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'{{Short description|British mathematician}} {{Use dmy dates|date=February 2020}} {{EngvarB|date=February 2020}} {{About|the British mathematician|the Lord-Lieutenant of Derbyshire|Peter Hilton (lord-lieutenant)}} {{Infobox scientist | image = Peter Hilton.jpg | caption = Peter Hilton in [[Nice]] in 1970 | name = Peter Hilton | birth_name = Peter John Hilton | birth_date = {{Birth date|df=y|1923|4|7}} | birth_place = [[London]], England | death_date = {{Death date and age|df=y|2010|11|6|1923|4|7}} | death_place = [[Binghamton, New York]], United States | fields = Mathematician | alma_mater = [[The Queen's College, Oxford]] | thesis_title = Calculation of the homotopy groups of <math>A_n^2</math>-polyhedra | thesis_url = | thesis_year = | doctoral_advisor = [[J. H. C. Whitehead]] | awards = | workplaces = [[University of Birmingham]]<br> [[Cornell University]]<br>[[Case Western Reserve University]]<br>[[Binghamton University]]<br>[[University of Central Florida]] }} '''Peter John Hilton''' (7 April 1923<ref name="all-sorts">Peter Hilton, "On all Sorts of Automorphisms", ''[[The American Mathematical Monthly]]'', 92(9), November 1985, p. 650</ref>{{spaced ndash}}6 November 2010<ref>{{Citation | title = Obituaries: Peter Hilton | date = 8 November 2010 | url = http://www.legacy.com/obituaries/pressconnects/obituary.aspx?n=peter-hilton&pid=146500873 | accessdate = 9 November 2010 }}</ref>) was a British mathematician, noted for his contributions to [[homotopy theory]] and for code-breaking during [[World War II]].<ref>{{cite journal|last=Pedersen|first= Jean|authorlink=Jean Pedersen|title=Peter Hilton: Code Breaker and Mathematician (1923–2010)|journal=[[Notices of the American Mathematical Society]]|year=2011|volume=58|issue=11|pages=1538–1540|url=https://www.ams.org/notices/201111/rtx111101538p.pdf|mr=2896083}}</ref> ==Early life== Hilton was born in [[London]], the son of Elizabeth Amelia (Freedman) and Mortimer Jacob Hilton, and was educated at [[St Paul's School (London)|St Paul's School]].<ref name="bp-about">"About the speaker", [http://www.nationalcodescentre.org/edu/lectures/turing.rhtm announcement] {{Webarchive|url=https://web.archive.org/web/20070222093557/http://www.nationalcodescentre.org/edu/lectures/turing.rhtm |date=22 February 2007 }} of a lecture given by Peter Hilton at Bletchley Park on 12 July 2006. Retrieved 18 January 2007.</ref><ref>{{Cite news | url=https://www.theguardian.com/science/2010/dec/02/peter-hilton-obituary | title=Peter Hilton obituary| newspaper=[[The Guardian]]| date=2 December 2010| last1=Stewart| first1=Ian}}</ref><ref>{{cite ODNB |id=102834 |last1 = James |first1 = I. M. |authorlink=Ioan James |title = Hilton, Peter John (1923–2010)}}</ref> He won a scholarship to [[the Queen's College, Oxford]] in 1940.<ref name="bp-about"/> ==Bletchley Park== During the [[World War II|Second World War]], as an undergraduate, Hilton was obliged to enroll in training with the [[Royal Artillery]], and was scheduled for [[conscription]] in summer 1942.<ref name="lwf-190">Peter Hilton, "Living with Fish: Breaking Tunny in the Newmanry and the Testery", p. 190 from pp. 189–203 in [[Jack Copeland]] ed, ''Colossus: The Secrets of [[Bletchley Park]]'s Codebreaking Computers'', [[Oxford University Press]], 2006.</ref> Instead, he was interviewed by a team touring universities looking for mathematicians with knowledge of German, and was offered a position in the [[Foreign Office]] without being told the nature of the work. The team was, in fact, recruiting on behalf of the [[Government Communications Headquarters#Government Code and Cypher School|Government Code and Cypher School]]. He accepted, and, aged 18, arrived at wartime [[codebreaking]] station [[Bletchley Park]] on 12 January 1942.