Terence John Lyons FRSE FRS FLSW is a British mathematician, specialising in stochastic analysis.

[5] Together with Patrick Kidger he proved a universal approximation theorem for neural networks of arbitrary depth.

[7] He was the Director of the Oxford-Man Institute at the University of Oxford from 15 June 2011 to 15 December 2015.

He also held a number of visiting positions in Europe and North America.

Together with Zhongmin Qian he wrote the monograph System Control and Rough Paths,[8] and together with Michael J. Caruana and Thierry Lévy the book Differential Equations Driven by Rough Paths.