Book Review My Life and Functions Reviewed by David Drasin his frustration that, My Life and Functions when preparing these, Walter K. Hayman he invariably would rec- Logic Press, October 2014 ognize how little he Printed and distributed by lulu.com knew of the subject’s 152 pages personal groundings, in- US$30.84 (hard cover) terests, or background. ISBN-13: 978-1-326-03224-1 Efforts to compen- US$15.34 (paperback) sate, including visits ISBN-13: 978-1-326-03020-9 to family members and associates, were little Walter Kurt Hayman has led a remarkably full and compensation. (His obit- interesting life, starting from accidents arising from uary of Rolf Nevanlinna his birth and ancestry to his later role as a leader of a [MR 0671785] displays major school of complex analysis. He was a prolific the seriousness and scientist, with extensive travels and interactions spirit with which he with major scientific and cultural leaders. As he fulfilled these responsibilities.) nears his ninetieth birthday his memory remains Some circumstances make having his own strong. This autobiography is a relaxed review of account especially notable. Walter was one of the his life, featuring abundant charming comments, large and talented German intellectual community anecdotes, insights and memories, with some which was displaced by the Nazi era; he emigrated illustrations. The author credits his current wife, to the UK at age twelve in 1938, only weeks before Marie Jennings, with the impetus to write this Kristallnacht dispelled any doubts of the future book. of Germans of Jewish ancestry (although by then Less emphasis is given to mathematics, and the the Haymans considered themselves Christian). author provides little insight into the mechanics or One great-grandparent was the celebrated pianist vision behind his achievements. His impish sense Fanny Mendelssohn, sister of Felix and an important of humor comes through consistently, and I could composer in her own right.1 The author’s middle fill paragraphs with some of his short quotations name refers to his maternal grandfather, Kurt and aphorisms. (One example is the thought that Hensel (who is credited with discovering p-adic his “athletic prowess was probably inherited from numbers); Hensel’s lemma is still part of the [his] father. He claimed to be the best tennis teacher graduate algebra curriculum. Walter’s final visit to in the world, since all his students beat him after his grandfather was shortly before leaving Germany, the first game.”) In recent years many of Walter’s publications 1Dover books still offers a selection of Fanny’s piano music, have been obituaries. Walter once mentioned and the recent very interesting documentary Mendelssohn, the Nazis and Me, directed by his daughter Sheila, includes David Drasin is professor emeritus of mathematics at Pur- testimony from Walter and fascinating insights from those due University. His email address is [email protected]. times. Another Mendelssohn sister, Rebecka, married the DOI: http://dx.doi.org/10.1090/noti1250 mathematician P. G. L. Dirichlet. May 2015 Notices of the AMS 517 and his warm memories of their mathematical Muslim Quaker.” At present, he is married to Marie and musical interactions must have influenced his Jennings, whom he met a few years after Wafika’s career choice. passing in 2001. The circumstances behind this The family’s status and contacts allowed him courtship are very touching, and their partnership and (when they arrived later) his parents to avoid flourishes to this day. the most severe hardships of a time of worldwide Walter won major recognition from his British economic insecurity, and Walter was able to colleagues throughout his career: both Junior attend excellent schools and Cambridge University. Berwick (now known as Berwick) and Senior Berwick Notable was Gourdonstown School, which had been Prizes (he was the first to receive both; the second founded in Scotland by his mother’s cousin Kurt double recipient only came decades later in 1994), Hahn soon after Hahn’s expulsion from Germany; culminating in the London Mathematical Society’s enrollees would include members of the British deMorgan Medal (1995), considered the society’s Royal Family. The generosity and help which top recognition for mathematical achievement. He Walter and his family encountered in England is was elected Fellow of the Royal Society at age thirty. gratefully acknowledged throughout, and it was In spite of these accolades, he willingly recounts an important motivation for his lifelong service many doubts, weaknesses, and insecurities. As and charitable activities (another came from his examples, his discomfort when first encountering joining the Society of Friends (Quakers) and his the towering leaders of his research area, Rolf marriage to Margaret Crann, whom he met at a Nevanlinna and Lars Ahlfors, or his having the Friends meeting while both were at Cambridge). naiveté to directly ask A. S. Besicovitch to compare Walter was always conscious of the responsibilities him to another student, Freeman Dyson: “He said which