# Peter Hilton

Last updated

Peter Hilton
Peter Hilton in Nice in 1970
Born
Peter John Hilton

7 April 1923
London, England
Died6 November 2010 (aged 87)
Binghamton, New York, United States
Alma mater The Queen's College, Oxford
Known for Eckmann–Hilton argument
Eckmann–Hilton duality
Hilton's theorem
Spouse(s)
Margaret Mostyn
(m. 19492010)
Children2
Scientific career
FieldsMathematician
Institutions University of Birmingham
Cornell University
Case Western Reserve University
Binghamton University
University of Central Florida
Thesis Calculation of the homotopy groups of ${\displaystyle A_{n}^{2}}$-polyhedra (1949)
Doctoral students Paul Kainen

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 World War II. [3]

## Early life

He was born in Brondesbury, London, the son Mortimer Jacob Hilton, a Jewish physician who was in general practice in Peckham, and his wife Elizabeth Amelia Freedman, and was brought up in Kilburn. [4] [5] The physiologist Sidney Montague Hilton (1921–2011) of the University of Birmingham Medical School was his elder brother. [6]

Hilton was educated at St Paul's School, London. [7] [8] [4] He went to The Queen's College, Oxford in 1940 to read mathematics, on an open scholarship, where the mathematics tutor was Ughtred Haslam-Jones. [7] [4] [9]

## Bletchley Park

A wartime undergraduate in wartime Oxford, on a shortened course, Hilton was obliged to train with the Royal Artillery, and faced scheduled conscription in summer 1942. [10] After four terms, he took the advice of his tutor, and followed up a civil service recruitment contact. [4] He had an interview 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. Aged 18, he arrived at the codebreaking station Bletchley Park on 12 January 1942. [11]

Hilton worked with several of the Bletchley Park deciphering groups. He was initially assigned to Naval Enigma in Hut 8. Hilton commented on his experience working with Alan Turing, whom he knew well for the last 12 years of his life, in his "Reminiscences of Bletchley Park" from A Century of Mathematics in America: [12]

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.

Hilton echoed similar thoughts in the Nova PBS documentary Decoding Nazi Secrets. [13]

In late 1942, Hilton transferred to work on German teleprinter ciphers. [10] 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. [14] 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. [14] Hilton has been counted as a member of the Newmanry, possibly on a part-time basis. [15]

### Recreational

A convivial pub drinker at Bletchley Park, Hilton also spent time with Turing working on chess problems and palindromes. [16] He there constructed a 51-letter palindrome: [17]

"Doc note, I dissent. A fast never prevents a fatness. I diet on cod."

He did not use paper or pencil while composing it, but lay on his bed, eyes closed, and assembled it mentally over one night. It took him five hours. [18]

## Mathematics

Hilton obtained his DPhil in 1949 from Oxford University under the supervision of John Henry Whitehead. His dissertation was "Calculation of the homotopy groups of ${\displaystyle A_{n}^{2}}$-polyhedra". [19] [20] 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 groups of a wedge of spheres. It addresses an issue that comes up in the theory of "homotopy operations". [21]

Turing, at the Victoria University of Manchester, in 1948 invited Hilton to see the Manchester Mark 1 machine. Around 1950, Hilton took a position at the university maths department. He was there in 1949, when Turing engaged in a discussion that introduced him to the word problem for groups. [22] Hilton worked with Walter Lederman. [23] Another colleague there was Hugh Dowker, who in 1951 drew his attention to the Serre spectral sequence. [24]

In 1952 Hilton moved to DPMMS in Cambridge, England, where he ran a topology seminar attended by John Frank Adams, Michael Atiyah, David B. A. Epstein, Terry Wall and Christopher Zeeman. [25] Via Hilton, Atiyah became aware of Jean-Pierre Serre's coherent sheaf proof of the Riemann–Roch theorem for curves, and found his first research direction in sheaf methods for ruled surfaces. [26]

In 1955 Hilton started work with Beno Eckmann on what became known as Eckmann-Hilton duality for the homotopy category. [27] Through Eckmann he became editor of the Ergebnisse der Mathematik und ihrer Grenzgebiete , a position he held from 1964 to 1983. [28]

Hilton returned to Manchester as Professor, in 1956. [29] In 1958, he became the Mason Professor of Pure Mathematics at the University of Birmingham. [7] 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 is featured in the book Mathematical People. [30]

## Death and family

Peter Hilton died on 6 November 2010 in Binghamton, New York, at age 87. He left behind his wife, Margaret Mostyn (born 1925), whom he married in 1949, and their two sons, who were adopted. [31] Margaret, a schoolteacher, had an acting career as Margaret Hilton in the US, in summer stock theatre. [4] She also played television roles. [32] She died in Seattle in 2020. [33]

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.

