His 1981 dissertation demonstrated for the first time the theoretical reason for the clearing of the Kirkwood gaps in the asteroid belt.
Work with colleague Gerald Sussman using a specially-built computer demonstrated that the solar system as a whole is chaotic on a timescale of about four million years,[9] confirming results from Jacques Laskar.
"[5] More recently, Wisdom's work has shed light on the complex evolution of the Moon[11][12] and the tidal heating and dynamics of Enceladus.
[13][14] In addition, Wisdom is credited with developing "numerous analytical and numerical techniques" that are fundamental to modern celestial mechanics,[5] most notably the symplectic map for the n-body problem (developed together with Matthew J. Holman),[15] which "now forms the core of nearly every solar system dynamics integration scheme in use today.
His 2003 paper in Science[16] on a new geometric phase effect which Wisdom calls "spacetime swimming" has attracted considerable attention, although it is not yet clear whether this effect has practical utility or even can be used to devise new tests of relativistic gravitation theories.