<ref>Hilton, "Living with Fish", p. 189</ref> He was initially put to work on Naval [[Enigma machine|Enigma]] in [[Hut 8]]. In late 1942, he transferred to work on German [[teleprinter]] ciphers.<ref name="lwf-190"/> A special section known as the "[[Testery]]" had been formed in July 1942 to work on one such cipher, codenamed "[[Lorenz cipher|Tunny]]", and Hilton was one of the early members of the group.<ref name="roberts">Jerry Roberts, "Major Tester's Section", p. 250 of pp. 249–259 in Jack Copeland ed, ''Colossus: The Secrets of Bletchley Park's Codebreaking Computers'', Oxford University Press, 2006.</ref> His role was to devise ways to deal with changes in Tunny, and to liaise with another section working on Tunny, the "[[Newmanry]]", which complemented the hand-methods of the Testery with specialised codebreaking machinery.<ref name="roberts"/> Occasionally the same message was sent repeated, a major security blunder that Bletchley park called a "depth." Hilton derived great satisfaction from being able to look at the encoded texts coming from two separate teleprinter messages, combine them and extract two messages in clear German.<ref>{{cite news|url=https://www.telegraph.co.uk/news/obituaries/science-obituaries/8124447/Professor-Peter-Hilton.html|title=Professor Peter Hilton|date=14 November 2010 |accessdate=14 November 2010|work=The Sunday Telegraph}} </ref><ref>{{cite news|title=Station X|publisher=Channel 4|year=1999|type=Television Documentary}}</ref> Hilton recounted his experience working with [[Alan Turing]] in [[Hut 8]] in his "Reminiscences of Bletchley Park" from ''A Century of Mathematics in America:''<ref>{{Cite web|url=https://www.ams.org/publicoutreach/math-history/hmath1-hilton22.pdf|title=A Century of Mathematics in America, Part 1, Reminiscences of Bletchley Park|last=Hilton|first=Peter|website=}}</ref>{{quote|I had the good fortune to work closely with Alan Turing and to know him well for the last 12 years of his short life. It is a rare experience to meet an authentic genius. Those of us privileged to inhabit the world of scholarship are familiar with the intellectual stimulation furnished by talented colleagues. We can admire the ideas they share with us and are usually able to understand their source; we may even often believe that we ourselves could have created such concepts and originated such thoughts. However, the experience of sharing the intellectual life of a genius is entirely different; one realizes that one is in the presence of an intelligence, a sensibility of such profundity and originality that one is filled with wonder and excitement. Alan Turing was such a genius, and those, like myself, who had the astonishing and unexpected opportunity, created by the strange exigencies of the Second World War, to be able to count Turing as colleague and friend will never forget that experience, nor can we ever lose its immense benefit to us.|sign=|source=}}Hilton echoed similar thoughts in the Nova [[PBS]] documentary ''Decoding Nazi Secrets''.<ref>{{Cite web|url=https://www.pbs.org/wgbh/nova/transcripts/2615decoding.html|title=NOVA, Transcripts, Decoding Nazi Secrets, PBS|publisher=PBS|access-date=29 August 2019}}</ref> ==Mathematics== Hilton obtained his [[Doctor of Philosophy|DPhil]] in 1949 from [[Oxford University]] under the supervision of [[J. H. C. Whitehead|John Henry Whitehead]]. His dissertation was "Calculation of the homotopy groups of <math>A_n^2</math>-polyhedra".<ref name="interview">David Joyner and David Kahn, editors, "Edited Transcript of Interview with Peter Hilton for ''Secrets of War''", in ''[[Cryptologia]]'' 30(3), July–September 2006, pp. 236–250.