John Horton Conway. 26 December 1937—11 April 2020

John Conway was without doubt one of the most celebrated British mathematicians of the last half century. He first gained international recognition in 1968 when he constructed the automorphism group of the then recently-discovered Leech lattice, and in so doing discovered three new sporadic simple groups. At around the same time he invented The Game of Life, which brought him to the attention of a much wider audience and led to a cult following of Lifers. He also combined the methods of Cantor and Dedekind for extending number systems to construct what Donald Knuth (ForMemRS 2003) called ‘surreal numbers’, the achievement of which Conway was probably most proud. Throughout his life he continued to make significant contributions to many branches of mathematics, including number theory, logic, algebra, combinatorics and geometry, and in his later years he teamed up with Simon Kochen to produce the Free Will theorem, which asserts that if humans have free will then, in a certain sense, so do elementary particles. In this biographical memoir I attempt to give some idea of the depth and breadth of Conway's contribution to mathematics.

Coleman Automorphisms of Extensions of Finite Characteristically Simple Groups by Some Finite Groups

Let [Formula: see text] be an extension of a finite characteristically simple group by an abelian group or a finite simple group. It is shown that every Coleman automorphism of [Formula: see text] is an inner automorphism. Interest in such automorphisms arises from the study of the normalizer problem for integral group rings.

Non-abelian anyons and some cousins of the Arad-Herzog conjecture

Long ago, Arad and Herzog (AH) conjectured that, in finite simple groups, the product of two conjugacy classes of length greater than one is never a single conjugacy class. We discuss implications of this conjecture for non-abelian anyons in 2 + 1-dimensional discrete gauge theories. Thinking in this way also suggests closely related statements about finite simple groups and their associated discrete gauge theories. We prove these statements and provide some physical intuition for their validity. Finally, we explain that the lack of certain dualities in theories with non-abelian finite simple gauge groups provides a non-trivial check of the AH conjecture.

Group Knowledge and Mathematical Collaboration: A Philosophical Examination of the Classification of Finite Simple Groups

In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very little attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects.

The Importance of the Epi-Transcriptome in Translation Fidelity

RNA modifications play an essential role in determining RNA fate. Recent studies have revealed the effects of such modifications on all steps of RNA metabolism. These modifications range from the addition of simple groups, such as methyl groups, to the addition of highly complex structures, such as sugars. Their consequences for translation fidelity are not always well documented. Unlike the well-known m6A modification, they are thought to have direct effects on either the folding of the molecule or the ability of tRNAs to bind their codons. Here we describe how modifications found in tRNAs anticodon-loop, rRNA, and mRNA can affect translation fidelity, and how approaches based on direct manipulations of the level of RNA modification could potentially be used to modulate translation for the treatment of human genetic diseases.