# John Horton Conway

John Horton Conwaydied4月11日的Covid-19。他82岁。在社会疏远措施中，对抗冠状病毒大流行，一个常见的避免是“生活继续”。但有时它没有。

Conway是普林斯顿大学的Emeritus教授。在数学家中，他以宽度和聪明而闻名，以及他的个性和似乎无限的好奇心。在Mathscinet中，他的论文中有一点是数字理论，大约六分之一的阶段理论，以及凸面或离散几何形状的十分之一。其余部分在MSC中分散约20个其他类。Conway设法在其他20个地区做出持久的贡献，例如他在代数拓扑和结理论中的工作，他在他身上命名为他：亚历山大康威多项式。同时，在幕后，康威经常贡献谜题，游戏和想法Martin Gardner，谁会在他身上写下他们着名专栏科学的美国人

In the Mathematical Reviews database, Conway has73 coauthors。很多人都很有名，但很多人都没有。Conway似乎受到好奇的推动，而不是与人们合作时的声誉。

Many people know of Conway because of theGame of Life（还here）。像许多新代理程序员一样，生活是我编程的第一件事之一。在我的情况下，它在使用打卡的Hewlett-Packard机器上的Fortran。这是一个伟大的项目，因为它也是一个非常简单的生物系统模型。对于年轻的数学专业，这个例子是值得注意的，因为到目前为止的课程中的所有模型和应用程序都是基于微积分。这显然不是。

Conway was one of the authors of the monumental一种tlas of Finite Groups。When I first heard about the Atlas, I thought, “That’s crazy.” I turned out to be half right, it was crazy brilliant. The core of the book is a compilation of the字符表of all the finite simple groups known at the time. 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. It was bulky to carry and had a tendency to bend and to curl at the edges. Our reviewer,罗伯特格里斯，建议表可以在磁带上提供。[注意：见http://brauer.maths.qmul.ac.uk/Atlas/.]地图集显然是一个灵感谎言团体和陈述的图谱，它在线完全。

Conway had a knack for naming things, as in his famous paper “Monstrous moonshine” with Simon Norton. (The complete review is below.) 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,$\mathbb{Z}$). The conjecture was proved inMR1172696.经过Richard Borcherds，谁是博士学位。康威学生。

Siobhan Roberts写了一个很好的康威概况这Guardian2015年。她还发表了一个引人入胜的传记，标题为Genius at play

MR0654501
Berlekamp, Elwyn R.;Conway, John H.;盖伊，理查德K.

Games in general.学术出版社，Inc。[Harcourt Braces Jovanovich，Publishers]，伦敦 - 纽约，1982.XXXI.+426+xipp. ISBN: 0-12-091150-7; 0-12-091101-9
90dxx（05-02 90-02）

MR0654502
Berlekamp, Elwyn R.;Conway, John H.;盖伊，理查德K.

90dxx（05-02 90-02）

Chapter 8: All small games, remote stars, computing atomic weights for analysing Hackenbush.

Chapter 10: Analysis of the union (move in any number of component games) of partizan games, normal play. (Smith’s result for impartial unions is cited in Chapter 11.) Analysis of urgent unions (the game ends as soon as its first component does) of partizan games, normal and misère play.
Chapter 11: Games with infinitely many positions but only finitely many moves: infinite ordinal numbers. Games which may not end: loopy partizan games [see also the reviewer and U. Tassa, Math. Proc. Cambridge Philos. Soc.92（1982），193-204]。Loopy Hackenbush。
Chapter 12: Loopy impartial games: to win need remoteness in addition to$p，n$labeling. Entailing move games such as the following: either split a stack of coins into two smaller ones, or remove the top coin from a stack. In the latter case, the opponent has to move in the same stack.

Chapter 14: Games played by turning coins. Connection with Nim-multiplication.

