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Peter Hilton: Codebreaker and Mathematician (1923–2010) Jean Pedersen, Coordinating Editor

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Peter Hilton: Codebreaker and Mathematician (1923–2010) Jean Pedersen, Coordinating Editor Peter Hilton: Codebreaker and Mathematician (1923–2010) Jean Pedersen, Coordinating Editor Peter Hilton was German. He then won a scholarship to Queen’s born in London on College, Oxford, where he read mathematics. When April 7, 1923, to he was eighteen, fate intervened for a second time. Elizabeth Freedman Peter began work at Bletchley Park in January and a family physi- 1942 (see Copeland’s contribution below for more cian, Mortimer Hilton, details); he thereby avoided service in the military, whose office was in where, as Peter said at the time, “I would surely Peckham. His parents die—of boredom!” On Peter’s eightieth birthday, hoped that he would Shaun Wylie, Peter’s coauthor, wrote: become either a doc- “This young chap from Oxford tor (as his brother joined us in Hut 8 at Bletchley, Photo courtesy of Jean Pedersen. Sydney did) or a and soon made his mark. When he Peter Hilton at Santa Clara lawyer. Fate first in- moved on to work on Fish, he did University (c. 1985). tervened when he was more than that; he dominated his run over by a Rolls Royce at the age of ten. During a long hospital stay section... he was brilliant at his job he discovered that he could use the plaster cast on and enormous fun to be with.” his left leg, which reached all the way to his navel, Peter was awarded an M.A. at Oxford in 1948, as a sort of white board; he solved mathematical a D.Phil. from Oxford in 1950 for his thesis, Cal- 2 problems on it, erasing them each morning. This culation of the Homotopy Groups of An-Polyhedra, is when, in his words, “It came to me that I really and a Ph.D. from Cambridge in 1952. loved mathematics and thoroughly enjoyed doing He married Margaret (Meg) Mostyn on Septem- it. I recall even having unkind thoughts about ber 14, 1949; they had two sons, Nicholas and visitors who came to see if I was all right, as they Tim. Peter and Meg shared a love of theater, Meg would interrupt me when I was really enjoying professionally and Peter very much less formally. what I was doing.” Indirectly, Peter’s love of theater led to our He attended St. Paul’s School in Hammersmith, meeting. In 1977 I was asked to get George Pólya, where, being enlightened educators, they left him with whom I had been studying informally for to study what he wanted in the later years. With about ten years, and Peter together to do a pre- unexplained prescience about the unrest leading sentation at a joint meeting of the Mathematical up to World War II, he decided to teach himself Association of America (MAA) and AMS in Seat- tle. They wanted Hilton to tell about “How Not Jean Pedersen is professor of mathematics and com- to Teach Mathematics” and then have Pólya give puter science at Santa Clara University. Her email is [email protected]. “Some Rules of Thumb”. When I wrote to Peter, he said “No!” He thought it would be more interesting The advice from Gerald Alexanderson and Ross Geoghe- gan, the technical assistance of Bin Shao with the text, (and fun) if he simulated a thoroughly bad demon- and the expertise of Chris Pedersen with the pictures are stration of teaching mathematics, and he agreed gratefully acknowledged. to do that, instead, if I would be the moderator. 1538 Notices of the AMS Volume 58, Number 11 The lectures took place on August 14, 1977. A repeat performance, which was televised [1], took place in the fall of 1978 at the San Diego meeting of the National Council of Teachers of Mathematics. Peter then agreed to come to Santa Clara University to give a colloquium talk. When he saw my office and heard about my interest in geometry, we discovered we both had a strong interest in polyhedra (from totally different points of view), and, as they say, the rest is history! Our mutual interest lay in the mathematics involved with geometry. Peter got interested in an algorithm I had developed that concerned a systematic method of folding a straight strip of Photo courtesy of Meg Hilton. paper, say, adding-machine tape, that produced Meg, Peter, and son Nicholas (c. 2008). increasingly good approximations for any given rational multiple of π, at equally spaced points the facts then you would share my along an edge of the paper. We began working conclusions, and you persuaded seriously on it in January of 1981 when we were me that if I believed in your ver- both at the Eidgenössische Technische Hochschule sion of the facts then I would share (ETH) in Zürich. This naturally took us into number your conclusions. It was a kind of theory, polyhedral geometry, and combinatorics, mathematical approach; an agree- and it continued for over thirty years until the