</ref> His principal research interests were in [[algebraic topology]], homological algebra, categorical algebra and mathematics education. He published 15 books and over 600 articles in these areas, some jointly with colleagues. [[Hilton's theorem]] (1955) is on the [[homotopy group]]s of a [[Wedge sum|wedge]] of [[sphere]]s. Around 1950, Hilton took a position at the [[University of Manchester]], where he worked with [[Walter Lederman]].<ref>{{cite book |last1=Ledermann |first1=Walter |title=Encounters of a Mathematician |date=1 February 2010 |publisher=Lulu.com |isbn=978-1-4092-8267-9 |page=99 |url=https://books.google.co.uk/books?id=TngVAgAAQBAJ&pg=PA99 |language=en}}</ref> In 1958, Hilton became the Mason Professor of Pure Mathematics at the [[University of Birmingham]].<ref name="bp-about"/> He moved to the United States in 1962 to be Professor of Mathematics at [[Cornell University]], a post he held until 1971.<ref name="all-sorts"/> From 1971 to 1973, he held a joint appointment as Fellow of the Battelle Seattle Research Center and Professor of Mathematics at the [[University of Washington]]. On 1 September 1972, he was appointed Louis D. Beaumont University Professor at [[Case Western Reserve University]]; on 1 September 1973, he took up the appointment. In 1982, he was appointed Distinguished Professor of Mathematics at [[Binghamton University]], becoming Emeritus in 2003. Latterly he spent each spring semester as Distinguished Professor of Mathematics at the [[University of Central Florida]]. Hilton is featured in the book ''Mathematical People''.<ref>D. Albers and [[Gerald L. Alexanderson|G.L. Alexanderson]], Mathematical People, Birkhauser, Boston, 1995. {{isbn|0-8176-3191-7}}</ref> === Recreational === Hilton constructed the 51-letter [[palindrome|English palindrome]] while working at Bletchley Park as a recreation from his job as a code breaker. <ref>Jack Good, "Enigma and Fish", p. 160 from pp. 149–166 in F. H. Hinsley and Alan Strip, editors, ''Codebreakers: The Inside Story of Bletchley Park'', 1993.</ref> <blockquote>"Doc note, I dissent. A fast never prevents a fatness. I diet on cod."</blockquote>He did not use paper or pencil while composing this palindrome but simply lay on his bed, eyes closed, and assembled it in his mind over one long night. It took him five hours. <ref>{{Cite web|last=Inc|first=Thinkmap|title=The Palindrome Game of the Enigma Codebreakers|url=https://www.vocabulary.com/articles/wc/the-palindrome-game-of-the-enigma-codebreakers|access-date=2021-02-13|website=www.vocabulary.com}}</ref> ==Death== Peter Hilton died on 6 November 2010 in [[Binghamton, New York|Binghamton]], New York, United States, at age 87. ==In popular culture== Hilton is portrayed by actor [[Matthew Beard (English actor)|Matthew Beard]] in the 2014 film ''[[The Imitation Game]]'', which tells the tale of [[Alan Turing]] and the cracking of [[Nazi Germany]]'s [[Enigma code]]. ==Academic positions== * Lecturer at [[University of Cambridge]], 1952–55 * Senior Lecturer at [[Victoria University of Manchester|University of Manchester]], England, 1956–58 * Mason Professor of Pure Mathematics, [[University of Birmingham]], England, 1958–62 * Visiting Professor at the Eidgenössische Technische Hochschule at Zürich, [[ETH Zurich]], 1966–67, 1981–82, 1988–89 * Visiting Professor at the [[Courant Institute of Mathematical Sciences]], New York University, 1967–68 * Visiting Professor at the Universitat Autònoma de Barcelona, [[Autonomous University of Barcelona]], 1989 * Professeur invité, [[University of Lausanne]], in 1996 ==Professional memberships== * [[American Mathematical Society]] * [[Mathematical Association of America]] * [[London Mathematical