Lars V. Hormander, a Swede who won the most prestigious award in mathematics for his groundbreaking work on partial differential equations, which has found broad applications across many branches of physics, died on Nov. 25 in Lund, Sweden. He was 81.

His death was announced by Lund University, where he was on the faculty for many years.

Partial differential equations govern, or predict, functions of physical phenomena, like heat, sound and electromagnetism. They crop up almost everywhere in science, from seismology to climatology, and were first studied by physicists. But understanding these equations soon became a major thrust of mathematics as well. "Many people have contributed," Lars Garding, Dr. Hormander's thesis adviser, once wrote, "but the deepest and most significant results are due to Hormander."

For this work -- the subject of his 1963 book,

Twenty years later he would publish a follow-up in a magisterial four-volume work, "The Analysis of Linear Partial Differential Equations," which is still considered the standard of the field.

"In the history of mathematics, one is hard-pressed to find any comparable 'expository' work that covers so much material, and with such depth and understanding of such a broad area of mathematics," read the citation for the American Mathematical Society's Leroy P. Steele Prize, which Dr. Hormander received in 2006.

Dr. Hormander's work helped clarify solutions to a wide class of differential equations that are important to many fields of science and mathematics.

Richard Melrose, the Simons professor of mathematics at the Massachusetts Institute of Technology, said Dr. Hormander's work produced an "effective machine" -- that is, an extensive theoretical apparatus -- that led to a deep understanding of the solutions to a wide and important class of differential equations that previously resisted analysis. "He was a very influential mathematician," he added, "who basically revolutionized the field of linear partial differential equations." Dr. Hormander's ideas have found many applications in mathematics and physics as well as in some surprising areas, like oil exploration, by helping engineers understand the structure of the earth through analysis of the impact of earthquakes.

Dr. Hormander's general theory of partial differential equations, Dr. Melrose explained, "allows you to understand what happens when an earthquake occurs in Chile and that signal propagates through the earth and shows up in a seismograph in China." The same techniques help physicists understand the structure of the subatomic world, and are applied in many other areas as well.

Lars Valter Hormander was born on Jan. 24, 1931, in Mjallby, a village in southern Sweden. He received his master's degree from Lund University. After a one-year break for military service, he completed his Ph.D. and left for the United States.

In 1963 he took a part-time position at Stanford University, but shortly thereafter he accepted a full professorship at the Institute for Advanced Study in Princeton, N.J. After two years there, he decided that the environment was too intense for him, so he returned to Sweden and Lund University.

Dr. Hormander was vice president of the International Mathematical Union between 1987 and 1990. In 1988, he was awarded Israel's prestigious Wolf Prize

December 6, 2012 © NY Times

His death was announced by Lund University, where he was on the faculty for many years.

Partial differential equations govern, or predict, functions of physical phenomena, like heat, sound and electromagnetism. They crop up almost everywhere in science, from seismology to climatology, and were first studied by physicists. But understanding these equations soon became a major thrust of mathematics as well. "Many people have contributed," Lars Garding, Dr. Hormander's thesis adviser, once wrote, "but the deepest and most significant results are due to Hormander."

For this work -- the subject of his 1963 book,

*Linear Partial Differential Operators*-- Dr. Hormander in 1962 received the Fields Medal, often called the Nobel Prize of mathematics.Twenty years later he would publish a follow-up in a magisterial four-volume work, "The Analysis of Linear Partial Differential Equations," which is still considered the standard of the field.

"In the history of mathematics, one is hard-pressed to find any comparable 'expository' work that covers so much material, and with such depth and understanding of such a broad area of mathematics," read the citation for the American Mathematical Society's Leroy P. Steele Prize, which Dr. Hormander received in 2006.

Dr. Hormander's work helped clarify solutions to a wide class of differential equations that are important to many fields of science and mathematics.

Richard Melrose, the Simons professor of mathematics at the Massachusetts Institute of Technology, said Dr. Hormander's work produced an "effective machine" -- that is, an extensive theoretical apparatus -- that led to a deep understanding of the solutions to a wide and important class of differential equations that previously resisted analysis. "He was a very influential mathematician," he added, "who basically revolutionized the field of linear partial differential equations." Dr. Hormander's ideas have found many applications in mathematics and physics as well as in some surprising areas, like oil exploration, by helping engineers understand the structure of the earth through analysis of the impact of earthquakes.

Dr. Hormander's general theory of partial differential equations, Dr. Melrose explained, "allows you to understand what happens when an earthquake occurs in Chile and that signal propagates through the earth and shows up in a seismograph in China." The same techniques help physicists understand the structure of the subatomic world, and are applied in many other areas as well.

Lars Valter Hormander was born on Jan. 24, 1931, in Mjallby, a village in southern Sweden. He received his master's degree from Lund University. After a one-year break for military service, he completed his Ph.D. and left for the United States.

In 1963 he took a part-time position at Stanford University, but shortly thereafter he accepted a full professorship at the Institute for Advanced Study in Princeton, N.J. After two years there, he decided that the environment was too intense for him, so he returned to Sweden and Lund University.

Dr. Hormander was vice president of the International Mathematical Union between 1987 and 1990. In 1988, he was awarded Israel's prestigious Wolf Prize

**B Schechter**December 6, 2012 © NY Times