Cook was born in Morgantown, West Virginia and grew up in Evanston, Illinois. His undergraduate studies were at the University of Illinois and the Budapest Semesters in Mathematics program. In the 1980s Cook qualified as a member of the six-person US team to the International Mathematical Olympiad. In 1990, Cook went to work for Wolfram Research, makers of the computer algebra system Mathematica. He did his doctoral work in Computation and Neural Systems at Caltech from 1999 to 2005. He is now at the Institute of Neuroinformatics at Zurich in Switzerland.
Work with Stephen Wolfram
In the 1990s Cook worked as a research assistant to Stephen Wolfram, assisting with work on Wolfram's book, A New Kind of Science. Among other things, he developed a proof showing that the Rule 110 cellular automaton is Turing-complete.
Cook presented his proof at the Santa Fe Institute conference CA98 before the publishing of Wolfram's book—an action that led Wolfram Research to accuse Cook of violating his NDA and resulted in the blocking of the publication of the proof in the conference proceedings.