ment about the proofs, whatever time of Peter’s death. The relevant mathemat- the hypotheses and theorems. It was a lesson that has served me ics is chronicled in our most recent book, A well throughout my life, in con- Mathematical Tapestry: Demonstrating the Beauti- versations about everything under ful Unity of Mathematics [2]. In Section 16.6 we the sun.” wrote about “Pólya and ourselves—Mathematics, tea and cakes”, which describes, as the title sug- I was blessed with two great mentors, first gests, more about our interactions with each other George Pólya (for far too short a time) and then and with Pólya. Peter Hilton. Pólya introduced me to polyhedral An event that demonstrates the joie de vivre of geometry, the wonders of “looking for patterns”, collaborating with Peter involved the construction and the importance of posing problems. Peter of a figure for one of our articles. We needed a star showed me how to generalize and how to see con- 11 nections between various parts of mathematics. { }-gon (i.e., the top edge of the tape would visit 3 Both Pólya and Peter made the doing of mathemat- every third vertex of a bounding regular convex ics an adventure constantly filled with excitement. 11-gon). I had pulled the tape a little too tight and Together Peter and I coauthored 144 papers and got a star { 10 }-gon. When I reported this mishap 3 6 books, often giving joint lectures on our current to Peter he said cheerfully, “Don’t worry, we say in topic of interest. the beginning these are only approximations!” He My family was enriched by our friendship with never failed to see the humorous side of things. Peter’s family. I was excited to watch Meg perform Although Peter excelled at abstract thinking, (as Jim Dale’s mother) in the production of the he always applied mathematics to real life. He Broadway Tony-Award-winning play, A Day in the came to understand the principle of mathematical Death of Joe Egg (right after she won the Clarence induction at the age of seven when drying dishes Dewent award for her role in Molly). I have fond for his mother. He realized that the old trick of memories of Peter, Meg, Kent (my husband), and drying two plates at a time could, in theory, be me on our land-cruise tour of Alaska. I smile extended by induction to n plates. As for applying recalling when Kent, Peter, and I walked through mathematics to social situations, Sir Christopher some drizzly California redwoods on what Peter Zeeman said in his letter on Peter’s eightieth called a “lovely London day”, and later we played birthday: three-handed bridge at our house (where Peter “From you I also learned how to got the bid with an appallingly bad dummy). talk politics, without endangering I will always miss Peter, but I am grateful for friendship. You taught me that if the memories and the years of collaboration we we disagreed about some conclu- shared. sions then we should go back and examine our beliefs about the un- References derlying facts. You acknowledged [1] Hilton-Pólya DVD, recorded on VHS in 1978, dig- thatifyoubelievedinmyversionof itized 2011. Available from Media Services, Santa December 2011 Notices of the AMS 1539 British universities searching for suitable recruits, and toward the end of 1941, at the University of Oxford, they interviewed a brilliant second- year mathematics undergraduate with a working knowledge ofGerman. Peter hadtaughthimselfthe language at school in order to read mathematical work. The panel snatched him up. By exposing the detailed thinking of the enemy, Peter and his fellow codebreakers saved an incal- culable number of lives. Occasionally he would even break messages signed by Hitler himself. The significance, horror, and fascination of the work is conveyed by this decrypt, dated December 1944, detailing an order from Hitler to General Guderian regarding the defense of Budapest [2]: “Evacu- Photo courtesy of Jean Pedersen. ation without fighting in case of unfavourable Kent and Jean Pedersen (on left) with Peter development...out of question. Every house to Hilton in the California redwoods (1996). be contested. Measures to prevent troops being endangered by the armed mob of the city to be Clara University, Santa Clara, CA 95053 (US$25.00 taken ruthlessly.” + postage and handling). [2] P. Hilton and J. Pedersen, with illustrations by Sylvie Donmoyer, A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics, Cambridge University Press, Jack Copeland During 1939–1945 Britain and her allies enjoyed unprecedented access to enemy radio communi- cations. The German military transmitted many thousands of encrypted messages each day, rang- ing from top-level signals, such as detailed sit- uation reports from generals at the front line, through to the important minutiae of war, such as weather reports and inventories of the contents of supply vessels.
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