John Horton Conway

John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician, and Professor Emeritus of Mathematics at Princeton University in New Jersey.

Quotes

 * When I was on the train from Liverpool to Cambridge to become a student, it occurred to me that no one at Cambridge knew I was painfully shy, so I could become an extrovert instead of an introvert.


 * ... I have said for twenty-five or thirty years that the one thing I would really like to know before I die is why the monster group exists."

Sphere Packings, Lattices and Groups (1988)

 * by J.H. Conway & N.J.A. Sloane (3rd edition, 1993)


 * [I]n two dimensions the... [19 point] hexagonal lattice solves the packing, kissing, covering and quantizing problems. ...[T]his ...book is ...a search for similar nice patterns in higher dimensions.
 * Preface to 1st edition


 * We are planning a sequel... The Geometry of Low-Dimensional Groups and Lattices which will contain two earlier papers...
 * Ref: John H. Conway, Complex and integral laminated lattices, TAMS 280 (1983) 463-490 [2,6,22]; John H. Conway, The, The Mitchell group, and related sphere packings PCPS 93 (1983) 421-440 [2,4,7,8,22]

1 Sphere Packing and Kissing Numbers

 * In this chapter we discuss the problem of packing spheres in and of packing points on the surface of a sphere . The kissing number problem is an important special case of the latter, and asks how many spheres can just touch another sphere of the same size.


 * The classical... problem is... how densely a large number of identical spheres ([e.g.,] ball bearings...) can be packed together. ...[C]onsider an aircraft hangar... [A]bout one quarter of the space will not be used... One... arrangement... the face-centered cubic (or fcc) lattice... spheres occupy $$\pi / \sqrt{18} = .7405...$$ of the total space.... the lattice packing has density $$.7405...$$.


 * The classical... problem... asks: is this the greatest density..? an unsolved problem, one of the most famous...


 * The general... problem... packing... in n-dimensional space. ...[T]here is nothing mysterious about n-dimensional space. A point in real n-dimensional space $$\R^n$$ is... a string of real numbers $$x = (x_1,x_2,x_3, ...,x_n)$$. A sphere in $$\R^n$$ with center $$u = (u_1,u_2,u_3, ...,u_n)$$ and radius $$\rho$$ consists of all points $$x$$... satisfying $$(x_1-u_1)^2 + (x_2-u_2)^2+ ... +(x_n-u_n)^2 = \rho^2$$.

Quotes about John Horton Conway

 * He is Archimedes, Mick Jagger, Salvador Dalí, and Richard Feynman, all rolled into one. He is one of the greatest living mathematicians, with a sly sense of humour, a polymath’s promiscuous curiosity, and a compulsion to explain everything about the world to everyone in it.