View source for Simon Donaldson

{{Short description|English mathematician (born 1957)}}
{{BLP sources|date=February 2013}}
{{Use dmy dates|date=May 2021}}
{{use British English|date=May 2012}}

{{Infobox scientist
| honorific_prefix  = [[Sir]]
| honorific_suffix  = {{postnominal|country=GBR|FRS|MAE}}
| name              = Simon Donaldson
| birth_name        = Simon Kirwan Donaldson
| image             = Simon Donaldson.jpg
| caption           = Donaldson in 2009
| image_size        = 
| birth_date        = {{Birth date and age|1957|8|20|df=y}}
| birth_place       = [[Cambridge]], England
| death_date        = 
| death_place       = 
| nationality       = British
| field             = [[Topology]]
| work_institutions = [[Imperial College London]]<br />[[Stony Brook University]]<br />[[Institute for Advanced Study]]<br />[[Stanford University]]<br />[[University of Oxford]]
| alma_mater        = [[Pembroke College, Cambridge]] ([[Bachelor of Arts|BA]])<br />[[Worcester College, Oxford]] ([[DPhil]])
| doctoral_advisor  = [[Michael Atiyah]]<br />[[Nigel Hitchin]]
| doctoral_students = [[Oscar Garcia Prada]]<br />[[Dominic Joyce]]<br />[[Dieter Kotschick]]<br />[[Graham Nelson]]<br />[[Paul Seidel]]<br />[[Ivan Smith (mathematician)|Ivan Smith]]<br />[[Gábor Székelyhidi]]<br />[[Richard Thomas (mathematician)|Richard Thomas]]<br />[[Michael Thaddeus]]
| thesis_title      = The Yang–Mills Equations on Kähler Manifolds
| thesis_year       = 1983
| thesis_url        = https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.345427
| known_for         = [[Topology]] of smooth (differentiable) four-dimensional [[manifold]]s<br />[[Donaldson theory]]<br />[[Donaldson theorem]]<br />[[Donaldson–Thomas theory]]<br />[[Kobayashi–Hitchin correspondence|Donaldson–Uhlenbeck–Yau theorem]]<br />[[K-stability]]<br />[[K-stability of Fano varieties]]<br />[[K-stability#Yau–Tian–Donaldson Conjecture|Yau–Tian–Donaldson conjecture]]
| awards            = [[Junior Whitehead Prize]] (1985)<br />[[Fields Medal]] (1986)<br />[[Royal Medal]] (1992)<br />[[Crafoord Prize]] (1994)<br />[[Pólya Prize (LMS)|Pólya Prize]] (1999)<br />[[King Faisal International Prize]] (2006)<br />[[Nemmers Prize in Mathematics]] (2008)<br />[[Shaw Prize]] in Mathematics (2009)<br /> [[Breakthrough Prize in Mathematics]] (2014)<br />[[Oswald Veblen Prize]] (2019)<br />[[Wolf Prize in Mathematics]] (2020)
}}

'''Sir Simon Kirwan Donaldson''' {{postnominal|country=GBR|FRS|MAE}} (born 20 August 1957) is an English mathematician known for his work on the [[topology]] of [[smooth function|smooth]] (differentiable) four-dimensional [[manifold]]s, [[Donaldson–Thomas theory]], and his contributions to [[Kähler geometry]]. He is currently a permanent member of the [[Simons Center for Geometry and Physics]] at [[Stony Brook University]] in New York,<ref name="scgp.stonybrook.edu">{{cite web |url = http://scgp.stonybrook.edu/people/faculty/bios/simon-donaldson |title=Simon Donaldson, Simons Center for Geometry and Physics }}</ref> and a Professor in Pure Mathematics at [[Imperial College London]].

