Lars Valter Hörmander (24 January 1931 – 25 November 2012) was a

Swedish Swedish or ' may refer to: Anything from or related to Sweden, a country in Northern Europe. Or, specifically: * Swedish language, a North Germanic language spoken primarily in Sweden and Finland ** Swedish alphabet, the official alphabet used by ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

who has been called "the foremost contributor to the modern theory of linear

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

". Hörmander was awarded the Fields Medal in 1962 and the

Wolf Prize The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for ''"achievements in the interest of mankind and friendly relations among people ... irrespective of nati ...

in 1988. In 2006 he was awarded the Steele Prize for Mathematical Exposition for his four-volume textbook ''Analysis of Linear Partial Differential Operators'', which is considered a foundational work on the subject. Hörmander completed his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

in 1955 at

Lund University , motto = Ad utrumque , mottoeng = Prepared for both , established = , type = Public research university , budget = SEK 9 billion Stockholm University, at Stanford University, and at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

. He returned to Lund University as a professor from 1968 until 1996, when he retired with the title of

professor emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

Biography

Education

Hörmander was born in

Mjällby Mjällby is a locality situated in Sölvesborg Municipality, Blekinge County, Sweden with 1,254 inhabitants in 2010. It is located on the Listerlandet peninsula. The town has traditionally lived of fishing. The nearby harbour of Nogersund is ...

, a village in

Blekinge Blekinge (, old da, Bleking) is one of the traditional Swedish provinces (), situated in the southern coast of the geographic region of Götaland, in southern Sweden. It borders Småland, Scania and the Baltic Sea. It is the country's secon ...

in southern Sweden where his father was a teacher. Like his older brothers and sisters before him, he attended the

realskola ''Realschule'' () is a type of secondary school in Germany, Switzerland and Liechtenstein. It has also existed in Croatia (''realna gimnazija''), the Austrian Empire, the German Empire, Denmark and Norway (''realskole''), Sweden (''realsk ...

(secondary school), in a nearby town to which he commuted by train, and the gymnasium (high school) in Lund from which he graduated in 1948. At the time when he entered the gymnasium, the principal had instituted an experiment of reducing the period of the education from three to two years, and the daily activities to three hours. This freedom to work on his own, " reaterthan the universities offer in Sweden today", suited Hörmander "very well". He was also positively influenced by his enthusiastic mathematics teacher, a

docent The title of docent is conferred by some European universities to denote a specific academic appointment within a set structure of academic ranks at or below the full professor rank, similar to a British readership, a French " ''maître de con ...

Lund University , motto = Ad utrumque , mottoeng = Prepared for both , established = , type = Public research university , budget = SEK 9 billion Master's degree A master's degree (from Latin ) is an academic degree awarded by universities or colleges upon completion of a course of study demonstrating mastery or a high-order overview of a specific field of study or area of professional practice.

from Lund University in 1950, Hörmander began his graduate studies under

Marcel Riesz Marcel Riesz ( hu, Riesz Marcell ; 16 November 1886 – 4 September 1969) was a Hungarian mathematician, known for work on summation methods, potential theory, and other parts of analysis, as well as number theory, partial differential equations ...

(who had also been the advisor for Hörmander's gymnasium teacher). He made his first research attempts in classical function theory and harmonic analysis, which "did not amount to much" but were "an excellent preparation for working in the theory of partial differential equations." He turned to partial differential equations when Riesz retired and

Lars Gårding Lars Gårding (7 March 1919 – 7 July 2014) was a Swedish mathematician. He made notable contributions to the study of partial differential equations and partial differential operators. He was a professor of mathematics at Lund University in S ...

who worked actively in that area was appointed professor. Hörmander took a one-year break for

military service Military service is service by an individual or group in an army or other militia, air forces, and naval forces, whether as a chosen job ( volunteer) or as a result of an involuntary draft (conscription). Some nations (e.g., Mexico) require ...

from 1953 to 1954, but due to his position in defense research was able to proceed with his studies even during that time. His

thesis ''On the theory of general partial differential operators'' was finished in 1955, inspired by the nearly concurrent Ph.D. work of Bernard Malgrange and techniques for hyperbolic differential operators developed by

and

Jean Leray Jean Leray (; 7 November 1906 – 10 November 1998) was a French mathematician, who worked on both partial differential equations and algebraic topology. Life and career He was born in Chantenay-sur-Loire (today part of Nantes). He studied at Éc ...

Fields Medal and years in the U.S.

Hörmander applied for a professorship at Stockholm University, but temporarily left for the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territori ...

while the request was examined. He spent quarters from winter to fall in respective order at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

, the

University of Kansas The University of Kansas (KU) is a public research university with its main campus in Lawrence, Kansas, United States, and several satellite campuses, research and educational centers, medical centers, and classes across the state of Kansas. T ...

, the

University of Minnesota The University of Minnesota, formally the University of Minnesota, Twin Cities, (UMN Twin Cities, the U of M, or Minnesota) is a public land-grant research university in the Twin Cities of Minneapolis and Saint Paul, Minnesota, United States. ...

, and finally at the

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...

