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{{Short description|British mathematician (1930–1989)}}
{{Other people}}
{{Use British English|date=February 2023}}
{{Use dmy dates|date=August 2014}}
{{Infobox scientist
| name              = Frank Adams
| honorific_suffix  = {{post-nominals|country=GBR|size=100%|FRS}}
| image             = Puppe Adams.jpg
| image_size        = 170px
| caption           = Adams (right) with Dieter Puppe in 1962
| birth_date        = {{Birth date|df=y|1930|11|5}}
| birth_place       = [[Woolwich]], London, United Kingdom
| death_date        = {{Death date and age|df=y|1989|1|7|1930|11|5}}
| death_place       = [[Brampton, Cambridgeshire]], United Kingdom
| fields            = Mathematics
| workplaces        = University of Cambridge
| alma_mater        = [[University of Cambridge]]
| doctoral_advisor  = [[Shaun Wylie]]
|thesis_title = On Spectral Sequences and Self-Obstruction Invariants
| thesis_url = http://www.worldcat.org/oclc/879389258
| thesis_year = 1956
| doctoral_students = [[Béla Bollobás]]<br />[[Peter Johnstone (mathematician)|Peter Johnstone]]<br />[[Andrew Ranicki]]<br />[[C. T. C. Wall]]<br>[[Lam Siu-por]]<ref name="mathgene">{{MathGenealogy |id=24507}}</ref>
| known_for         = [[Adams spectral sequence]]<br>[[Adams operation]]s<br>[[Adams conjecture]]
| awards            = [[Berwick Prize]] (1963)<br>[[Senior Whitehead Prize]] (1974)<br>[[Sylvester Medal]] (1982)
}}
'''John Frank Adams''' {{post-nominals|country=GBR|size=100%|FRS}}<ref name="frs">{{Cite journal | last = James | first = Ioan M. | author-link = Ioan James| doi = 10.1098/rsbm.1990.0021 | title = Frank Adams. 5 November 1930-7 January 1989 | journal = [[Biographical Memoirs of Fellows of the Royal Society]] | volume = 36 | pages = 2–16| year = 1990 | jstor = 770077| title-link = John Frank Adams | doi-access = free }}</ref> (5 November 1930 – 7 January 1989) was a British mathematician, one of the major contributors to [[homotopy theory]].<ref>{{Cite book | editor1-last = Ray | editor1-first = Nigel | editor2-first = Grant | doi = 10.1017/CBO9780511526305.003 | chapter = The work of J. F. Adams | title = Adams Memorial Symposium on Algebraic Topology | volume = 1 | pages = 1–28 | year = 1992 | isbn = 9780511526305 | editor2-last = Walker }}</ref><ref>{{Cite journal | last1 = James | first1 = Ioan M. | author-link1 = Ioan James | last2 = Wall | first2 = C. T. C. | author-link2 = C. T. C. Wall| doi = 10.1112/S0024609397002968 | title = John Frank Adams | journal = [[Bulletin of the London Mathematical Society]] | volume = 29 | issue = 4 | pages = 489 | year = 1997 | doi-access = free }}</ref><ref>{{MacTutor Biography|id=Adams_Frank}}</ref>

==Life==
He was born in [[Woolwich]], a suburb in south-east London, and attended [[Bedford School]]. He had a younger brother, [[Michael Adams (RAF officer)|Michael Adams]], who rose to the rank of Air Vice-Marshal in the Royal Air Force. He began his academic career at [[Trinity College, Cambridge]], as a student of [[Abram Samoilovitch Besicovitch|Abram Besicovitch]], but soon switched to [[algebraic topology]]. He received his [[PhD]] from the [[University of Cambridge]] in 1956.  His thesis, written under the direction of [[Shaun Wylie]], was titled ''On spectral sequences and self-obstruction invariants''. He held the [[Fielden Chair of Pure Mathematics|Fielden Chair]] at the [[University of Manchester]] (1964–1970), and became [[Lowndean Professor of Astronomy and Geometry]] at the University of Cambridge (1970–1989). He was elected a Fellow of the [[Royal Society]] in 1964.

