Frank Adams FRS
Adams (right) with Dieter Puppe in 1962
Born	(1930-11-05)5 November 1930 Woolwich, London, United Kingdom
Died	7 January 1989(1989-01-07) (aged 58) Brampton, Cambridgeshire, United Kingdom
Alma mater	University of Cambridge
Known for	Adams spectral sequence Adams operations Adams conjecture
Awards	Berwick Prize (1963) Senior Whitehead Prize (1974) Sylvester Medal (1982)
Scientific career
Fields	Mathematics
Institutions	University of Cambridge
Thesis	On Spectral Sequences and Self-Obstruction Invariants (1956)
Doctoral advisor	Shaun Wylie
Doctoral students	Béla Bollobás Peter Johnstone Andrew Ranicki C. T. C. Wall Lam Siu-por[1]

John Frank AdamsFRS^[2] (5 November 1930 – 7 January 1989) was a British mathematician, one of the major contributors tohomotopy theory.^[3][4][5]

He was born inWoolwich, a suburb in south-east London, and attendedBedford School. He had a younger brother,Michael Adams, who rose to the rank of Air Vice-Marshal in the Royal Air Force. He began his academic career atTrinity College, Cambridge, as a student ofAbram Besicovitch, but soon switched toalgebraic topology. He received hisPhD from theUniversity of Cambridge in 1956. His thesis, written under the direction ofShaun Wylie, was titledOn spectral sequences and self-obstruction invariants. He held theFielden Chair at theUniversity of Manchester (1964–1970), and becameLowndean Professor of Astronomy and Geometry at the University of Cambridge (1970–1989). He was elected a Fellow of theRoyal Society in 1964.

His interests includedmountaineering—he would demonstrate how to climb right round a table at parties (aWhitney traverse)—and the game ofGo.

He died in a car crash inBrampton. There is a memorial plaque for him in the Chapel ofTrinity College, Cambridge.

In the 1950s,homotopy theory was at an early stage of development, and unsolved problems abounded. Adams made a number of important theoretical advances inalgebraic topology, but his innovations were always motivated by specific problems. Influenced by the French school ofHenri Cartan andJean-Pierre Serre, he reformulated and strengthened their method ofkilling homotopy groups inspectral sequence terms, creating the basic tool ofstable homotopy theory now known as theAdams spectral sequence. This begins withExt groups calculated over the ring ofcohomology operations, which is theSteenrod algebra in the classical case. He used thisspectral sequence to attack the celebratedHopf invariant one problem, which he completely solved in a 1960 paper by making a deep analysis ofsecondary cohomology operations. TheAdams–Novikov spectral sequence is an analogue of the Adams spectral sequence using anextraordinary cohomology theory in place of classical cohomology: it is a computational tool of great potential scope.

Adams was also a pioneer in the application ofK-theory. He invented theAdams operations in K-theory, which are derived from theexterior powers; they are now also widely used in purely algebraic contexts. Adams introduced them in a 1962 paper to solve the famousvector fields on spheres problem. Subsequently he used them to investigate theAdams conjecture, which is concerned (in one instance) with the image of theJ-homomorphism in the stablehomotopy groups of spheres. A later paper of Adams andMichael F. Atiyah uses the Adams operations to give an extremely elegant and much faster version of the above-mentionedHopf invariant one result.

In 1974 Adams became the first recipient of theSenior Whitehead Prize, awarded by theLondon Mathematical Society.^[6] He was a visiting scholar at theInstitute for Advanced Study in 1957–58.^[7]

Adams had many talented students, and was highly influential in the development ofalgebraic topology in Britain and worldwide. HisUniversity of Chicago lectures were published in a 1996 series titled "Chicago Lectures in Mathematics Series", such asLectures on Exceptional Lie Groups andStable Homotopy and Generalised HomologyISBN 0-226-00524-0 .

The main mathematics research seminar room in theAlan Turing Building at theUniversity of Manchester is named in his honour.

• Adams filtration

• Adams, J. Frank (1992),May, J. Peter; Thomas, Charles B. (eds.),The selected works of J. Frank Adams. Vol. I, Cambridge University Press,ISBN 0-521-41063-0,MR 1203312
• Adams, J. Frank (1992),May, J. Peter; Thomas, Charles B. (eds.),The selected works of J. Frank Adams. Vol. II, Cambridge University Press,ISBN 978-0-521-11068-6,MR 1203312

• Frank Adams atFind a Grave

• 1930 births
• 1989 deaths
• Mathematicians from London
• 20th-century British mathematicians
• English mathematicians
• British topologists
• Academics of the Victoria University of Manchester
• Academics of the University of Cambridge
• Road incident deaths in England
• People educated at Bedford School
• Alumni of Trinity College, Cambridge
• Fellows of Trinity College, Cambridge
• Fellows of the Royal Society
• Foreign associates of the National Academy of Sciences
• Lowndean Professors of Astronomy and Geometry
• Institute for Advanced Study visiting scholars
• Homotopy theory
• People from Woolwich

• Articles with short description
• Short description matches Wikidata
• Use British English from February 2023
• Use dmy dates from August 2014
• Articles with hCards