came from his prominence and successes. quite rightly that Dyson was better.” It appears that Walter was reluctant to ask The center of his professional career was his J. E. Littlewood to be his thesis supervisor, but thirty years at Imperial College until the first of he noticed that Mary L. Cartwright’s work was his retirements in 1985. The Hayman Monday one of the few directly cited in Littlewood’s morning seminar (at 11 sharp) featured work monograph Lectures on the Theory of Functions of students, colleagues, and recent literature, [MR 0012121], which made her a logical choice. augmented by presentations from a steady stream He and Cartwright remained close until her death, of visitors. Walter was proud of his department’s and Walter’s obituary of Dame Mary [MR 1866432] outstanding status in the British academic world. is a fascinating tribute. His pride in helping the department flourish is His marriage to Margaret lasted forty-seven evident when discussing recruiting the complex years, and their partnership also had consequences dynamist I. N. Baker to the faculty well before for the mathematical world. Margaret later was the subject became fashionable. That the Fields appointed Head of Maths (mathematics) at Putney Medalists Klaus Roth (now deceased) and Simon High School and became well known in British Donaldson were among his colleagues is of course education circles. In 1965 Walter and Margaret mentioned. He also discusses the contributions were invited by the Ministry of Education to a and interesting personalities among his students workshop on competitions. During the following and his clerical support staff (anyone who has summer, when the Hayman family made a motor encountered Walter’s handwriting will appreciate trip to the Moscow International Congress, Walter the effort needed to bring his work to the scientific was able to meet the Russian minister of education. public). The result was that, upon their return to the UK, Walter always thrived at mathematical confer- the Haymans arranged that Britain participate ences, where his direct, energetic, and unsnobbish in the International Mathematical Olympiad. The behavior was atypical among leading mathemati- British team was the first non-Socialist entry, and cians I have known. He considered himself today over one hundred nations compete. In her duty-bound to ask questions, not being afraid private life, Margaret was a respected violin player; to show that one need not be an expert to partici- Hayman’s family life often included chamber music pate: “There’s nothing worse than a dead silence featuring the parents with their three daughters. at the end of a lecture,” an inevitable result of Upon Margaret’s death, Walter married his “[m]athematicians are very used to listening to former student Wafika al-Katifi and accepted her lectures which we do not understand.” A familiar Moslem faith. This trajectory of religious affiliations scene at meetings would be Walter with a younger would result in remarkable situations; for example, attendee patiently addressing mathematical ques- once when in Israel, “I stayed in a Presbyterian tions. These interactions often would lead to Guest House in Jerusalem…and I found myself detailed answers at the meeting or by mail soon on Sunday morning accompanying the hymns on after (this process was important for my career), the piano, a curious place and occupation for a and he became an important research catalyst to 518 Notices of the AMS Volume 62, Number 5 the complex analysis community. In his phrasing, “…I found myself acting as a sort of Post Office.” His standing in British mathematics during the Cold War, along with this zeal for travel and sci- entific contact, had other consequences; however, many significant trips are not mentioned in the book. Visits to the USSR (1960) and China (1977) (both with Margaret) brought important recogni- tion to mathematicians in both countries. In 1960 he was writing his book on meromorphic functions, where work of A. A. Goldberg would be highlighted. At the time, Goldberg was little known, since he was at Uzhgorod, a small provincial university. Moscow authorities were likely surprised that Goldberg’s name was the first on a list Walter provided his hosts, and Goldberg was able to come to Moscow while Hayman was lecturing there. This imprimatur seems to have impressed the Soviet authorities, and Goldberg was then able to defend his (second) thesis and become a professor at Lviv University, Photo courtesy of Christine Cockett,of Department Mathematics, University of York, UK. where he developed a major research program and Walter Hayman. group. Their 1977 China trip came soon after the end of China’s Cultural Revolution. An American dele- in London [MR 0217268]; it was praised not only gation, led by Saunders Mac Lane, had visited China for the quality and abundance of problems but for shortly before, during the Cultural Revolution, but its coherent organization into research areas, ac- Walter’s interest had already been piqued by a companied by general background discussion.