[1] McIntosh studied at the University of New England with a bachelor's degree in 1962 (as a student he also received the University Medal ) and PhD in 1966 with Frantisek Wolf at the University of California, Berkeley, ( Representation of Accretive Bilinear Forms in Hilbert Space by Maximal Accretive Operator ).

McIntosh was involved in solving the Calderon conjecture in the theory of singular integral operators.

In 2002, he solved with Pascal Auscher, Michael T. Lacey, Philipp Tchamitchian and Steve Hofmann the open Kato root problem for elliptic differential operators.

He also deals with singular integral operators, boundary value problems of partial differential equations with applications (such as scattering theory of the Maxwell equations in irregular areas), spectral theory and functional calculus of operators in Banach spaces, analysis with Clifford algebras, barriers for the heat kernel equation and functional calculus for elliptic partial differential operators.

In 1986 he became a fellow of the Australian Academy of Science, whose Hannan Medal he received in 2015.