Richard Courant (January 8, 1888 – January 27, 1972) was a German-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, mathematical structure, structure, space, Mathematica ...
. He is best known by the general public for the book ''
What is Mathematics?'', co-written with
Herbert Robbins. His research focused on the areas of
real analysis
In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include co ...
,
mathematical physics
Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...
, the
calculus of variations
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions
and functional (mathematics), functionals, to find maxima and minima of f ...
and
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
The function is often thought of as an "unknown" that solves the equation, similar to ho ...
s. He wrote textbooks widely used by generations of students of physics and mathematics. He is also known for founding the
institute now bearing his name.
Life and career
Courant was born in
Lublinitz, in the
Prussian Province of Silesia
The Province of Silesia (; ; ) was a province of Prussia from 1815 to 1919. The Silesia region was part of the Prussian realm since 1742 and established as an official province in 1815, then became part of the German Empire in 1871. In 1919, as ...
(now in Poland). His parents were Siegmund Courant and Martha Freund of
Oels.
Edith Stein
Edith Stein (; ; in religion Teresa Benedicta of the Cross; 12 October 1891 – 9 August 1942) was a German philosopher who converted to Catholic Church, Catholicism and became a Discalced Carmelites, Discalced Carmelite nun. Edith Stein was mu ...
was Richard's cousin on the maternal side. During his youth his parents moved often, including to
Glatz, then to
Breslau and in 1905 to
Berlin
Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
. He stayed in Breslau and entered the
university
A university () is an educational institution, institution of tertiary education and research which awards academic degrees in several Discipline (academia), academic disciplines. ''University'' is derived from the Latin phrase , which roughly ...
there, then continued his studies at the
University of Zürich
The University of Zurich (UZH, ) is a public university, public research university in Zurich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 from the existing colleges of the ...
and the
University of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...
. He became
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time.
Hilbert discovered and developed a broad range of fundamental idea ...
's assistant in Göttingen and obtained his doctorate there in 1910. He was obliged to serve in
World War I
World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...
, but was wounded shortly after enlisting and therefore dismissed from the military. Courant left the
University of Münster
The University of Münster (, until 2023 , WWU) is a public research university located in the city of Münster, North Rhine-Westphalia in Germany.
With more than 43,000 students and over 120 fields of study in 15 departments, it is Germany's ...
in 1921 to take over
Erich Heckes position at the
University of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...
. There he founded the Mathematical Institute, which he headed as director from 1928 until 1933.
Courant left
Germany
Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...
in 1933, earlier than many
Jewish
Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of History of ancient Israel and Judah, ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, rel ...
escapees. He did not lose his position due to being Jewish, as his previous service as a front-line soldier exempted him; however, his public membership in the
social-democratic left was reason enough (for the Nazis) for dismissal.
In 1936, after one year at
Cambridge
Cambridge ( ) is a List of cities in the United Kingdom, city and non-metropolitan district in the county of Cambridgeshire, England. It is the county town of Cambridgeshire and is located on the River Cam, north of London. As of the 2021 Unit ...
, Courant accepted a professorship at
New York University
New York University (NYU) is a private university, private research university in New York City, New York, United States. Chartered in 1831 by the New York State Legislature, NYU was founded in 1832 by Albert Gallatin as a Nondenominational ...
in New York City. There he founded an institute for graduate studies in
applied mathematics
Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...
. The
Courant Institute of Mathematical Sciences (as it was renamed in 1964) is now one of the most respected research centers in applied mathematics.
Courant and
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time.
Hilbert discovered and developed a broad range of fundamental idea ...
authored the influential
textbook
A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions, but also of learners ( ...
''
Methoden der mathematischen Physik'', which, with its revised editions, is still current and widely used since its publication in 1924. With
Herbert Robbins he coauthored a popular overview of higher mathematics, intended for the general public, titled ''
What is Mathematics?''. With
Fritz John he also coauthored the two-volume work ''Introduction to Calculus and Analysis,'' first published in 1965.
Courant's name is also attached to the
finite element method
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat tran ...
,
with his numerical treatment of the plain torsion problem for multiply-connected domains, published in 1943.
