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, classical and quantum mechanics, mathematical physics, 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 forms one of the two major directions of his current research work. The other is the study of wave localization in disordered media, a fascinating topic with numerous important applications, for example, to the design of more efficient, and so more sustainable, LED lighting. In 2017, Arnold and nine other scientists formed the international and interdisciplinary Simons Collaboration on Localization of Waves, supported by the Simons Foundation through 2025.

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. In 2001, he moved to University of Minnesota and assumed the position of Director of the renowned Institute for Mathematics and its Applications (IMA) in August 2001. In 2008, when he stepped down from the directorship, he was named McKnight Presidential Professor of Mathematics at University of Minnesota, where he remains today. Around the same time, he was also elected President of the Society for Industrial and Applied Mathematics (SIAM), the world's leading professional organization for applied mathematicians and computational scientists, serving in 2009 and 2010.

Arnold has written over 100 papers, several of which are among the most cited papers in mathematics according to MathSciNet. He is Editor-in-Chief of the prestigious review journal, Acta Numerica, serves on the editorial board of numerous journals, including Communications of the American Mathematical Society and Foundations of Computational Mathematics. Among his honors are:

  • Giovanni Sacchi Landriani Prize, awarded by the Instituto Lombardo, Milan, 1991.
  • Fellow of SIAM, AMS, AAAS.
  • Guggenheim Fellow, 2008-2009.
  • Plenary lecture at International Congress of Mathematicians, 2002.
  • Foreign member of the Norwegian Academy of Science and Letters, elected 2009.
  • AMS-MAA Invited Address, Joint Math Meetings, 2009.
  • NSF-CBMS Lecturer, 2012.
  • Overseas Fellow of Churchill College, Cambridge University, elected 2013.
  • SIAM Prize for Distinguished Service to the Profession, 2013.
  • J. Tinsley Oden Medal, awarded by the US Association of Computational Mechanics, 2015.
  • Plenary lecture at Joint Math Meetings, 2021.
  • Peter Henrici Prize awarded by ETH Zürich and SIAM, 2023.

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, ICERM at Brown University, the Fine Institute for Theoretical Physics at Minnesota, and the Erwin Schrödinger Institute in Vienna. 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 April 3, 2023