John Haigh, who died on 9 March 2021 aged 79, was the pre-eminent populariser of probability for his time. Through many publications and media appearances, he perfected the rare art of explaining subtle concepts and calculations to those who would claim no mathematical knowledge. Though his audiences may not have realised it, his standards were high; he never shielded them from a calculation they could do or a concept they could master. He recounted with delight how a colleague had reported her stockbroker husband saying to her at midnight ‘I can’t come to bed just yet dear: I have to finish one of the calculations in Dr Haigh’s book’.

John was born on 31 December 1941 and grew up as an only child in Skelmanthorpe, a village near Huddersfield in Yorkshire, where his father worked in the woollen mill and his mother in the canteen. His Methodist upbringing gave John a valuable objectivity in later life as an expert on gambling: gambling was frowned upon, but winning through gambling was especially deprecated. From grammar school (‘three hours homework every night’), he won a State Scholarship to read mathematics at Brasenose College Oxford, gaining first-class honours and a University Prize in 1963. Soccer provided a social as well as sporting escape from the general rugby-playing ex-public-school milieu, and John rose to win a Blue, playing for his university against Cambridge at Wembley (where Oxford lost 5–2). Students then were not supposed to gain both a Blue and a First, as the sporty and scholarly subpopulations of undergraduates were largely distinct.

D. G. Kendall left Oxford during John’s undergraduate years to be the first holder of the Chair of Mathematical Statistics at Cambridge, and his reputation was such that it was no surprise for bright students to follow him to the other place and join the re-invigorated Statistical Laboratory. With a government grant, John started as one of DGK’s research students in 1963, enrolling at Gonville and Caius College. He was unlucky in the existence of a link between Caius and his Oxford College, as without that he would have joined Kendall’s college, the recently founded Churchill, which looked after its many graduate students, whereas the old colleges neglected them.

The young Mr Kingman, as Sir John Kingman then was, took over some of Kendall’s research students in 1964. John Haigh was among them, and when Kingman left for the University of Sussex, it was natural for him to follow, though remaining registered for a Cambridge PhD. From his research studentship, John progressed to a lectureship at Sussex, where he stayed for the rest of his career, though spending summers in the 1970s at Melbourne and Stanford, and the year 1983–1984 at the University of Guelph in Canada. At Sussex, he was promoted to Senior Lecturer in 1989 and to Reader in 1993. Retirement was a progress through many stages, and John was still giving a lecture course to first-year undergraduates in his 70s.

John’s thesis was on random equivalence relations, a combinatorial topic but with a biological motivation; early papers were thus on applications of probability to questions in biology and genetics. Collaboration with the biologist John Maynard Smith led to five important joint papers, laying down the mathematical theory of concepts such as evolutionarily stable strategy, which underpin much of later thinking about evolution. Subsequent work, mostly single-authored but interspersed with joint papers with various co-authors, established John as an expert on combinatorial applied probability, especially with reference to evolution, game theory and games of chance. There was even a foray into operational research, with three papers on manpower planning.

The UK National Lottery began in 1994 and gained John’s immediate interest: his first paper on it was published less than a year later. He went on to become the academic expert on the game, contributing a read paper to the Society, ‘The statistics of the National Lottery’, in 1997. Work on this and other gambles led to John’s highly successful popular book Taking Chances: Winning with Probability (OUP), one of the Books of the Year in 1999 for the Independent newspaper. The second edition remains in print, and there are Spanish and Chinese translations.

Other books followed: in 2002 an undergraduate text, Probability Models (Springer), and in 2005, with Rob Eastaway, How to Take a Penalty, another popular success, running to an updated edition as The Hidden Mathematics of Sport (Portico) in 2011, and with a new edition due in 2021. In 2012, John was a natural choice to contribute Probability: A Very Short Introduction to Oxford University Press’s successful series of such titles.