Society]] * [[Cambridge Philosophical Society]] * [[Royal Statistical Society]] * Honorary member of the Mathematical Society of Belgium * Honorary member of [[Phi Beta Kappa Society]] * First-Vice-President of the [[Mathematical Association of America]] 1978–1980 ==Honours== * Silver Medal, [[University of Helsinki]], 1975 * Doctor of Humanities (hon. causa), N. [[University of Michigan]], 1977 * Corresponding Member, [[Brazilian Academy of Sciences]], 1979 * Doctor of Science (hon. causa), [[Memorial University of Newfoundland]], 1983 * Doctor of Science (hon. causa), [[Autonomous University of Barcelona]], 1989 * In August 1983, an international conference on algebraic topology was held, under the auspices of the Canadian Mathematical Society, to mark Hilton's 60th Birthday. Professor Hilton was presented with a Festschrift of papers dedicated to him ([[London Mathematical Society]] Lecture Notes, Volume 86, 1983). The [[American Mathematical Society]] has published the proceedings under the title ‘Conference on Algebraic Topology in Honor of Peter Hilton’<ref>Contemporary Mathematics 37, AMS, 1985</ref> * Hilton was selected in October 1992, to deliver the invited lecture at the ‘Georges de Rham’ day at the [[University of Lausanne]]. * An International Conference was held in Montreal in May 1993, to mark the 70th birthday of Hilton. The proceedings were published as The Hilton Symposium, CRM Proceedings and Lecture Notes, Volume 6, American Mathematical Society (1994), edited by [[Guido Mislin]]. * In 1994, Hilton was the Mahler Lecturer of the Australian Mathematical Society. * In the summers of 2001 and 2002, Hilton was Visiting Erskine Fellow at the University of Canterbury, Christchurch, New Zealand.<ref>{{cite web |title=Philosophy |url=https://www.canterbury.ac.nz/engage/erskine/roll/department/philosophy/ |website=The University of Canterbury |language=en-nz}}</ref> * In winter term of 2005 Hilton received an appointment as Courtesy Faculty in the College of Arts and Sciences at University of South Florida. ==Hilton's former PhD students== {{unreferenced section|date=July 2012}} * Martin Arkowitz, [[Cornell University]] 1960 * Imre Bokor, [[ETH Zurich]] 1988 * Bryce Brogan, [[Case Western Reserve University]] 1977 * Charles Cassidy, [[Université Laval]] 1977 * Keith Hardie, [[University of Cambridge]] 1958 * Robert Haas, [[Case Western Reserve University]] 1977 * [[Paul Chester Kainen|Paul Kainen]], [[Cornell University]] 1970 * Paulo Leite, [[University of São Paulo]] 1979 * Karl Lorensen, [[Binghamton University]] 1997 * Robert Militello, [[Binghamton University]] 1991 * Irwin Pressman, [[Carleton University]] 1965 * Vidhyanath Rao, [[Case Western Reserve University]] 1981 * Heather Ries, [[Binghamton University]] 1992 * Dirk Scevenels, [[KU Leuven]] 1995 * Christopher Schuck, [[Binghamton University]] 1992 * Chia-Hui Shih Kuo, [[Cornell University]] 1964 * Johnnie Slagle, [[University of Washington]] 1973 * Michael Stewart, [[University of Washington]] 1973 * Changchao Su, [[Binghamton University]] 2000 * Yel-Chiang Wu, [[Cornell University]] 1967 * S. Yahya, [[University of Birmingham]] 1962 ==Bibliography== <!-- He co-authored a book on [[Homology (mathematics)|homology]] with fellow wartime codebreaker [[Shaun Wylie]], published in 1960, titled, "Homology Theory: An Introduction to Algebraic Topology"<ref>Jack Good, "From Hut 8 to the Newmanry", p. 206 from pp. 204–222 in B. Jack Copeland editor, ''Colossus: The Secrets of Bletchley Park's Codebreaking Computers'', Oxford University Press, 2006.</ref> --> * Peter J. Hilton, ''An introduction to homotopy theory'', Cambridge Tracts in Mathematics and Mathematical Physics, no. 43, [[Cambridge University Press]], 1953.