Peter Hilton

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## Early life

## Career

### Hilton's theorem

## Death

## In popular culture

## Academic positions

## Professional memberships

## Honours

## Professional affiliations

## Hilton's former PhD students

## Bibliography

## References

## External links

This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

Peter Hilton | |
---|---|

Peter Hilton in Nice in 1970 | |

Born | Peter John Hilton 7 April 1923 London, England |

Died | 6 November 2010 Binghamton, New York, U.S. | (aged 87)

Alma mater | The Queen's College, Oxford |

Scientific career | |

Fields | Mathematician |

Institutions | University of Birmingham Cornell University Case Western Reserve University Binghamton University University of Central Florida |

**Peter John Hilton** (7 April 1923^{[1]} – 6 November 2010^{[2]}) was a British mathematician, noted for his contributions to homotopy theory and for code-breaking during the Second World War.^{[3]}

Hilton was born in London, the son of Elizabeth Amelia (Freedman) and Mortimer Jacob Hilton, and was educated at St Paul's School.^{[4]}^{[5]}^{[6]} He won a scholarship to the Queen's College, Oxford in 1940.^{[4]}

During the 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.^{[7]} 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 Code and Cypher School. He accepted, and, aged 18, arrived at wartime codebreaking station Bletchley Park on 12 January 1942.^{[8]}

He was initially put to work on Naval Enigma in Hut 8. In late 1942, he transferred to work on German teleprinter ciphers.^{[7]} A special section known as the "Testery" had been formed in July 1942 to work on one such cipher, codenamed "Tunny", and Hilton was one of the early members of the group.^{[9]} 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.^{[9]} 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.^{[10]}^{[11]}
Hilton obtained his DPhil in 1949 from Oxford University under the supervision of John Henry Whitehead. His dissertation was titled, "Calculation of the Homotopy Groups of *A*_{n}^{2}-polyhedra".^{[12]}

Hilton recounted his experience working with Alan Turing in Hut 8 in his "Reminiscences of Bletchley Park" from *A Century of Mathematics in America:*^{[13]}

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.

Hilton echoed similar thoughts in the Nova PBS documentary *Decoding Nazi Secrets*.^{[14]}

In 1958, he became the Mason Professor of Pure Mathematics at the University of Birmingham.^{[4]} He moved to the United States in 1962 to be Professor of Mathematics at Cornell University, a post he held until 1971.^{[1]} 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 constructed the 51-letter palindrome "Doc note, I dissent. A fast never prevents a fatness. I diet on cod."^{[15]}

Hilton's 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 is featured in Mathematical People.^{[16]}

Named after Hilton is Hilton's theorem (1955) on the homotopy groups of a wedge of spheres.

Peter Hilton died in Binghamton, New York, United States, at age 87.

Hilton is portrayed by 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.

- Lecturer at University of Cambridge, 1952-55
- Senior Lecturer at University of York, 1955-56
- Senior Lecturer at 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

- 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

- 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 Professor 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'
^{[17]} - 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, Professor Hilton was the Mahler Lecturer of the Australian Mathematical Society.
- In the summers of 2001 and 2001, Professor Hilton was Visiting Erskine Fellow at the University of Canterbury, Christchurch, New Zealand.
- In winter term of 2005 Professor Hilton received an appointment as Courtesy Faculty in the College of Arts and Sciences at University of South Florida.