== Biography ==
Donaldson's father was an electrical engineer in the physiology department at the [[University of Cambridge]], and his mother earned a science degree there.<ref>[http://www.shawprize.org/en/shaw.php?tmp=3&twoid=12&threeid=41&fourid=22&fiveid=11 Simon Donaldson Autobiography, The Shaw Prize, 2009]</ref> Donaldson gained a [[Bachelor of Arts|BA]] degree in mathematics from [[Pembroke College, Cambridge]], in 1979, and in 1980 began postgraduate work at [[Worcester College, Oxford]], at first under [[Nigel Hitchin]] and later under [[Michael Atiyah]]'s supervision. Still a postgraduate student, Donaldson proved in 1982 a result that would establish his fame. He published the result in a paper "Self-dual connections and the topology of smooth 4-manifolds" which appeared in 1983. In the words of Atiyah, the paper "stunned the mathematical world."<ref name="Atiyah 1986">{{cite journal |last=Atiyah |first=M. |author-link = Michael Atiyah |name-list-style=amp |title = On the work of Simon Donaldson |journal =[[Proceedings of the International Congress of Mathematicians]] |year=1986 }}</ref>

Whereas [[Michael Freedman]] classified topological four-manifolds, Donaldson's work focused on four-manifolds admitting a [[differentiable structure]], using [[instantons]], a particular solution to the equations of [[Yang–Mills]] [[gauge theory]] which has its origin in [[quantum field theory]]. One of Donaldson's first results gave severe restrictions on the [[Intersection form (4-manifold)|intersection form]] of a smooth four-manifold. As a consequence, a large class of the topological four-manifolds do not admit any [[smooth structure]] at all. Donaldson also derived polynomial invariants from [[gauge theory]]. These were new topological invariants sensitive to the underlying smooth structure of the four-manifold. They made it possible to deduce the existence of "exotic" smooth structures—certain topological four-manifolds could carry an infinite family of different smooth structures.

After gaining his [[Doctor of Philosophy|DPhil]] degree from [[Oxford University]] in 1983, Donaldson was appointed a Junior Research Fellow at [[All Souls College, Oxford]]. He spent the academic year 1983–84 at the [[Institute for Advanced Study]] in [[Princeton, New Jersey|Princeton]], and returned to [[Oxford University|Oxford]] as [[Wallis Professor of Mathematics]] in 1985. After spending one year visiting [[Stanford University]],<ref>[http://www.debretts.com/people/biographies/browse/d/1854/Simon+Kirwan.aspx Biography at DeBretts] {{webarchive|url=https://web.archive.org/web/20130620191352/http://www.debretts.com/people/biographies/browse/d/1854/Simon+Kirwan.aspx |date=20 June 2013 }}</ref> he moved to [[Imperial College London]] in 1998 as Professor of Pure Mathematics.<ref>[https://www.ukwhoswho.com/view/10.1093/ww/9780199540884.001.0001/ww-9780199540884-e-13910 "Donaldson, Sir Simon (Kirwan)"], ''[[Who's Who (UK)|Who's Who]]'' (online ed., [[Oxford University Press]], December 2018). Retrieved 2 June 2019.</ref>

In 2014, he joined the [[Simons Center for Geometry and Physics]] at [[Stony Brook University]] in New York, United States.<ref name="scgp.stonybrook.edu"/>

==Awards==
Donaldson was an invited speaker of the [[International Congress of Mathematicians]] (ICM) in 1983,<ref name="International Mathematical Union (IMU)">{{cite web | title=ICM Plenary and Invited Speakers | website=International Mathematical Union (IMU) | url=https://www.mathunion.org/icm-plenary-and-invited-speakers?combine=Donaldson | access-date=2022-09-03}}</ref> and a plenary speaker at the ICM in 1986,<ref>{{cite book|author=Donaldson, Simon K|chapter=The geometry of 4-manifolds|title=Proceedings of the International Congress of Mathematicians (Berkeley 1986)|editor=AM Gleason|volume=1|pages=43–54|year=1986|citeseerx=10.1.1.641.1867}}</ref> 1998,<ref>{{cite book|author=Donaldson, S. K.|chapter=Lefschetz fibrations in symplectic geometry|title=Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II|year=1998|pages=309–314|chapter-url=https://www.elibm.org/ft/10011708000}}</ref> and 2018.<ref>{{cite web|url=https://www.mathunion.org/icm-plenary-and-invited-speakers?combine=Donaldson|title=ICM Plenary and Invited Speakers, International Mathematical Union (IMU)|website=mathunion.org}}</ref>

In 1985, Donaldson received the [[Junior Whitehead Prize]] from the [[London Mathematical Society]]. In 1994, he was awarded the [[Crafoord Prize]] in Mathematics. In February 2006, Donaldson was awarded the [[King Faisal International Prize]] for science for his work in pure mathematical theories linked to physics, which have helped in forming an understanding of the laws of matter at a subnuclear level. In April 2008, he was awarded the [[Nemmers Prize in Mathematics]], a mathematics prize awarded by [[Northwestern University]].

