[2] Gough was educated at Hackney Downs School before attending the University of Cambridge (St John's College) where he studied at the Department of Applied Mathematics and Theoretical Physics (DAMTP).
[9] In 1976, he and his PhD student Jørgen Christensen-Dalsgaard predicted that the global oscillation frequencies of the Sun could be used to infer its deep structure.
Gough and his students subsequently published extensively on the internal structure of the Sun and the calculation thereof, including determining features like the depth of the solar convection zone,[12] the Sun's interior rotation,[13] the protosolar helium abundance[14] and the main-sequence age.
[15] He pioneered seismological investigation into the equation of state in the Sun and the helium abundance in stellar convection zones.
[16][17] His doctoral students have included the Raja of Mahmudabad, Chris Jones, Douglas N. C. Lin, John Gribbin, Jørgen Christensen-Dalsgaard, Michael Thompson, Margarida Cunha, Marcus Brüggen and Pascale Garaud.