A North Carolina native, Robert Bryant received his PhD in mathematics in 1979 at the University of North Carolina at Chapel Hill, working under Robert B. Gardner. After serving on the faculty at Rice University for seven years, he moved to Duke University in 1987, where he held the Juanita M. Kreps Chair in Mathematics until moving to the University of California at Berkeley in July 2007. He has held numerous visiting positions at universities and research institutes around the world. He visited MSRI during the 2001–02 academic year as a Clay Mathematics Visiting Professor, and he was in residence at MSRI during the Fall 2003 term as a co-organizer of the program in Differential Geometry.

His research interests center on exterior differential systems and the geometry of differential equations as well as their applications to Riemannian geometry, special holonomy, and mathematical physics. In addition to his teaching and research in differential geometry, he served as the Program Chair of the Northern California, Nevada, and Hawaii Section of the Mathematical Association of America, 2008-2011. He currently serves on the editorial boards of the Duke Mathematical Journal, Communications in Analysis and Geometry, and the Journal of the AMS.

He has served as the director of the Park City/IAS Mathematics Institute, as a Vice President of the American Mathematical Society, and on the Board of Directors of the Vietnam Education Foundation. He currently serves on the International Committee for the National Mathematics Center of Nigeria, on the Board of Directors of the Banff International Research Station, and as an ‘external member’ of the Conseil d’Administration de l’Institut Henri Poincaré. He served on the Board of Trustees of the MSRI beginning in 1999, becoming the Chair of the Board in 2001 and serving in that capacity until the end of his term in 2004. He became the fifth Director of MSRI on August 1, 2007 and served in that capacity for 6 years, until July 31, 2013, when he returned to Duke University as Professor.

He is a fellow of the American Academy of Arts and Sciences and of the American Mathematical Society and a member of the National Academy of Sciences.