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. These locations offered "much to learn" in partial differential equations, with the exception of Chicago of which he however notes the

Antoni Zygmund Antoni Zygmund (December 25, 1900 – May 30, 1992) was a Polish mathematician. He worked mostly in the area of mathematical analysis, including especially harmonic analysis, and he is considered one of the greatest analysts of the 20th century. ...

seminar held by

Elias Stein Elias Menachem Stein (January 13, 1931 – December 23, 2018) was an American mathematician who was a leading figure in the field of harmonic analysis. He was the Albert Baldwin Dod Professor of Mathematics, Emeritus, at Princeton University, whe ...

and

Guido Weiss Guido Leopold Weiss (born 29 December 1928 in Trieste, died 25 December 2021 in St. Louis) was an American mathematician, working in analysis, especially Fourier analysis and harmonic analysis. Childhood Weiss was born in Trieste Italy int ...

to have strengthened his familiarity with harmonic analysis. In the theory of linear differential operators, "many people have contributed but the deepest and most significant results are due to Hörmander", according to Hörmander's doctoral advisor, Lars Gårding. Hörmander won the Fields medal in 1962. Hörmander was given a position as a part-time professor at Stanford in 1963 but was soon thereafter offered a professorship at the

in Princeton, New Jersey. He first wished not to leave Sweden but attempts to find a research professorship in Sweden failed and "the opportunity to do research full time in a mathematically very active environment was hard to resist", so he accepted the offer and resigned from both Stanford and Stockholm and began at the Institute in the fall of 1964. Within two years of "hard work", he felt that the environment at the institute was too demanding, and in 1967 decided to return to Lund after one year. He later noted that his best work at the institute was done during the remaining year.

Later years

Hörmander mostly remained at

Lund University , motto = Ad utrumque , mottoeng = Prepared for both , established = , type = Public research university , budget = SEK 9 billion microlocal analysis In mathematical analysis, microlocal analysis comprises techniques developed from the 1950s onwards based on Fourier transforms related to the study of variable-coefficients-linear and nonlinear partial differential equations. This includes gener ...

was held. He also visited Stanford in 1971, 1977, and 1982, and the

University of California, San Diego The University of California, San Diego (UC San Diego or colloquially, UCSD) is a public land-grant research university in San Diego, California. Established in 1960 near the pre-existing Scripps Institution of Oceanography, UC San Diego is t ...

in winter 1990. Hörmander was briefly director of the Mittag-Leffler Institute in Stockholm between 1984 and 1986 but only accepted a two-year appointment as he "suspected that the administrative duties would not agree well" with him, and found that "the hunch was right". He also served as vice president of the

International Mathematical Union The International Mathematical Union (IMU) is an international non-governmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports ...

between 1987 and 1990. Hörmander retired emeritus in Lund in January 1996. In 2006 he was honored with the Steele Prize for Mathematical Exposition from the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. He was made a member of the Royal Swedish Academy of Sciences in 1968. In 1970 he gave a plenary address (Linear Differential Operators) at the ICM in

Nice Nice ( , ; Niçard dialect, Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes departments of France, department in France. The Nice urban unit, agg ...

. He received the 1988

"for fundamental work in modern analysis, in particular, the application of pseudo differential and

Fourier integral operator In mathematical analysis, Fourier integral operators have become an important tool in the theory of partial differential equations. The class of Fourier integral operators contains differential operators as well as classical integral operators as ...

s to linear partial differential equations". In 2012 he was selected as a fellow of the

, but died on 25 November 2012, before the list of fellows was released.

Important publications

His book ''Linear Partial Differential Operators'', which largely was the cause for his Fields Medal, has been described as "the first major account of this theory". It was published by

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 ...

in 1963 as part of the '' Grundlehren'' series. Hörmander devoted five years to compiling the four-volume monograph, ''The Analysis of Linear Partial Differential Operators'', first published between 1983 and 1985. A follow-up of his ''Linear Partial Differential Operators'', "illustrate the vast expansion of the subject" over the past 20 years, and is considered the "standard of the field". In addition to these works, he has written a recognised introduction to several complex variables based on his 1964 Stanford lectures, and wrote the entries on

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

s in

Nationalencyklopedin ''Nationalencyklopedin'' (; "The National Encyclopedia" in English), abbreviated NE, is a comprehensive contemporary Swedish-language encyclopedia, initiated by a favourable loan from the Government of Sweden of 17 million Swedish kronor in 1 ...

. * * * * * * * *

Notes

* Wolf Foundation. ''The 1988 Wolf Foundation Prize In Mathematics''. Retrieved September 20, 2005

* L. Gårding. ''Hörmander's work on linear differential operators''. Proceedings of the International Congress of Mathematicians. Stockholm, 1962 (Stockholm, 1963). As quoted by O'Connor & Robertson. * Wolf Foundation. * Unknown. "About the Author".

Amazon.com Amazon.com, Inc. ( ) is an American multinational technology company focusing on e-commerce, cloud computing, online advertising, digital streaming, and artificial intelligence. It has been referred to as "one of the most influential econo ...

entry for ''The Analysis of Linear Partial Differential Operators I''. Retrieved September 20, 200

* Wolf Foundation.

References

Bibliography

* Hörmander, Lars. Autobiography. ''Fields Medallists' Lectures''. M. Sir Michael Atiyah & D. Iagolnitzer (editors). World Scientific. * J. J. O'Connor & E. F. Robertson.
Lars Hörmander
'. MacTutor archive biography. Retrieved September 20, 2005

External links

* {{DEFAULTSORT:Hormander, Lars 1931 births 2012 deaths 20th-century Swedish mathematicians 21st-century Swedish mathematicians Complex analysts Directors of the Mittag-Leffler Institute Fellows of the American Mathematical Society Fields Medalists Members of the Royal Swedish Academy of Sciences Foreign associates of the National Academy of Sciences Institute for Advanced Study faculty PDE theorists People connected to Lund University Wolf Prize in Mathematics laureates Stockholm University faculty Courant Institute of Mathematical Sciences faculty