In 2009, he was awarded the [[Shaw Prize]] in Mathematics (jointly with [[Clifford Taubes]]) for their contributions to geometry in 3 and 4 dimensions.<ref name="The Shaw Prize 2009">{{cite web |title=The Shaw Prize|website=shawprize.org |date=16 June 2009 |url=http://www.shawprize.org/laureates/mathematical-sciences/2009 }}</ref>

In 2014, he was awarded the [[Breakthrough Prize in Mathematics]] "for the new revolutionary invariants of 4-dimensional manifolds and for the study of the relation between stability in algebraic geometry and in global differential geometry, both for bundles and for Fano varieties."<ref>{{cite web |url=https://breakthroughprize.org/News/18 |title= Five Winners Receive Inaugural Breakthrough Prize in Mathematics|website=breakthroughprize.org |date=23 June 2014 |access-date=21 May 2022}}</ref>

In January 2019, he was awarded the [[Oswald Veblen Prize in Geometry]] (jointly with [[Xiuxiong Chen]] and [[Song Sun]]).<ref name=veblen /> In 2020 he received the [[Wolf Prize in Mathematics]] (jointly with [[Yakov Eliashberg]]).<ref>[https://wolffund.org.il/the-wolf-prize/#Laureates Wolf Prize 2020], wolffund.org.il. Accessed 8 January 2023.</ref>

In 1986, he was elected a [[Fellow of the Royal Society]] (FRS) and received a [[Fields Medal]] at the [[International Congress of Mathematicians]] (ICM) in Berkeley. He became a [[Member of the Academia Europaea]] (MAE) in 1993.<ref>[https://www.ae-info.org/ae/Member/Donaldson_Simon Member: Simon Donaldson] - website [[Academia Europaea]]</ref> In 2010, Donaldson was elected a foreign member of the [[Royal Swedish Academy of Sciences]].<ref name="kva">[http://www.kva.se/en/News/2010/New-foreign-members-elected-to-the-academy/ New foreign members elected to the academy], press announcement from the Royal Swedish Academy of Sciences, 26 May 2010.</ref>

He was [[Knight Bachelor|knighted]] in the 2012 [[New Year Honours]] for services to mathematics.<ref>{{London Gazette |issue=60009 |date=31 December 2011 |page=1 |supp=y}}</ref> In 2012, he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society]. Retrieved 10 November 2012.</ref>

In March 2014, he was awarded the degree "Docteur Honoris Causa" by [[Université Joseph Fourier, Grenoble]]. In January 2017, he was awarded the degree "Doctor Honoris Causa" by the Universidad Complutense de Madrid, Spain.<ref>{{Cite web |title=Doctores "Honoris Causa" {{!}} Facultad de Ciencias Matemáticas |url=https://matematicas.ucm.es/doctores-honoris-causa |access-date=2023-10-27 |website=matematicas.ucm.es}}</ref>

==Research==
{{Further|Donaldson theory}}

Donaldson's work is on the application of [[mathematical analysis]] (especially the analysis of elliptic [[partial differential equations]]) to problems in geometry. The problems mainly concern [[gauge theory (mathematics)|gauge theory]], [[4-manifold]]s, complex [[differential geometry]] and [[symplectic geometry]]. The following theorems have been mentioned:{{by whom|date=March 2021}}

