John Frank Adams FRS[2] (5 November 1930 – 7 January 1989) was a British mathematician, one of the major contributors to homotopy theory.

Adams made a number of important theoretical advances in algebraic topology, but his innovations were always motivated by specific problems.

He used this spectral sequence to attack the celebrated Hopf invariant one problem, which he completely solved in a 1960 paper by making a deep analysis of secondary cohomology operations.

Subsequently he used them to investigate the Adams conjecture, which is concerned (in one instance) with the image of the J-homomorphism in the stable homotopy groups of spheres.

The main mathematics research seminar room in the Alan Turing Building at the University of Manchester is named in his honour.