Michael Thompson graduated from the University of Cambridge in mechanical sciences in 1958. He holds two Cambridge doctorates, a PhD (1962) and an ScD (1977). He spent a year in the Department of Aeronautics and Astronautics at Stanford University before joining UCL in 1964, where he was appointed Professor (1977), then Director of the Centre for Nonlinear Dynamics (1991).

Based on his research into elastic buckling phenomena, he published three books on instabilities, bifurcations and catastrophes. A fourth book, introducing the new dynamics to applied scientists, is now in its second edition as Nonlinear Dynamics and Chaos (2002).

Michael was elected Fellow of the Royal Society in 1985. In 1992, he was awarded the Alfred Ewing Medal of the Institution of Civil Engineers. From 1998–2007, he was Editor of the journal Philosophical Transactions of the Royal Society A. In 2004, he was awarded a Gold Medal by the Institute of Mathematics and its Applications for lifetime contributions to mathematics.