Publicity around his first book led to many invitations to speak and write articles about ways in which ‘probability’ can impinge on everyday existence, and John became something of a media pundit, appearing in TV discussions with Carol Vorderman, Peter Snow and others on topics ranging from roulette to pyramid selling. With a natural authority of manner, and remaining obviously a Yorkshireman despite having moved south permanently at 18, John could be relied upon for a transparent exposure of any fraudulent arithmetical claim put out by a marketing department. He was profiled in the Independent on Sunday (1999) and the Guardian (2005). At the other end of the newspaper spectrum, his analysis of the likelihood of the team who score first winning a football match appeared in the Sun.

Further media exposure came as part of ‘spreading the word’, to young people especially: John was the Schools Lecturer in 2005–2006 for the RSS, and in 2006 one of the two speakers for the London Mathematical Society’s Popular Lectures. Non-media exposure also increasingly came John’s way. He and the author of this obituary were supplied by the RSS as its team to report on ‘The randomness of the National Lottery’ to the regulator for the lottery’s first 3 years. Our reports, received in a manner that betrayed lack of comprehension, were shelved, but a number of years later one was leaked to the press, and still had enough interest to merit the main headline in the Observer one Sunday.

Other consultancy work followed, such as for the Advertising Standards Authority, and was combined with appearances as expert witness on the topic of ‘randomness’ in criminal trials, including high-profile cases involving alleged fixing of horse races.

Back at the University of Sussex, John developed a legendary reputation for being able to convince even the most recalcitrant non-mathematical student that statistics could and should be grappled with. He created the stochastic component of the course Forensic Science and the Legal Process, bravely taught to a mixed group of chemistry students and law students. Latterly, in semi-retirement, he invented and gave the course Mathematics in Everyday Life, well received as part of the core curriculum for first-year mathematics. That too gave rise to a textbook, with the same title, published by Springer in 2016 and now in a second edition.

Service to his university and his discipline was a salient part of John’s career. Within Sussex University, he served 6 years as Chairman of Mathematics, through a fraught period of near-forced early retirements, major reorganisation and threat of closure—and, eventually, of renewal, in which he played a visionary role. John also organised Sussex’s initial registration under the Data Protection Act, chaired a succession of major committees, served on the Senate for almost 14 years and on the University Council for 9.

External service began early, with work as an examiner for the pre-merger Institute of Statisticians, continuing with what eventually became the RSS Graduate Diploma all the way until examinations ceased in 2017. Also for the RSS, John was involved with all the journals: Assistant Editor of Series B, Joint Editor of Series D, Book Reviews Editor for the journals generally, and stints on the editorial boards of Series A and Significance. He chaired the Sussex Local Group, now alas no longer in existence. Similarly, for the Mathematical Association, he chaired the Sussex Branch and co-organised its Mathematics Masterclasses. He served for 20 years as University Assessor for appointments to the Statistician grade in the Civil Service, until outsourcing finally succeeded in making the job not worth the trouble.

In his mid-70s, John developed a blood condition that left him increasingly tired in the intervals between successive transfusions. He was very open about his condition, reporting to friends in autumn 2020 that he was happy still to be around after being told in the spring to expect only a few months to live. He continued to be intellectually active, expressing delight that his 9-and-half-year-old grandchild was fascinated when he showed her ‘properties of the Möbius Strip and, on the laptop, some of Escher’s Impossible Figures’. John was still corresponding in his last few days with Rob Eastaway about probability problems in sport.

Never given to display, John was well suited to marriage but took some years to achieve that state. He and Kay had two sons, Adam and Daniel, but Daniel died of colon cancer in 2007, aged 27. John is survived by Kay, Adam and Izzy (Isabella), daughter of Adam and his wife Kelly.