* The diagonalizability theorem {{harvs|last=Donaldson|year1=1983a|year2=1983b|year3=1987a}}: If the [[intersection theory|intersection form]] of a smooth, closed, simply connected [[4-manifold]] is positive- or negative-definite then it is diagonalizable over the integers. This result is sometimes called [[Donaldson's theorem]].
* A smooth [[h-cobordism]] between simply connected 4-manifolds need not be trivial {{harv|Donaldson|1987b}}. This contrasts with the situation in higher dimensions.
* A stable [[holomorphic vector bundle]] over a non-singular projective [[algebraic variety]] admits a [[Hermitian–Einstein metric]] {{harv|Donaldson|1987c}}, proven using an [[inductive proof]] and the theory of determinant bundles and [[Quillen metric]]s.<ref>Another proof of a somewhat more general result was given by {{cite journal |last1=Uhlenbeck |first1=Karen |author1-link = Karen Uhlenbeck |name-list-style=amp |last2=Yau |first2=Shing-Tung |author2-link = Shing-Tung Yau |title = On the existence of Hermitian-Yang-Mills connections in stable vector bundles |journal=[[Comm. Pure Appl. Math.]] |volume=39 |year=1986 |issue = S, suppl |pages = S257–S293 |doi = 10.1002/cpa.3160390714 |mr=0861491 }}</ref>
* A non-singular, projective algebraic surface can be diffeomorphic to the connected sum of two oriented 4-manifolds only if one of them has negative-definite intersection form {{harv|Donaldson|1990}}. This was an early application of the [[Donaldson invariant]] (or [[instanton]] invariants).
* Any compact symplectic manifold admits a symplectic [[Lefschetz pencil]] {{harv|Donaldson|1999}}.

Donaldson's recent work centers on a problem in complex differential geometry concerning a conjectural relationship between algebro-geometric "stability" conditions for smooth projective varieties and the existence of "[[Extremal Kähler metric|extremal]]" [[Kähler manifold|Kähler metrics]], typically those with constant [[scalar curvature]] (see for example [[cscK metric]]). Donaldson obtained results in the toric case of the problem (see for example {{harvtxt|Donaldson|2001}}). He then solved the [[Kähler–Einstein metric|Kähler–Einstein]] case of the problem in 2012, in collaboration with Chen and Sun. This latest spectacular achievement involved a number of difficult and technical papers. The first of these was the paper of {{harvtxt|Donaldson|Sun|2014}} on Gromov–Hausdorff limits. The summary of the existence proof for Kähler–Einstein metrics appears in {{harvtxt|Chen|Donaldson|Sun|2014}}. Full details of the proofs appear in {{harvs|txt|last1=Chen|last2=Donaldson|last3=Sun|year1=2015a|year2=2015b|year3=2015c}}.

=== Conjecture on Fano manifolds and Veblen Prize ===
{{See also|K-stability|K-stability of Fano varieties}}
In 2019, Donaldson was awarded the [[Oswald Veblen Prize in Geometry]], together with [[Xiuxiong Chen]] and [[Song Sun]], for proving a long-standing conjecture on [[Fano manifolds]], which states "that a Fano manifold admits a [[Kähler–Einstein metric]] if and only if it is [[K-Stability|K-stable]]". It had been one of the most actively investigated topics in geometry since its proposal in the 1980s by [[Shing-Tung Yau]] after he proved the [[Calabi conjecture]]. It was later generalized by [[Gang Tian]] and Donaldson. The solution by Chen, Donaldson and Sun was published in the ''[[Journal of the American Mathematical Society]]'' in 2015 as a three-article series, "Kähler–Einstein metrics on Fano manifolds, I, II and III".<ref name=veblen>{{cite web |url = http://www.ams.org/news?news_id=4705 |title=2019 Oswald Veblen Prize in Geometry to Xiuxiong Chen, Simon Donaldson, and Song Sun |date=2018-11-19 |website=American Mathematical Society |access-date=2019-04-09 }}</ref>

