Knutson did his undergraduate studies at the California Institute of Technology, and received his Ph.D. in 1996 from the Massachusetts Institute of Technology under the joint advisorship of Victor Guillemin and Lisa Jeffrey. He was on the faculty at the University of California, Berkeley before moving to the University of California, San Diego in 2005–2008 and then to Cornell University in 2009. In 2005, he and Terence Tao won the Levi L. Conant Prize of the American Mathematical Society for their paper "Honeycombs and Sums of Hermitian Matrices".
- Faculty profile, Cornell University, accessed 2012-06-20.
- Donahue, Bill (December 2004), "The Mathematics of . . . Juggling: An algebra whiz reveals the secrets of keeping a lot of balls in the air", Discover.
- Allen Ivar Knutson at the Mathematics Genealogy Project
- Department history, UCSD mathematics department, accessed 2012-06-20.
- 2005 Conant Prize, AMS, accessed 2012-06-20.
- The mathematics of juggling one-hour YouTube lecture