# nLab John Horton Conway

Not to be confused with John Bligh Conway?, the analyst.

# Contents

## Introduction

John Horton Conway (born 26 December 1937, died 11 April 2020) was an English mathematician. He developed new ideas in many branches of mathematics, notable, here, for the Conway polynomial of a knot, and for study of the Conway groups, $Co_{1}, Co_{2}, Co_{3}$, three of the sporadic finite simple groups.

## Reminiscences

By Gavin Wraith, at the nForum in this post.

I first met John Conway while he was manning a stall for the Archimedeans at the beginning-of-the-year student fair in the Guildhall in Cambridge. He was demonstrating a computer, built of string and meccano, that had to be fed ball-bearings. I think it was 1957.

One of the first mathematical lollipops he showed me was a very slick proof that a triangle of nonzero area whose sides were in rational proportion and whose angles were in rational proportion must be equilateral. Hint: the cyclotomic field of $N$-th roots of unity has $\phi(N)$ automorphisms. But ruler-and-compass construction shows that there can only be 2 triangles with given sides. So $N$ has to be 3 times a power of 2.

In those days it was knots and sphere-packing. Later came games. For years he had a running exchange of puzzles with someone in the North of England who made them as toys. He was very hands-on: popper beads for demonstrating knots and links, and strange wooden devices for calculating the touching-graph of circle-packings using pennies and a ruler to shove them up tight.

The last time I saw him not in the Mill Lane maths department tearoom he was tiling his kitchen floor with Penrose kites and darts. My mother used to babysit his daughters. Some of the faculty at Cambridge thought that he was a disturbing influence on their students; not serious enough.

## References

category: people

Last revised on April 27, 2020 at 09:39:30. See the history of this page for a list of all contributions to it.