== Selected publications ==
* {{cite journal |last=Donaldson |first=Simon K. |title=An application of gauge theory to four-dimensional topology |journal=[[J. Differential Geom.]] |volume=18 |issue=2 |year=1983a |pages=279–315 |mr=710056 |doi=10.4310/jdg/1214437665 |doi-access=free }}
* {{cite journal |last=Donaldson |first=Simon K. |author-mask=3 |title=Self-dual connections and the topology of smooth 4-manifolds |journal=[[Bull. Amer. Math. Soc.]] |volume=8 |issue=1 |year=1983b |pages=81–83 |doi=10.1090/S0273-0979-1983-15090-5 |mr=0682827 |doi-access=free }}
*{{Cite journal |last=Donaldson |first=Simon K. |author-mask=3 |title=Instantons and geometric invariant theory|journal=Comm. Math. Phys. |volume=93 |issue=4 |year=1984b |pages=453–460 |mr=0892034 |url= https://projecteuclid.org/euclid.cmp/1103941177 |bibcode=1984CMaPh..93..453D |doi=10.1007/BF01212289 |s2cid=120209762 }}
*{{Cite journal |last=Donaldson |first=Simon K. |author-mask=3 |title=The orientation of Yang-Mills moduli spaces and 4-manifold topology |journal=[[J. Differential Geom.]] |volume=26 |year=1987a |issue=3 |pages=397–428 |mr=910015 |doi=10.4310/jdg/1214441485 |doi-access=free }}
*{{Cite journal |last=Donaldson |first=Simon K. |author-mask=3 |title=Irrationality and the h-cobordism conjecture |journal=J. Differential Geom. |volume=26 |issue=1 |year=1987b |pages=141–168 |mr=0892034 |doi=10.4310/jdg/1214441179 |doi-access=free }}
*{{Cite journal |last=Donaldson |first=Simon K. |author-mask=3 |title=Infinite determinants, stable bundles and curvature |journal=[[Duke Math. J.]] |volume=54 |year=1987c |issue=1 |pages=231–247 |doi=10.1215/S0012-7094-87-05414-7 | mr=0885784 }}
*{{Cite journal |last=Donaldson |first=Simon K. |author-mask=3 |title=Polynomial invariants for smooth four-manifolds |journal=[[Topology (journal)|Topology]] |volume=29 |year=1990 |issue=3 |pages=257–315 |doi=10.1016/0040-9383(90)90001-Z | mr=1066174 |doi-access= }}
*{{Cite journal |last=Donaldson |first=Simon K. |author-mask=3 |title=Lefschetz pencils on symplectic manifolds |journal=[[J. Differential Geom.]] |volume=53 |year=1999 |issue=2 |pages=205–236 |mr=1802722 |doi=10.4310/jdg/1214425535 |doi-access=free }}
*{{Cite journal |last=Donaldson |first=Simon K. |author-mask=3 |title=Scalar curvature and projective embeddings. I |journal=[[J. Differential Geom.]] |volume=59 |year=2001 |issue=3 |pages=479–522 |mr=1916953 |doi=10.4310/jdg/1090349449 |doi-access=free }}
*{{Cite journal |last1=Donaldson |first1=Simon K. |author-mask=3 | last2=Sun |first2=Song |title= Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry |journal=[[Acta Math.]] |volume=213 |issue=1 |year=2014 |pages=63–106 |doi=10.1007/s11511-014-0116-3 | mr=3261011 |arxiv=1206.2609 |s2cid=120450769 }}
*{{Cite journal |last1=Chen |first1=Xiuxiong |last2=Donaldson   |first2=Simon |last3=Sun |first3=Song |title=Kähler-Einstein metrics and stability |journal=[[International Mathematics Research Notices|Int. Math. Res. Notices]] |volume=2014 |issue= 8|year=2014 |pages=2119–2125 |doi=10.1093/imrn/rns279 | mr=3194014 |arxiv=1210.7494 |s2cid=119165036 }}
*{{Cite journal |last1=Chen |first1=Xiuxiong |last2=Donaldson   |first2=Simon |last3=Sun |first3=Song |title=Kähler-Einstein metrics on Fano manifolds I: Approximation of metrics with cone singularities |journal=[[J. Amer. Math. Soc.]] |volume=28 |issue=1 |year=2015a |pages=183–197 |doi=10.1090/S0894-0347-2014-00799-2 |mr=3264766 |arxiv=1211.4566 |s2cid=119641827 }}
*{{Cite journal |last1=Chen |first1=Xiuxiong |last2=Donaldson |first2=Simon |last3=Sun |first3=Song |title=Kähler-Einstein metrics on Fano manifolds II: Limits with cone angle less than 2π |journal=[[J. Amer. Math. Soc.]] |volume=28 |issue=1 |year=2015b |pages=199–234 |doi=10.1090/S0894-0347-2014-00800-6 | mr=3264767 |arxiv=1212.4714 |s2cid=119140033 }}
*{{Cite journal |last1=Chen |first1=Xiuxiong |last2=Donaldson   |first2=Simon |last3=Sun |first3=Song |title=Kähler-Einstein metrics on Fano manifolds III: Limits as cone angle approaches 2π and completion of the main proof |journal=[[J. Amer. Math. Soc.]] |volume=28 |issue=1 |year=2015c |pages=235–278 |doi=10.1090/S0894-0347-2014-00801-8 |mr=3264768 |arxiv=1302.0282 |s2cid=119575364 }}
'''Books'''
* {{cite book |last1=Donaldson |first1=S.K. |last2=Kronheimer |first2=P.B. |authorlink2=Peter B. Kronheimer |title=The geometry of four-manifolds |series=Oxford Mathematical Monographs |publisher=[[Oxford University Press]] |location=New York |year=1990 |isbn=0-19-853553-8 |mr=1079726 |url-access=registration |url=https://archive.org/details/geometryoffourma0000dona }}<ref>{{cite journal |last = Hitchin |first = Nigel |author-link=Nigel Hitchin |title = Review: ''The geometry of four-manifolds'', by S. K. Donaldson and P. B. Kronheimer|journal=Bull. Amer. Math. Soc. (N.S.) |year=1993|volume=28|issue=2|pages=415–418 |url = http://www.ams.org/journals/bull/1993-28-02/S0273-0979-1993-00377-X/|doi=10.1090/s0273-0979-1993-00377-x |doi-access=free }}</ref>
* {{cite book|last1=Donaldson|first1=S.K.|title=Floer homology groups in Yang-Mills theory|series=Cambridge Tracts in Mathematics|publisher=Cambridge University Press|year=2002|location=Cambridge|isbn=0-521-80803-0|volume=147}}
* {{Cite book|last=Donaldson |first=Simon |title=Riemann surfaces |series=Oxford Graduate Texts in Mathematics |volume=22 |publisher=[[Oxford University Press]] |location = Oxford |year=2011 |isbn=978-0-19-960674-0 |mr=2856237 |doi=10.1093/acprof:oso/9780198526391.001.0001 }}<ref>{{cite journal |last=Kra |first = Irwin |author-link=Irwin Kra |title=Review: ''Riemann surfaces'', by S. K. Donaldson |journal=Bull. Amer. Math. Soc. (N.S.) |year=2012 |volume=49 |issue=3 |pages=455–463 |url = http://www.ams.org/journals/bull/2012-49-03/S0273-0979-2012-01375-7/ |doi=10.1090/s0273-0979-2012-01375-7 |doi-access=free }}</ref>

