Wolfgang R. Wasow
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Wolfgang R. Wasow (25 July 1909 – 11 September 1993) was an American
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 ...
known for his work in asymptotic expansions and their applications in
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.


Early life

Wasow was born as Wolfgang Richard Thal in Vevey, Switzerland, to Jewish parents, Alma Thal and Max Richard Kleineibst, who had met in Paris. Alma Thal was from Jelgava in Latvia, a part of
Czarist Russia The Tsardom of Russia or Tsardom of Rus' also externally referenced as the Tsardom of Muscovy, was the centralized Russian state from the assumption of the title of Tsar by Ivan IV in 1547 until the foundation of the Russian Empire by Peter I in ...
at the time. Her family had sent her to Switzerland to put an end to her political activities. Richard Kleineibst was also a political activist and later gained prominence as a leftwing social democrat in the
Weimar Republic The Weimar Republic (german: link=no, Weimarer Republik ), officially named the German Reich, was the government of Germany from 1918 to 1933, during which it was a constitutional federal republic for the first time in history; hence it is al ...
. He became a founding member of
Socialist Workers' Party of Germany The Socialist Workers' Party of Germany (german: Sozialistische Arbeiterpartei Deutschlands, SAPD) was a centrist Marxist political party in Germany. It was formed as a left-wing party with around 20,000 members which split off from the SPD in ...
in 1931 and was the first editor in chief of Sozialistische Arbeiter-Zeitung, its main organ. Alma Thal moved to Germany in 1910 and then several more times within Germany. And so Wolfgang grew up first in Munich, and then in Freiburg, Heidelberg and Berlin. When Alma Thal married the Munich photographer Eduard Wasow, Wolfgang took his name. In 1921, Wolfgang Wasow was sent to a boarding school, the Freie Schul- und Werkgemeinschaft Letzlingen, founded by Bernhard Uffrecht, located in the Magdeburg district of
Prussia Prussia, , Old Prussian: ''Prūsa'' or ''Prūsija'' was a German state on the southeast coast of the Baltic Sea. It formed the German Empire under Prussian rule when it united the German states in 1871. It was ''de facto'' dissolved by an em ...
. He passed the
Abitur ''Abitur'' (), often shortened colloquially to ''Abi'', is a qualification granted at the end of secondary education in Germany. It is conferred on students who pass their final exams at the end of ISCED 3, usually after twelve or thirteen year ...
exam and graduated from the school in 1928. After studies at Humboldt and Sorbonne, he enrolled at
Göttingen Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...
and passed the Staatsexamen (a government licensing examination for future teachers) in mathematics, physics and geology in 1933.


Emigration

Wasow left Germany in 1933 and spent time in Paris and Cambridge before taking a job as a teacher at boarding schools for children of (predominantly Jewish) German emigrants in Italy, first in
Florence Florence ( ; it, Firenze ) is a city in Central Italy and the capital city of the Tuscany region. It is the most populated city in Tuscany, with 383,083 inhabitants in 2016, and over 1,520,000 in its metropolitan area.Bilancio demografico an ...
(1935–37) and then in
Lana Lana may refer to: *Lana (given name) *Francesco Lana de Terzi (1631–1687), Italian Jesuit priest and scientist *Lana (wrestler), professional wrestler and pro wrestling manager *'' Wild Energy. Lana'', a 2006 Ukrainian fantasy novel Sciences * ...
in Alto Adige (1937–38). After the closure of the latter school in 1938 due to the passage of the Italian Racial Laws, Wasow emigrated to England and then to the United States in 1939.


Academic career

Wasow taught at Goddard College (1939–1941) and Connecticut College (1941–42) and was at the same time a PhD student in mathematics under the supervision of
Kurt Otto Friedrichs Kurt Otto Friedrichs (September 28, 1901 – December 31, 1982) was a noted German-American mathematician. He was the co-founder of the Courant Institute at New York University, and a recipient of the National Medal of Science. Biography Friedri ...
at New York University. He received his PhD in 1942 and stayed to work as an instructor for mathematics until 1946. He then held academic and research positions at Swarthmore,
UCLA The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...
and
University of Wisconsin–Madison A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...
1946–1957, interrupted by a
Fulbright The Fulbright Program, including the Fulbright–Hays Program, is one of several United States Cultural Exchange Programs with the goal of improving intercultural relations, cultural diplomacy, and intercultural competence between the people of ...
Fellowship in Rome (1954–55). He was appointed full professor of mathematics in 1957 at
Madison Madison may refer to: People * Madison (name), a given name and a surname * James Madison (1751–1836), fourth president of the United States Place names * Madison, Wisconsin, the state capital of Wisconsin and the largest city known by this ...
and Rudolf E. Langer Professor of Mathematics in 1973. He was department chair 1970–72. He retired in 1980. Wolfgang Wasow's main research area was
singular perturbation theory In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero. More precisely, the solution cannot be uniformly approximated by an asymptotic expansion : ...
. A classical application is the thin boundary layer that forms on a solid surface as a fluid flows over it. Above the boundary layer, the fluid behaves approximately like a
perfect fluid In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density \rho_m and ''isotropic'' pressure ''p''. Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in whi ...
. But within the boundary layer, the velocity of the flow changes rapidly from the high velocity above the boundary layer to a velocity of 0 at the solid surface. Many technical problems can be modeled this way, including the flow of a liquid through a pipe and the flow of air over an airplane wing. Boundary layer problems are instances of a more general class of problems that today is part of the field of singular perturbations. Starting with his 1941 PhD thesis, Wasow was one of the main contributors to developing a mathematical theory of the boundary layer problem and singular perturbations. The organizers of a symposium in his honor at the Mathematics Research Center at
Madison Madison may refer to: People * Madison (name), a given name and a surname * James Madison (1751–1836), fourth president of the United States Place names * Madison, Wisconsin, the state capital of Wisconsin and the largest city known by this ...
write: Wasow was "a substantial contributor to the study of
singular perturbation In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero. More precisely, the solution cannot be uniformly approximated by an asymptotic expansion : ...
s for over twenty years". His textbook "Asymptotic expansions for ordinary differential equations" was the first "authoritative treatment" of the subject. The Wolfgang Wasow Memorial Lecture, an annual lecture at the
University of Wisconsin–Madison A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...
, was established in Wasow's honor by his children in 1993.


Personal life

Wasow had three sons: Tom Wasow (linguist), Bernard Wasow (economist), and Oliver Wasow (artist). He also had two step-children. Wolfgang Wasow self-published an autobiography for his family in 1986.


References


External links

* {{DEFAULTSORT:Wasow, Wolfgang R. 1909 births 1993 deaths University of Wisconsin–Madison faculty 20th-century American mathematicians Swiss emigrants to the United States