Burkholder spent most of his professional career as a professor in the Department of Mathematics of the University of Illinois at Urbana-Champaign.
After his retirement in 1998, Donald Burkholder remained a professor emeritus in the Department of Mathematics of the University of Illinois at Urbana-Champaign and a CAS Professor Emeritus of Mathematics at the Center for Advanced Study, University of Illinois at Urbana-Champaign.
[2] Burkholder received a PhD in statistics in 1955 from the University of North Carolina at Chapel Hill, under the direction of Wassily Hoeffding.
[3] He was appointed an assistant professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign in 1955[4] where he remained until his retirement in 1998.
"[11][12] In 2009 Burkholder was named a SIAM Fellow by the Society for Industrial and Applied Mathematics "for advances in martingale transforms and applications of probabilistic methods in analysis".