- Member, Phi Beta Kappa Speakers Panel
- Consultant, John Wiley and Sons, Inc.
- Consultant, SRA/McGraw Hill Publishing Company
- Consultant, Children's Television Workshop
- Chairman, International Advisory Board, Institut des Sciences Mathématiques, Montréal
- Editor, Publicacions Matemàtiques
- Editor, Expositiones Mathematicae
- Editor, International Journal of Mathematics and Mathematical Sciences
- Editor, Mathematical Reports
- Member, American Mathematical Society Committee on Human Rights of Mathematics
- Chairman, Mathematical Association of America Committee on Award for Distinguished Service
- Chairman, Mathematical Association of America Committee on Award of Chauvenet Prize
- Member, Mathematical Association of America Panel on Remediation
- Member, Mathematical Association of America Panel on Public Representation
- Member, Advisory Committee on Mathematics and Science, Council for Basic Education
- Secretary, International Commission of Mathematical Instruction
- Editor, NICO (Brussels)
- Consultant, National Institute of Education, Department of Health Education And Welfare
- Chairman, United States National Research Council Committee on Applied Mathematical Training
- Member, United States Commission on Mathematical Instruction, National Research Council
- Chairman, Mathematical Association of America Committee on National Awards
- Principal Editor, Ergebnisse der Mathematik Series, published by Springer Verlag
- EdChairman, National Advisory Board, Comprehensive School Mathematics Project
- Member, Committee on the Undergraduate Program in Mathematics, Mathematical Association of America
- Chairman, National Research Council Committee on Graduate and Postdoctoral Training in Mathematics
- Chairman, United States Commission on Mathematical Instruction, National Research Council
- Member, Teacher Training Panel, Committee on the Undergraduate Program in Mathematics, Mathematical Association of America
- Joint chairman, Cambridge Conference on School Mathematics
- Member, National Advisory Committee, Boston University Mathematics Project
- Member, Committee on Films, Mathematical Association of America
- Member, Subcommittee on Translations, Mathematical Association of America
- Member, Committee on Postdoctoral Fellowships, American Mathematical Society
- Chairman, New York State Department of Education Panel on PhD Program in Mathematics (September 1976)
- Editor, Journal of Pure and Applied Algebra
- Chairman, Committee to Select Phi Beta Kappa Award in Science (Book Award)

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- 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 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

- Peter J. Hilton,
*An introduction to homotopy theory*, Cambridge Tracts in Mathematics and Mathematical Physics, no. 43, Cambridge University Press, 1953.^{[18]}ISBN 0-521-05265-3 MR0056289 - Peter J. Hilton, Shaun Wylie,
*Homology theory: An introduction to algebraic topology*, Cambridge University Press, New York, 1960.^{[19]}ISBN 0-521-09422-4 MR0115161 - Peter Hilton,
*Homotopy theory and duality*, Gordon and Breach, New York-London-Paris, 1965 ISBN 0-677-00295-5 MR0198466 - 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 MR0478146 - 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 MR1438546 - 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

- ^
^{a}^{b}Peter Hilton, "On all Sorts of Automorphisms",*The American Mathematical Monthly*, 92(9), November 1985, p. 650 **^***Obituaries: Peter Hilton*, 8 November 2010, retrieved 2010**^**Pedersen, Jean (2011). "Peter Hilton: Code Breaker and Mathematician (1923-2010)" (PDF).*Notices of the American Mathematical Society*.**58**(11): 1538-1540. MR 2896083.- ^
^{a}^{b}^{c}"About the speaker", announcement Archived 22 February 2007 at the Wayback Machine of a lecture given by Peter Hilton at Bletchley Park on 12 July 2006. Retrieved 18 January 2007. **^**Stewart, Ian (2 December 2010). "Peter Hilton obituary".*The Guardian*.**^**James, I. M. (2014). "Hilton, Peter John (1923-2010), code breaker and mathematician : Oxford Dictionary of National Biography - oi". doi:10.1093/ref:odnb/102834.- ^
^{a}^{b}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. **^**Hilton, "Living with Fish", p. 189- ^
^{a}^{b}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. **^**"Professor Peter Hilton".*The Sunday Telegraph*. 14 November 2010. Retrieved 2010.**^**"Station X" (Television Documentary). Channel 4. 1999.**^**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.**^**Hilton, Peter. "A Century of Mathematics in America, Part 1, Reminiscences of Bletchley Park" (PDF).**^**"NOVA | Transcripts | Decoding Nazi Secrets | PBS". PBS. Retrieved 2019.**^**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.**^**D. Albers and G.L. Alexanderson, Mathematical People, Birkhauser, Boston, 1995. ISBN 0-8176-3191-7**^**Contemporary Mathematics 37, AMS, 1985**^**Curtis, Morton L. (1954). "Review:*An introduction to homotopy theory*, by P. J. Hilton".*Bulletin of the American Mathematical Society*.**60**(2): 182-185. doi:10.1090/s0002-9904-1954-09797-5.**^**Massey, William S. (1964). "Review:*An introduction to algebraic topology*, by P. J. Hilton and S. Wylie".*Bulletin of the American Mathematical Society*.**70**(3): 333-335. doi:10.1090/s0002-9904-1964-11085-5.

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