His interests included [[mountaineering]]—he would demonstrate how to climb right round a table at parties (a [[Hassler Whitney|Whitney]] traverse)—and the game of [[go (game)|Go]].

He died in a car crash in [[Brampton, Cambridgeshire|Brampton]].  There is a memorial plaque for him in the Chapel of [[Trinity College, Cambridge]].

==Work==
In the 1950s, [[homotopy theory]] was at an early stage of development, and unsolved problems abounded.  Adams made a number of important theoretical advances in [[algebraic topology]], but his innovations were always motivated by specific problems.  Influenced by the French school of [[Henri Cartan]] and [[Jean-Pierre Serre]], he reformulated and strengthened their method of [[Homotopy groups of spheres|killing homotopy groups]] in [[spectral sequence]] terms, creating the basic tool of [[stable homotopy theory]] now known as the [[Adams spectral sequence]]. This begins with [[Ext group]]s calculated over the ring of [[cohomology operation]]s, which is the [[Steenrod algebra]] in the classical case. 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 operation]]s.  The [[Adams–Novikov spectral sequence]] is an analogue of the Adams spectral sequence using an [[extraordinary cohomology theory]] in place of classical cohomology: it is a computational tool of great potential scope.

Adams was also a pioneer in the application of [[K-theory]]. He invented the [[Adams operation]]s in K-theory, which are derived from the [[exterior power]]s; they are now also widely used in purely algebraic contexts.  Adams introduced them in a 1962 paper to solve the famous [[vector fields on spheres]] problem. 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]]. A later paper of Adams and [[Michael Atiyah|Michael F. Atiyah]] uses the Adams operations to give an extremely elegant and much faster version of the above-mentioned [[Hopf invariant one]] result.

In 1974 Adams became the first recipient of the [[Senior Whitehead Prize]], awarded by the [[London Mathematical Society]].<ref>{{cite web
|url = http://www.lms.ac.uk/activities/prizes_com/pastwinners.html#swhitehead
|title = List of Prizewinners
|author = London Mathematical Society
|access-date = 8 July 2007
|archive-date = 15 April 2009
|archive-url = https://web.archive.org/web/20090415002741/http://www.lms.ac.uk/activities/prizes_com/pastwinners.html#swhitehead
|url-status = dead
}}</ref> He was a visiting scholar at the [[Institute for Advanced Study]] in 1957–58.<ref>[http://www.ias.edu/people/cos/ Institute for Advanced Study: A Community of Scholars]</ref>

Adams had many talented students, and was highly influential in the development of [[algebraic topology]] in Britain and worldwide. His [[University of Chicago]] lectures were published in a 1996 series titled "Chicago Lectures in Mathematics Series", such as ''Lectures on Exceptional Lie Groups'' and ''Stable Homotopy and Generalised Homology'' {{ISBN|0-226-00524-0}} .

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

==See also==
*[[Adams filtration]]

==References==
{{reflist}}

==Publications==
*{{citation | last=Adams |first= J. Frank |title=The selected works of J. Frank Adams. Vol. I| url=https://books.google.com/books?id=EaMrGEsf4XgC | publisher=Cambridge University Press |year=1992| isbn=0-521-41063-0 |mr=1203312 |editor-first=J. Peter |editor-last=May |editor-link=J. Peter May |editor2-first= Charles B. |editor2-last=Thomas}}
*{{citation | last=Adams |first= J. Frank |title=The selected works of J. Frank Adams. Vol. II| url=https://books.google.com/books?id=1AlcPgAACAAJ | publisher=Cambridge University Press |year=1992| isbn=978-0-521-11068-6 |mr=1203312 |editor-first=J. Peter |editor-last=May |editor-link=J. Peter May | editor2-first= Charles B. |editor2-last=Thomas}}

==External links==
*{{Find a Grave|21648}}

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