## 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’ [34]
• 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. [35]
• 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

According to the Mathematics Genealogy Project site, Hilton supervised at least 27 doctoral students, including Paul Kainen at Cornell University. [19]

## Bibliography

• Peter J. Hilton, An introduction to homotopy theory, Cambridge Tracts in Mathematics and Mathematical Physics, no. 43, Cambridge University Press, 1953. [36] ISBN   0-521-05265-3 MR 0056289
• Peter J. Hilton, Shaun Wylie, Homology theory: An introduction to algebraic topology, Cambridge University Press, New York, 1960. [37] ISBN   0-521-09422-4 MR 0115161
• Peter Hilton, Homotopy theory and duality, Gordon and Breach, New York-London-Paris, 1965 ISBN   0-677-00295-5 MR 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 MR 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 MR 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

## Related Research Articles

Alan Mathison Turing was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. Turing is widely considered to be the father of theoretical computer science and artificial intelligence.

Bletchley Park is an English country house and estate in Bletchley, Milton Keynes (Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following 1883 for the financier and politician Sir Herbert Leon in the Victorian Gothic, Tudor, and Dutch Baroque styles, on the site of older buildings of the same name.

Colossus was a set of computers developed by British codebreakers in the years 1943–1945 to help in the cryptanalysis of the Lorenz cipher. Colossus used thermionic valves to perform Boolean and counting operations. Colossus is thus regarded as the world's first programmable, electronic, digital computer, although it was programmed by switches and plugs and not by a stored program.

Maxwell Herman Alexander Newman, FRS,, generally known as Max Newman, was a British mathematician and codebreaker. His work in World War II led to the construction of Colossus, the world's first operational, programmable electronic computer, and he established the Royal Society Computing Machine Laboratory at the University of Manchester, which produced the world's first working, electronic stored-program electronic computer in 1948, the Manchester Baby.

William Thomas TutteOC FRS FRSC was an English and Canadian codebreaker and mathematician. During the Second World War, he made a brilliant and fundamental advance in cryptanalysis of the Lorenz cipher, a major Nazi German cipher system which was used for top-secret communications within the Wehrmacht High Command. The high-level, strategic nature of the intelligence obtained from Tutte's crucial breakthrough, in the bulk decrypting of Lorenz-enciphered messages specifically, contributed greatly, and perhaps even decisively, to the defeat of Nazi Germany. He also had a number of significant mathematical accomplishments, including foundation work in the fields of graph theory and matroid theory.

Fish was the UK's GC&CS Bletchley Park codename for any of several German teleprinter stream ciphers used during World War II. Enciphered teleprinter traffic was used between German High Command and Army Group commanders in the field, so its intelligence value (Ultra) was of the highest strategic value to the Allies. This traffic normally passed over landlines, but as German forces extended their geographic reach beyond western Europe, they had to resort to wireless transmission.

The Lorenz SZ40, SZ42a and SZ42b were German rotor stream cipher machines used by the German Army during World War II. They were developed by C. Lorenz AG in Berlin. The model name SZ was derived from Schlüssel-Zusatz, meaning cipher attachment. The instruments implemented a Vernam stream cipher.

John Henry Constantine Whitehead FRS, known as Henry, was a British mathematician and was one of the founders of homotopy theory. He was born in Chennai, in India, and died in Princeton, New Jersey, in 1960.

Alfred Dillwyn "Dilly" Knox, CMG was a British classics scholar and papyrologist at King's College, Cambridge and a codebreaker. As a member of the Room 40 codebreaking unit he helped decrypt the Zimmermann Telegram which brought the USA into the First World War. He then joined the Government Code and Cypher School (GC&CS).

John Frank Adams was a British mathematician, one of the major contributors to homotopy theory.

Captain Raymond C. "Jerry" Roberts, MBE was a British wartime codebreaker and businessman. During the Second World War, Roberts worked at the Government Code and Cypher School (GC&CS) at Bletchley Park from 1941 to 1945. He was a leading codebreaker and linguist, who worked on the Lorenz cipher system – Hitler's most top-level code.

Shaun Wylie was a British mathematician and World War II codebreaker.

The Newmanry was a section at Bletchley Park, the British codebreaking station during World War II. Its job was to develop and employ statistical and machine methods in Cryptanalysis of the Lorenz cipher. It worked very closely with the Testery where a complementary set of operations were performed to complete the decryption of each message. Formally called the Statistical section, it was known as the Newmanry after its founder and head, Max Newman. It was responsible for the various Robinson machines and the ten Colossus computers. Some of the cryptanalysts had joint appointments with the Testery.

Charles Eryl Wynn-Williams, was a Welsh physicist, noted for his research on electronic instrumentation for use in nuclear physics. His work on the scale-of-two counter contributed to the development of the modern computer.