<ref>{{cite journal| last=Curtis| first= Morton L.| authorlink=Morton L. Curtis | title = Review: ''An introduction to homotopy theory'', by P. J. Hilton| journal=[[Bulletin of the American Mathematical Society]] |year=1954|volume=60|issue=2|pages=182–185| doi=10.1090/s0002-9904-1954-09797-5| doi-access=free}}</ref> {{isbn|0-521-05265-3}} {{MathSciNet| id=0056289}} * Peter J. Hilton, [[Shaun Wylie]], ''Homology theory: An introduction to algebraic topology'', [[Cambridge University Press]], New York, 1960.<ref>{{cite journal|last=Massey|first= William S.|authorlink=William S. Massey|title=Review: ''An introduction to algebraic topology'', by P. J. Hilton and S. Wylie|journal=[[Bulletin of the American Mathematical Society]] |year=1964|volume=70|issue=3|pages=333–335|doi=10.1090/s0002-9904-1964-11085-5|doi-access=free}}</ref> {{isbn|0-521-09422-4}} {{MathSciNet| id=0115161}} * Peter Hilton, ''Homotopy theory and duality'', Gordon and Breach, New York-London-Paris, 1965 {{isbn|0-677-00295-5}} {{MathSciNet| id=0198466}} * H.B. Griffiths and P.J. Hilton, "A Comprehensive Textbook of Classical Mathematics", Van Nostrand Reinhold, London, 1970, {{isbn|978-0442028640}} * Peter J. Hilton, Guido Mislin, Joe Roitberg, ''Localization of nilpotent groups and spaces'', North-Holland Publishing Co., Amsterdam-Oxford, 1975. {{isbn|0-444-10776-2}} {{MathSciNet| id=0478146}} * Peter Hilton, [[Jean Pedersen]], ''Build your own polyhedra. Second edition'', Dale Seymour Publications, Palo Alto, 1994. {{isbn|0-201-49096-X}} * Peter Hilton, Derek Holton, [[Jean Pedersen]], ''Mathematical reflections: In a room with many mirrors. Corrected edition'', [[Undergraduate Texts in Mathematics]], [[Springer-Verlag]], New York, 1996. {{isbn|0-387-94770-1}} * Peter J. Hilton, Urs Stammbach, ''A course in homological algebra. Second edition'', [[Graduate Texts in Mathematics]], vol 4, [[Springer-Verlag]], New York, 1997. {{isbn|0-387-94823-6}} {{MathSciNet| id=1438546}} * Hans Walser, ''[[99 Points of Intersection]]'', translated by Peter Hilton and [[Jean Pedersen]], MAA Spectrum, Mathematical Association of America, 2006. {{isbn|978-0-88385-553-9}} * Peter Hilton, Derek Holton, [[Jean Pedersen]], ''Mathematical vistas: From a room with many windows'', [[Undergraduate Texts in Mathematics]], [[Springer-Verlag]], New York, 2010. {{isbn|1-4419-2867-7}} * Peter Hilton, [[Jean Pedersen]], ''A mathematical tapestry: Demonstrating the beautiful unity of mathematics'', [[Cambridge University Press]], Cambridge, 2010. {{isbn|0-521-12821-8}} ==References== {{reflist}} ==External links== * {{MacTutor Biography|id=Hilton}} * {{MathGenealogy |id=6773}} * {{cite web|url=http://www.math.binghamton.edu/peter/|title= Home page |location= Binghamton University}} * {{cite web|url=http://news2.ucf.edu/FY2002-03/030407.html|title=The World Celebrates Professor's Birthday| publisher= [[University of Central Florida]]|archive-url=https://web.archive.org/web/20050519224647/http://news2.ucf.edu/FY2002-03/030407.html|archive-date=19 May 2005}} {{Authority control}} {{DEFAULTSORT:Hilton, Peter}} [[Category:1923 births]] [[Category:2010 deaths]] [[Category:20th-century British mathematicians]] [[Category:21st-century British mathematicians]] [[Category:Topologists]] [[Category:People educated at St Paul's School, London]] [[Category:Alumni of The Queen's College, Oxford]] [[Category:Bletchley Park people]] [[Category:Academics of the Victoria University of Manchester]] [[Category:Academics of the University of Birmingham]] [[Category:State University of New York faculty]] [[Category:Cornell University faculty]] [[Category:Binghamton University faculty]] [[Category:Courant Institute of Mathematical Sciences faculty]]'