a plenary speaker at the International Congress of Mathematicians in Kyoto (1990). The latter invitation, one of only 15 at a meeting held every four years, was quite exceptional for someone so young. By 1990 he was promoted to Professor at Berkeley while considering several offers from universities in the U.S. and Europe, among them Bochum, where he returned in the fall of 1990 as a full professor.
In his research Andreas Floer developed a new method for "counting" the solutions of maximum-minimum problems arising in geometry. A certain quantity called the "index" traditionally used to classify solutions was infinite, and therefore unhelpful, in many important but apparently intractable problems. Andreas realized that the difference between the indices of any two solutions could still be defined and could be used where the index itself was useless. Combining this observation with detailed, careful analysis, and using work of many other mathematicians as well as his own, Andreas developed a theory that led to the solution of a number of outstanding problems. The value of his work was grasped immediately by specialists in differential geometry, topology, and mathematical physics, for whom "Floer homology" has become an essential part of their problem-solving toolkit.
Although Andreas' fame came from his research, he had an intense personal concern with questions of teaching. Thanks in part to his German education, he was dissatisfied with the traditional American "by the book" approach to undergraduate courses. While teaching a course in real analysis, he had taken the material apart from top to bottom, reanalyzing standard concepts and theorems in order to prepare his students for mathematics as it is done today.
Andreas is survived by his mother, Marlies Floer, and his brothers, Detlef and Rainer Floer. To them we extend our heartfelt sympathy. The death of such a brilliant young mathematician at the height of his creative powers is a special tragedy: we rejoice and marvel at the deep and seminal insights he had already had, but mourn the loss to science and mankind of the further beautiful and important discoveries he would have made.
John Addison
Andrew Casson
Alan Weinstein
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