== References ==
{{Reflist}}

== External links ==
{{Wikiquote}}
* {{MacTutor Biography |id = Donaldson}}
* {{MathGenealogy |id = 36909 }}
* [http://www.ma.ic.ac.uk/~skdona/ Home page at Imperial College]
* {{cite web |url = https://www.youtube.com/watch?v=P8-MjtCmyzg |title=Some recent developments in Kähler geometry and exceptional holonomy – Simon Donaldson – ICM2018 |website = YouTube |date=19 September 2018 }} (Plenary Lecture 1)

{{Clear}}
{{Fields medalists}}
{{Shaw Prize}}
{{Breakthrough Prize laureates}}
{{Veblen Prize recipients}}
{{FRS 1986}}

{{Authority control}}

{{DEFAULTSORT:Donaldson, Simon}}
[[Category:1957 births]]
[[Category:Living people]]
[[Category:20th-century English mathematicians]]
[[Category:21st-century English mathematicians]]
[[Category:Differential geometers]]
[[Category:Algebraic geometers]]
[[Category:Fellows of the Royal Society]]
[[Category:Foreign associates of the National Academy of Sciences]]
[[Category:Foreign members of the Russian Academy of Sciences]]
[[Category:Members of the Royal Swedish Academy of Sciences]]
[[Category:Members of the French Academy of Sciences]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Fields Medalists]]
[[Category:Wallis Professors of Mathematics]]
[[Category:Fellows of All Souls College, Oxford]]
[[Category:Academics of Imperial College London]]
[[Category:Alumni of Pembroke College, Cambridge]]
[[Category:Alumni of Worcester College, Oxford]]
[[Category:Royal Medal winners]]
[[Category:Whitehead Prize winners]]
[[Category:Knights Bachelor]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Wolf Prize in Mathematics laureates]]
[[Category:Scientists from Cambridge]]