John Haigh 于 2021 年 3 月 9 日去世，享年 79 岁，是他那个时代最杰出的概率普及者。通过许多出版物和媒体露面，他完善了向那些声称没有数学知识的人解释微妙概念和计算的罕见艺术。虽然他的观众可能没有意识到这一点，但他的标准很高；他从来没有让他们远离他们可以做的计算或他们可以掌握的概念。他高兴地讲述了一位同事如何报告她的股票经纪人丈夫在午夜对她说“亲爱的，我还不能睡觉：我必须完成黑格博士书中的一个计算”。

约翰出生于 1941 年 12 月 31 日，在约克郡哈德斯菲尔德附近的一个村庄 Skelmanthorpe 作为独生子长大，他的父亲在那里的毛纺厂工作，母亲在食堂工作。他的卫理公会教养使约翰在以后的生活中作为赌博专家获得了宝贵的客观性：赌博不受欢迎，但获胜通过赌博尤其被弃用。从文法学校开始（“每晚三小时作业”），他获得了牛津布拉森诺斯学院数学系国家奖学金，并于 1963 年获得一等荣誉和大学奖。在前公立学校环境中打橄榄球，约翰赢得了蓝军，在温布利（牛津以 5-2 输掉了比赛）为他的大学对阵剑桥。学生不应该同时获得蓝色和第一，因为本科生的运动和学术亚群在很大程度上是不同的。

DG Kendall 在约翰本科期间离开牛津大学，成为剑桥大学数学统计主席的第一位持有人，他的声誉如此之高，以至于聪明的学生跟随他到另一个地方并加入重新焕发活力的统计实验室也就不足为奇了. 在政府资助下，约翰于 1963 年成为 DGK 的研究学生之一，就读于冈维尔和凯厄斯学院。不幸的是，凯厄斯和他的牛津学院之间存在联系，否则他会加入肯德尔学院，最近成立的丘吉尔学院，该学院负责照顾许多研究生，而旧学院则忽略了他们。

年轻的金曼先生，就像当时的约翰金曼爵士，在 1964 年接管了肯德尔的一些研究生。约翰海格就是其中之一，当金曼离开去萨塞克斯大学时，他很自然地跟随，尽管仍然注册了剑桥博士。从他的研究学生身份，约翰继续在苏塞克斯大学担任讲师，他在那里度过了余下的职业生涯，尽管 1970 年代夏天在墨尔本和斯坦福度过，1983-1984 年在加拿大圭尔夫大学度过。在苏塞克斯，他于 1989 年晋升为高级讲师，1993 年晋升为读者。退休是经历了许多阶段的进步，约翰仍然在为 70 多岁的一年级本科生讲课。

约翰的论文是关于随机等价关系的，这是一个组合主题，但具有生物学动机；因此，早期的论文是关于将概率应用于生物学和遗传学问题的。与生物学家约翰·梅纳德·史密斯 (John Maynard Smith) 的合作导致了五篇重要的联合论文，奠定了诸如进化稳定策略等概念的数学理论，这些理论为后来关于进化的许多思考奠定了基础。随后的工作，主要是单一作者，但穿插着与不同合著者的联合论文，使约翰成为组合应用概率方面的专家，尤其是在进化、博弈论和机会博弈方面。甚至还涉足了运筹学，发表了三篇关于人力规划的论文。

英国国家彩票始于 1994 年，引起了约翰的直接兴趣：不到一年后，他发表了第一篇关于它的论文。他继续成为该游戏的学术专家，于 1997 年向该协会贡献了一篇阅读论文“国家彩票的统计数据”。在这方面和其他赌博方面的工作导致约翰非常成功的畅销书《把握机会：赢得概率(OUP)，独立报1999 年的年度图书之一。第二版仍在印刷中，有西班牙文和中文译本。

其他书籍紧随其后：2002 年本科教科书《概率模型》（Springer），2005 年与 Rob Eastaway 合着的《如何接受处罚》，另一个受欢迎的成功，2011 年更新为The Hidden Mathematics of Sport (Portico) ，并在 2021 年推出新版本。 2012 年，John 是自然选择，他为牛津大学出版社成功出版的此类书籍系列贡献了《概率：非常简短的介绍》。

