Douglas N. Arnold

photo of D. Arnold

Douglas N. Arnold is the McKnight Presidential Professor of Mathematics at the University of Minnesota. He is a research mathematician and educator specializing in computational mathematics. He also has a strong interest in mathematics in interdisciplinary research and in the public understanding of the role of mathematics.

Prof. Arnold's research interests include numerical analysis, partial differential equations, mechanics, and in particular, the interplay between these fields. Much of his work concerns the computer solution of partial differential equations, focusing on the development and understanding of methods for simulating physical phenomena ranging from the deformation of elastic plates and shells to the collision of black holes. Around 2002 he initiated the finite element exterior calculus, a new approach to the stability of finite element methods based on geometric and topological structure underlying the relevant partial differential equations. The development and applications of the finite element exterior calculus remains a major direction of his current research work.

From 2001 through 2008, Prof. Arnold served as director of the Institute for Mathematics and its Applications (IMA). Under Arnold's leadership this indisciplinary mathematical research institute grew to be the largest mathematics research investment in the history of the National Science Foundation. In 2009 and 2010, Arnold served as President of the Society for Industrial and Applied Mathematics, the world's leading professional organization for applied mathematicians and computational scientists.

Prof. Arnold received his Ph.D. degree in Mathematics from the University of Chicago in 1979. From 1979 through 1989 he was on the faculty of the University of Maryland. In 1989 he moved to Penn State University where he was appointed Distinguished Professor Mathematics, and where he remained until moving to University of Minnesota and assuming the position of Director at the Institute for Mathematics and its Applications in August 2001.

Arnold has written about 100 papers and serves as Editor-in-Chief or on the editorial boards of numerous journals. Several of his journal articles are among the most cited in mathematics according to MathSciNet and he was designated a highly cited research by Thomson Reuters both times they released such a list, in 2001 and 2014. (Nonetheless, Arnold is highly critical of such shallow bibliometrics, and cautions against their misuse.) In 1991 he was awarded the first International Giovanni Sacchi Landriani Prize by the Lombardy Institute Academy of Arts and Letters in 1991 for "outstanding contributions to the field of numerical methods for partial differential equations." He is highly sought after as a speaker and has delivered plenary lectures at the International Congress of Mathematicians in 2002 and the Joint Mathematics Meetings in 2009, as well as an NSF-CBMS Lecture Series in 2012. In 2008 he was awarded a Guggenheim Fellowship, and, in 2009, was elected a foreign member of the Norwegian Academy of Science and Letters. In the same year he was appointed a SIAM Fellow for his "contributions to finite elements and the numerical analysis of partial differential equations." In 2011 he was elected a Fellow of the American Association for the Advancement of Science (AAAS), and in 2012 he was appointed a Fellow of the American Mathematical Society (AMS). In 2013 he was the recipient of the SIAM Prize for Distinguished Service to the Profession., and in 2015 the US Association for Computational Mechanics awarded him its J. Tinsley Oden Medal.

Arnold serves or has served on a variety of advisory and scientific boards, including the Board of Mathematical Sciences and Applications of the National Research Council, the U.S. National Committee for Mathematics, the Mathematical and Physical Sciences Advisory Committee of the National Science Foundation, the Program Committees for both the International Congress of Mathematicians and the International Congress of Industrial and Applied Mathematics, and the scientific boards of research institutes around the world, including DIMACS, the Centre of Mathematics for Applications in Oslo, the Maxwell Institute for Mathematical Sciences in Edinburgh, and the IMS in Singapore, and ICERM at Brown University.. At Penn State he was awarded the George W. Atherton Award for Excellence in Teaching by the University in 1996, the Teresa Cohen Service Award by the Mathematics Department in 1998, and the Distinguished Service Award by the Eberly College of Science in 2000.

Among Arnold's priorities are efforts to increase public understanding of mathematics and its role in society, and he is frequently cited in print and broadcast media. In 2007 he coauthored an award winning video, Möbius Transformations Revealed, which went viral on YouTube, garnering about two million views.

Updated October 30, 2014