This method is now one of the ways to solve
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
The function is often thought of as an "unknown" that solves the equation, similar to ho ...
s
numerically. Courant is a namesake of the
Courant–Friedrichs–Lewy condition and the
Courant minimax principle In mathematics, the Courant minimax principle gives the eigenvalues of a real symmetric matrix. It is named after Richard Courant.
Introduction
The Courant minimax principle gives a condition for finding the eigenvalues for a real symmetric matri ...
.
Courant was an elected member of both the
American Philosophical Society
The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...
(1953) and the United States
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...
(1955). In 1965, the
Mathematical Association of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university
A university () is an educational institution, institution of tertiary edu ...
recognized his contributions to Mathematics with their Award for Distinguished Service to Mathematics.
Courant died of a
stroke
Stroke is a medical condition in which poor cerebral circulation, blood flow to a part of the brain causes cell death. There are two main types of stroke: brain ischemia, ischemic, due to lack of blood flow, and intracranial hemorrhage, hemor ...
in
New Rochelle, New York
New Rochelle ( ; in ) is a Political subdivisions of New York State#City, city in Westchester County, New York, Westchester County, New York (state), New York, United States. It is a suburb of New York City, located approximately from Midtow ...
on January 27, 1972, aged 84.
Perspective on mathematics
Commenting upon his analysis of experimental results from in-laboratory soap film formations, Courant explained why the existence of a physical solution does not obviate
mathematical proof
A mathematical proof is a deductive reasoning, deductive Argument-deduction-proof distinctions, argument for a Proposition, mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use othe ...
. Here is a quote from Courant on his mathematical perspective:
Personal life
In 1912, Courant married
Nelly Neumann, who had earned her doctorate at Breslau in
synthetic geometry
Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulates ...
in 1909. They lived together in Göttingen until they were divorced in 1916. She was later murdered by the Nazis in 1942 for being Jewish.
In 1919, Courant married Nerina (Nina) Runge (1891–1991), a daughter of the Göttingen professor for Applied Mathematics,
Carl Runge (of
Runge–Kutta fame).
Richard and Nerina had four children:
Ernest
Ernest is a given name derived from the Germanic languages, Germanic word ''ernst'', meaning "serious", often shortened to Ernie.
Notable people and fictional characters with the name include:
People
*Archduke Ernest of Austria (1553–1595), ...
, a
particle physicist
Particle physics or high-energy physics is the study of fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the scale of protons and ...
and innovator in particle accelerators; Gertrude (1922–2014), a biologist and wife of the mathematician
Jürgen Moser (1928–1999);
Hans (1924-2019), a physicist who participated in the
Manhattan Project
The Manhattan Project was a research and development program undertaken during World War II to produce the first nuclear weapons. It was led by the United States in collaboration with the United Kingdom and Canada.
From 1942 to 1946, the ...
; and Leonore (known as "Lori," 1928–2015), a professional violist and wife of the mathematician Jerome Berkowitz (1928–1998) and subsequently wife of mathematician
Peter Lax until her death.
Publications
*
*
*
*
*
*
archive (translated from German: ''Methoden der mathematischen Physik I'', 2nd ed, 1931)
* (translated from German: ''Methoden der mathematischen Physik II'', 1937)
*
[
]
*
References
Sources
*
*
External links
*
*
Oral History interview transcript with Richard Courant on 9 May 1962, American Institute of Physics, Niels Bohr Library & ArchivesNational Academy of Sciences Biographical Memoir2015 Video Interview with Hans Courant by Atomic Heritage FoundationVoices of the Manhattan Project
US News Rankings of Applied Mathematics Programs
{{DEFAULTSORT:Courant, Richard
1888 births
1972 deaths
20th-century American mathematicians
20th-century German mathematicians
German military personnel of World War I
Mathematical analysts
Mathematics popularizers
Foreign members of the USSR Academy of Sciences
Jewish emigrants from Nazi Germany to the United States
Silesian Jews
University of Göttingen alumni
Academic staff of the University of Münster
Academics of the University of Cambridge
New York University faculty
People associated with the University of Zurich
University of Breslau alumni
People from the Province of Silesia
People from Lubliniec
Scientists from New Rochelle, New York
German textbook writers
Knights Commander of the Order of Merit of the Federal Republic of Germany
Fluid dynamicists
Mathematicians from New York (state)
Jewish scientists
Fellows of the American Physical Society
Members of the American Philosophical Society
American textbook writers