Douglas Norman "Doug" Arnold is a mathematician whose research focuses on the

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

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

s with applications in

mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects r ...

and other fields in physics. , he is McKnight Presidential Professor of Mathematics at 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 university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Tw ...

Biography

Arnold studied mathematics as an undergraduate at

Brown University Brown University is a private research university in Providence, Rhode Island. Brown is the seventh-oldest institution of higher education in the United States, founded in 1764 as the College in the English Colony of Rhode Island and Providenc ...

, gaining his B.A. in 1975. He continued his studies at the

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

, where he received a Ph.D. in 1979. He then moved to work at the

University of Maryland, College Park The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland. Founded in 1856, UMD is the flagship institution of the University System of Mary ...

. In 1989, he moved to

Penn State University The Pennsylvania State University (Penn State or PSU) is a public state-related land-grant research university with campuses and facilities throughout Pennsylvania. Founded in 1855 as the Farmers' High School of Pennsylvania, Penn State became ...

where he occupied a chair until 2002. He became director of the

Institute for Mathematics and its Applications The Institute for Mathematics and its Applications located at the University of Minnesota is an organization established in 1982 by the National Science Foundation (NSF) of the United States. Mission The primary mission of the IMA is to increase ...

(IMA) in Minnesota in 2001. At the end of his term as director of the IMA, he becomes the McKnight Presidential Professor of Mathematics at the University of Minnesota. He served as president of the

Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific socie ...

in 2009 and 2010. Arnold's research initially focused on the finite element method for the solution of problems in

elasticity Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the cl ...

. This expanded to take other applications into account, like the collision of

black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...

s. Especially well known is Arnold's development of the finite element exterior calculus, a discrete version of

exterior calculus In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, ...

that can be used to analyze the stability of finite element methods. This was the topic of the plenary lecture Arnold gave at the 2002

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

. Together with a colleague (Jonathan Rogness), Arnold produced a video explaining

Möbius transformation In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form f(z) = \frac of one complex variable ''z''; here the coefficients ''a'', ''b'', ''c'', ''d'' are complex numbers satisfying ''ad'' ...

s which won an honorable mention in a contest sponsored by Science magazine and the

National Science Foundation The National Science Foundation (NSF) is an independent agency of the United States government that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National I ...

in 2007. The video was watched over a million times at

YouTube YouTube is a global online video platform, online video sharing and social media, social media platform headquartered in San Bruno, California. It was launched on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim. It is owned by ...

. Other honors include winning the International Giovanni Sacchi Landriani Prize in 1991, the award of a

Guggenheim Fellowship Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

in 2008 and election as a foreign member of the

Norwegian Academy of Science and Letters The Norwegian Academy of Science and Letters ( no, Det Norske Videnskaps-Akademi, DNVA) is a learned society based in Oslo, Norway. Its purpose is to support the advancement of science and scholarship in Norway. History The Royal Frederick Univer ...

in 2009. In 2012 he became a fellow of 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, ...

. In 2009, he was named a fellow of the

.SIAM Fellows
/ref> Arnold is married to

Maria-Carme Calderer Maria-Carme T. Calderer (Berga, 1951) is a professor of mathematics at University of Minnesota. Her research concerns applied mathematics. Career Calderer received her Ph.D. from Heriot-Watt University in 1980. She was a postdoctoral researcher ...

, a professor of mathematics at

References

External links

Home page at the University of Minnesota
* {{DEFAULTSORT:Arnold, Douglas Norman 20th-century American mathematicians 21st-century American mathematicians Numerical analysts Fellows of the American Mathematical Society Fellows of the Society for Industrial and Applied Mathematics Living people Members of the Norwegian Academy of Science and Letters Presidents of the Society for Industrial and Applied Mathematics Year of birth missing (living people) Brown University alumni University of Chicago alumni