{"id":2743,"date":"2020-04-13T23:45:15","date_gmt":"2020-04-14T03:45:15","guid":{"rendered":"http:\/\/blogs.ams.org\/beyondreviews\/?p=2743"},"modified":"2020-04-14T07:21:38","modified_gmt":"2020-04-14T11:21:38","slug":"john-horton-conway","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/beyondreviews\/2020\/04\/13\/john-horton-conway\/","title":{"rendered":"John Horton Conway"},"content":{"rendered":"

John Horton Conway<\/a> died<\/a> on April 11 of COVID-19. He was 82 years old. In the midst of social distancing measures to fight the coronavirus pandemic, a common refrain is “life goes on”.\u00a0 But sometimes it doesn’t.<\/p>\n

Conway was an emeritus professor at Princeton University.\u00a0 Among mathematicians, he was known for his breadth and cleverness, as well as his personality and his seemingly infinite curiosity.\u00a0 \u00a0In MathSciNet, a bit over one quarter of his papers are in number theory, about a sixth in group theory, and a tenth in convex or discrete geometry.\u00a0 The rest are dispersed about 20 other classes in the MSC.\u00a0 Conway managed to make lasting contributions in those other 20 areas, such as his work in algebraic topology and knot theory, where he has an invariant named after him: the Alexander-Conway polynomial.\u00a0 Meanwhile, behind the scenes, Conway was frequently contributing puzzles, games, and ideas to Martin Gardner<\/a>, who would write about them in his famous column in\u00a0Scientific American<\/em><\/a>.<\/p>\n

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In the Mathematical Reviews database, Conway has 73 coauthors<\/a>.\u00a0 \u00a0A lot of them are famous, but a lot of them not.\u00a0 Conway seemed driven by curiosity, not by reputations when working with people.<\/p>\n

Many people know of Conway because of the Game of Life<\/a> (also here<\/a>).\u00a0 Like many neophyte programmers, Life was one of the first things I programmed.\u00a0 In my case it was in Fortran on a Hewlett-Packard machine that used punch cards.\u00a0 It was a great project for beginning programming because it was also a very simple model of a biological system.\u00a0 For a young math major, this example was notable because all the models and applications in classes so far were based on calculus.\u00a0 This clearly was not.<\/p>\n

A lot of people also know Conway as one of the coauthors of the impressive and classic book Winning Ways for your Mathematical Plays<\/a>.\u00a0 (Sadly, the other two coauthors, Elwyn Berlekamp<\/a> and Richard Guy<\/a>, also died in the past year or so.)\u00a0 The beginning\u00a0 and end of our review of the first edition of the book quickly tell you the truth about it: “The two volumes are crammed to the brim with information, colored illustrations and examples … The thrust of the book lies in the direction of formulating exact or suboptimal polynomial strategies for very broad classes of combinatorial games. It is likely to remain an eminent leader in this field for many years to come.”\u00a0 His book on sphere packings<\/a> with Neil Sloane<\/a>\u00a0is another classic.<\/p>\n

Conway was one of the authors of the monumental Atlas of Finite Groups<\/a>.\u00a0 When I first heard about the Atlas, I thought, “That’s crazy.”\u00a0 I turned out to be half right, it was crazy brilliant.\u00a0 The core of the book is a compilation of the character tables<\/a> of all the finite simple groups known at the time.\u00a0 By some miracle, the authors were able to convince the publisher to produce the book in a large format (42 x 31.6 x 2.9 cm), which was helpful for bigger groups with bigger tables.\u00a0 \u00a0It was bulky to carry and had a tendency to bend and to curl at the edges.\u00a0 Our reviewer, Robert Griess<\/a>, suggested that the tables be made available on tape.\u00a0 [Note: See http:\/\/brauer.maths.qmul.ac.uk\/Atlas\/.]<\/a> The Atlas was clearly an inspiration for the Atlas of Lie Groups and Representations<\/a>, which is completely online.<\/p>\n

Conway had a knack for naming things, as in his famous paper “Monstrous moonshine” with Simon Norton.\u00a0 (The complete review is below.)\u00a0 The paper conjectures remarkable correspondences between conjugacy classes of the finite simple group called the Monster and congruence subgroups of the modular group, PSL(2,$\\mathbb{Z}$).\u00a0 The conjecture was proved in MR1172696<\/a> by Richard Borcherds<\/a>, who was a Ph.D. student of Conway.<\/p>\n

Conway’s influence was wide, as was his renown.\u00a0 Shortly after Conway’s death, nice posts quickly began springing up, a few by mathematicians who knew Conway only slightly, but had strong memories of their handful of interactions with him.\u00a0 Here are links to just a few of them.<\/p>\n