[3] He obtained his Doctor of Philosophy from Princeton University in 1966 with his thesis, Triangulating homotopy equivalences, under the supervision of William Browder.

[7][9] In 1981, he became the Albert Einstein Chair in Science (Mathematics) at the Graduate Center of the City University of New York[10] and reduced his duties at the IHÉS to a half-time appointment.

[11] Along with Browder and his other students, Sullivan was an early adopter of surgery theory, particularly for classifying high-dimensional manifolds.

[2] In an influential set of notes in 1970, Sullivan put forward the radical concept that, within homotopy theory, spaces could directly "be broken into boxes"[12] (or localized), a procedure hitherto applied to the algebraic constructs made from them.

[20][21] In 1987, Sullivan and Burton Rodin proved Thurston's conjecture about the approximation of the Riemann map by circle packings.

[22] Sullivan and Moira Chas started the field of string topology, which examines algebraic structures on the homology of free loop spaces.

[25] In 1975, Sullivan and Bill Parry introduced the topological Parry–Sullivan invariant for flows in one-dimensional dynamical systems.