围绕他的第一本书的宣传导致了许多关于“概率”如何影响日常生活的演讲和撰写文章的邀请，约翰成为了某种媒体专家，出现在与卡罗尔·沃德曼、彼得·斯诺和其他人的电视讨论中。从轮盘赌到传销。凭借与生俱来的举止权威，尽管 18 岁已永久移居南方，但显然仍是约克郡人，因此可以依靠约翰透明地揭露营销部门提出的任何欺诈性算术索赔。周日独立报（1999 年）和卫报（2005 年）对他进行了介绍。在报纸光谱的另一端，他对首先得分的球队赢得足球比赛的可能性的分析出现在孙。

进一步的媒体曝光是“传播信息”的一部分，尤其是对年轻人：约翰在 2005-2006 年担任 RSS 的学校讲师，并在 2006 年成为伦敦数学学会大众讲座的两位发言人之一。约翰的方式也越来越多地出现在非媒体曝光上。他和这篇讣告的作者由 RSS 作为其团队提供，以在彩票的前 3 年向监管机构报告“国家彩票的随机性”。我们的报告以一种暴露出缺乏理解的方式收到，被搁置，但几年后，一份被泄露给媒体，仍然有足够的兴趣值得在一个星期天成为观察家的主要标题。

随后进行了其他咨询工作，例如广告标准局，并结合作为刑事审判中“随机性”主题的专家证人出庭，包括涉及涉嫌操纵赛马的备受瞩目的案件。

回到萨塞克斯大学，约翰因能够说服即使是最顽固的非数学学生相信统计数据可以而且应该解决这一问题而享有盛誉。他创建了法医科学和法律程序课程的随机部分，勇敢地教授给化学学生和法律学生的混合群体。后来，在半退休状态下，他发明并开设了日常生活中的数学课程，作为一年级数学核心课程的一部分受到了好评。这也产生了一本同名的教科书，由 Springer 于 2016 年出版，现在是第二版。

为他的大学和他的学科服务是约翰职业生涯的重要组成部分。在苏塞克斯大学，他担任了 6 年的数学系主席，经历了近乎被迫提前退休、重大重组和关闭威胁以及最终更新的紧张时期，他在其中发挥了远见卓识的作用。约翰还根据数据保护法组织了苏塞克斯的初始注册，主持了一系列主要委员会，在参议院任职近 14 年，在大学理事会任职 9 年。

外部服务很早就开始了，他在合并前的统计学家研究所担任审查员，一直到最终成为 RSS 研究生文凭的工作一直持续到 2017 年考试停止。此外，对于 RSS，John 参与了所有期刊：B系列助理编辑，D系列联合编辑，一般期刊的书评编辑，以及A系列和Significance编辑委员会的工作. 他是苏塞克斯当地小组的主席，可惜现在已经不复存在了。同样，对于数学协会，他主持了苏塞克斯分会并共同组织了其数学大师班。他担任了 20 年的大学评估员，担任公务员统计员级别的任命，直到外包最终成功使这项工作变得不值得。

在 70 多岁的时候，约翰患上了一种血液病，这让他在连续输血之间的时间间隔越来越累。他对自己的病情非常开放，并在 2020 年秋季向朋友报告说，在春天被告知只能活几个月之后，他很高兴仍然在身边。他继续在智力上活跃，当他向她 9 岁半的孙子展示“莫比乌斯带的财产以及在笔记本电脑上的埃舍尔的一些不可能的数字”时，他表示很高兴。在过去的几天里，约翰仍然与罗伯·伊斯特威就体育运动中的概率问题保持联系。

约翰从不表现出来，非常适合婚姻，但花了几年时间才达到这种状态。他和凯有两个儿子，亚当和丹尼尔，但丹尼尔于 2007 年因结肠癌去世，享年 27 岁。约翰的遗体是凯、亚当和伊莎贝拉（伊莎贝拉），亚当和他的妻子凯利的女儿。