The Testery was a section at Bletchley Park, the British codebreaking station during World War II. It was set up in July 1942 as the "FISH Subsection" under Major Ralph Tester, hence its alternative name. Four founder members were Tester himself and three senior cryptographers were Captain Jerry Roberts, Captain Peter Ericsson and Major Denis Oswald. All four were fluent in German. From 1 July 1942 on, this team switched and was tasked with breaking the German High Command's most top-level code Tunny after Bill Tutte successfully broke Tunny system in Spring 1942.

Ralph Paterson Tester was an administrator at Bletchley Park, the British codebreaking station during World War II. He founded and supervised a section named the Testery for breaking Tunny.

Turingery or Turing's method was a manual codebreaking method devised in July 1942 by the mathematician and cryptanalyst Alan Turing at the British Government Code and Cypher School at Bletchley Park during World War II. It was for use in cryptanalysis of the Lorenz cipher produced by the SZ40 and SZ42 teleprinter rotor stream cipher machines, one of the Germans' Geheimschreiber machines. The British codenamed non-Morse traffic "Fish", and that from this machine "Tunny".

Cryptanalysis of the Lorenz cipher was the process that enabled the British to read high-level German army messages during World War II. The British Government Code and Cypher School (GC&CS) at Bletchley Park decrypted many communications between the Oberkommando der Wehrmacht in Berlin and their army commands throughout occupied Europe, some of which were signed "Adolf Hitler, Führer". These were intercepted non-Morse radio transmissions that had been enciphered by the Lorenz SZ teleprinter rotor stream cipher attachments. Decrypts of this traffic became an important source of "Ultra" intelligence, which contributed significantly to Allied victory.

Catherine Mary Caughey used Colossus computers for codebreaking at Bletchley Park during World War II.

## References

1. Peter Hilton, "On all Sorts of Automorphisms", The American Mathematical Monthly , 92(9), November 1985, p. 650
2. Obituaries: Peter Hilton, 8 November 2010, retrieved 9 November 2010
3. Pedersen, Jean (2011). "Peter Hilton: Code Breaker and Mathematician (1923–2010)" (PDF). Notices of the American Mathematical Society . 58 (11): 1538–1540. MR   2896083.
4. James, I. M. "Hilton, Peter John (1923–2010)". Oxford Dictionary of National Biography (online ed.). Oxford University Press. doi:10.1093/ref:odnb/102834.(Subscription or UK public library membership required.)
5. "Jewish Personnel at Bletchley Park in World War II". www.jewishvirtuallibrary.org.
6. "Sidney Montague Hilton 17 March 1921–28 January 2011" (PDF). static.physoc.org. pp. 62–63.
7. "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.
8. Stewart, Ian (2 December 2010). "Peter Hilton obituary". The Guardian .
9. Titchmarsh, E. C. (1963). "Ughtred Shuttleworth Haslam-Jones | Titchmarsh, E. C. | download". Journal of the London Mathematical Society. s1-38 (1).
10. 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.
11. Hilton, "Living with Fish", p. 189
12. Hilton, Peter. "A Century of Mathematics in America, Part 1, Reminiscences of Bletchley Park" (PDF).
13. "NOVA, Transcripts, Decoding Nazi Secrets, PBS". PBS. Retrieved 29 August 2019.
14. 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.
15. Reeds, James A.; Diffie, Whitfield; Field, J. V. (7 July 2015). Breaking Teleprinter Ciphers at Bletchley Park: An edition of I.J. Good, D. Michie and G. Timms: General Report on Tunny with Emphasis on Statistical Methods (1945). John Wiley & Sons. p. 553. ISBN   978-0-470-46589-9.
16. Sugarman, Martin (2011). "A supplement to 'Breaking the codes: Jewish personnel at Bletchley Park'". Jewish Historical Studies. 43: 219. ISSN   0962-9696.
17. 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.
18. Inc, Thinkmap. "The Palindrome Game of the Enigma Codebreakers". www.vocabulary.com. Retrieved 13 February 2021.
19. 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.
20. Whitehead, George W. (6 December 2012). Elements of Homotopy Theory. Springer Science & Business Media. p. xiii. ISBN   978-1-4612-6318-0.
21. Hodges, Andrew (30 November 2012). Alan Turing: The Enigma. Random House. p. 412. ISBN   978-1-4481-3781-7.
22. Ledermann, Walter (1 February 2010). Encounters of a Mathematician. Lulu.com. p. 99. ISBN   978-1-4092-8267-9.
23. Dowker, Hugh (31 January 1985). Aspects of Topology: In Memory of Hugh Dowker 1912-1982. Cambridge University Press. p. 281. ISBN   978-0-521-27815-7.
24. James, I. M. (24 August 1999). History of Topology. Elsevier. p. 654. ISBN   978-0-08-053407-7.
25. Atiyah, Michael (28 April 1988). Collected Works: Michael Atiyah Collected Works: Volume 1: Early Papers; General Papers. Clarendon Press. p. 2. ISBN   978-0-19-853275-0.