 His later research on gauge field theories, particularly Yang–Mills theory, stimulated important interactions between geometry and physics, most notably in the work of Edward Witten.Atiyah's students included 
Peter Braam 1987,
Simon Donaldson 1983,
K. David Elworthy 1967,
Howard Fegan 1977,
Eric Grunwald 1977,
Nigel Hitchin 1972,
Lisa Jeffrey 1991,
Frances Kirwan 1984,
Peter Kronheimer 1986,
Ruth Lawrence 1989,
George Lusztig 1971,
Jack Morava 1968,
Michael Murray 1983,
Peter Newstead 1966,
Ian R. Porteous 1961,
John Roe 1985,
Brian Sanderson 1963,
Rolph Schwarzenberger 1960,
Graeme Segal 1967,
David Tall 1966,
and Graham White 1982.Other contemporary mathematicians who influenced Atiyah include Roger Penrose, Lars Hörmander, Alain Connes and Jean-Michel Bismut.