John Guckenheimer worked at the University of California at Santa Cruz before joining the Cornell University Department of Mathematics in 1985 and was later appointed the Abram R. Bullis Professor of Mathematics. He also served as Associate Dean for Scientific Computing in the Department of Computing and Information Science. He was elected President of the Society for Industrial and Applied Mathematics. He was a Guggenheim and American Mathematical Society fellow and a Leroy P. Steele Prize winner. His research areas included neuroscience, algorithms for periodic orbits, and dynamics in systems with multiple time scales.