Finally some comments about notation for other finite groups. Several recommendations in 5.2 really are at variance with general usage. The authors mention$C_m$对于循环的订单组$m$.but not${\ bf z} _m$! Their term “diagonal product”$A\triangle B$被称为回调或纤维产品。基本组的最常见的符号是$p^{1+2n}$或者$p_ \ epsilon ^ {1 + 2n}$。Since notation for an extension$A\cdot B$沿着升序读取左右读取，写入更适合$（a \ times b）\ frac12 $$\ frac12（a \ times b） （ii）：在第6节中讨论了各个表的组织。有关良好的示例，请参阅第XXIV页面。让G是简单的群体。表格块与每个块对应于表单的扩展 m.g.a 那where m .是Schur乘法器的循环商a是外部万态体群的循环子组;因为有原因为什么这些案件足以（几乎），见6.5和6.6。 在块的左侧是向下运行的字符列表（\ chi_1 = 1，\ chi_2，\ chi_3，\ cdots）及其指标（0， + 或者 - 由于角色不是真实的，由真正的代表提供，或者是真实的，但没有得到真正的代表所带来的）。横跨顶部是一个有几行关于列的信息（由共轭类索引，C_i,\;i=1,\cdots,k）。这experience of the last 25 years has shown the importance of enriching the traditional “classic” character table to include power maps (i.e., forn\in{\bf Z}那which classes contain the n th powers of elements from a fixed class), factorizations (i.e. if g \以c_i$$\pi$是一组素质和$g = g_ \ pi g _ {\ pi'}$是这unique commuting factorization of$g$在to a$\pi$-element and a$\ pi'$-element, which$C_j$包含$g_ \ pi$), and so on. A simple application of this information, which is not possible to execute with a strictly classical table, is to find the dimension of the space of cubic invariants on a module$v$affording the character$\ chi$。对称张量立方体的角色$v $$g\mapsto \frac16\{\chi(g)^3+3\chi(g)\chi(g^2)+2\chi(g)^3\}所以它的内在产品具有琐碎的特征G给出答案。 这difficulty of getting these blocks correct increases generally according to the sequencem=1$$a=1$;$a=1$;$m，a$arbitrary. Indeed the authors acknowledge errors which turned up as the book went to press (see page xxxii, bottom). How the notations extend across the several upward and downward extensions is articulated well.
（iii）：最后一部分一种tlastext consists of three tables and a list of references. (1) Partitions and classes of characters for$s_n$那useful, say, in working out particular invariants of the group in question. (2) Involvement of sporadic groups in one another (the single “?” in this一种tlas表现在被声称是“$-$“在R. A. Wilson的最近工作中）。（3）超过250个简单群体的订单，基础10的订单和分解形式和SCUR乘法器和外部万态体组。
（iv）参考书目仅限于（i）关于有限简单群体的家庭的一些非常一般的作品和（ii）26个散发群中的每一个的冗长物品清单。
Absolute初学者的调查文章（无证据）值得一提，可以进入（i），例如，由R. Carter的纸张[J.伦敦数学。SOC。40(1965), 193–240;MR0174655.] for groups of Lie type and a paper by the reviewer [in数学和物理中的顶点运算符(Berkeley, Calif., 1983), 217–229, Springer, New York, 1985;MR0781380] for sporadic groups. Also, references for Schur multiplier and automorphism groups would be of general interest.

Norton已显示自发布以来发现的错误列表。一个是不合适的字符表！值得一提的是，聊天何何最近发现了最大的$7$-local subgroup of the Monster not on the一种tlaslist. There may be a problem with the list of maximal subgroups for${\rm Co} _1$
{审核人的言论：审稿人对少数情况下奖学金的不正确感到失望（尽管XXXII第8.5.1节的免责声明）。没有完全证明怪物字符表的正确性（虽然没有怀疑）。（a）共轭类的测定需要足够了解子组中的元素的胶合剂${\bf M}$形式$2^{1+24}\cdot{\rm Co}_1$;这authors guessed the basic information, then proceeded. (b) The existence of the irreducible character of degree 196883 was taken as a hypothesis (196883 is the smallest number which could be the degree of a nonprincipal character); a proof that such a character exists was claimed by Norton in 1981 but no manuscript has appeared, and its relationship with (a) has not been explicitly stated; existence of such a character is necessary to complete the program devised by J. G. Thompson [Bull. London Math. Soc.11.（1979），没有。3,340-346;MR0554400.] for proving uniqueness of${\bf M}$
{It would have been helpful to have some recent references, e.g. to the reviewer’s recent work on code loops. The reviewer understands that future editions will contain no new references.
{The book is attractive in appearance. The cover is a cherry red with white writing on stiff cardboard. The authors’ names form a neat matrix listed vertically in alphabetical order (which agrees with their respective ages, apparently), each with two initials and a 6-letter last name. The price is extremely fair. The authors are to be commended for their influence on the price and for getting the publisher to replace the originally intended soft binding.
{这本书对于大多数公文包来说都是很大的大。在审稿人的副本上绑定的绑定变形并干扰了易于关闭和开放的书，以平躺在桌子上。由于与结合的斗争，附近的页面的边缘已经开始受到困扰。一个想法是使磁带上的表格，可能是打算计算机计算的用户的重大努力。
{数学社区（和物理社区）应该感谢造物者一种tlasfor their extremely fine service. An appreciation and use of the finite simple groups might be expected to spread noticeably faster as a result.}

Reviewed byR. L. Griess

MR0258014
Conway，J. H.

55.20

In this essential paper (i) a new efficient notation for describing specific knots is expounded, (ii) identities are reported which reflect the behaviour of knot invariants on changing some structure elements coded in the notation, (iii) lists of all prime knots up to 11 crossings and of all prime links up to 10 crossings are given in this notation, a census which checks (and corrects) and enlarges the existing tables still based on Tait’s, Little’s and Kirkman’s work before 1900. The ideas are presented here in expository style, whereas a more technical paper with more complete presentation of the subject is promised.

Reviewed byH. E. DeBrunner.