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.

Robert McNeill Alexander. 7 July 1934—21 March 2016

Neill Alexander graduated in natural sciences at the University of Cambridge in 1955. After a PhD at Cambridge and a lecturership at the University College of North Wales in Bangor, he was appointed to the chair of the Department of Pure and Applied Zoology at the University of Leeds in 1969. At that stage, he switched his research interests abruptly from fishes to the mechanics of legged locomotion. He conducted experiments with a variety of mammals, calculating forces, stresses and strains in muscle fibres, bones and tendons. His speciality became the application of mathematical models to animal locomotion, including repurposing the Froude number, devised by the Victorian engineer William Froude (FRS 1870) for use with ships, to estimate the speed of dinosaurs based on the spacing of their fossil footprints. Subsequent work included modelling the optimization of mammal performance and the minimization of energy costs. In 1992, following an announcement that London Zoo would have to close as a result of shortage of funds, Neill was appointed secretary of the Zoological Society of London. During the period of his secretaryship, the Society's finances recovered, with both its zoos (London and Whipsnade) breaking even in 1993 and the Society returning a surplus in each subsequent year. Neill was awarded the CBE in 2000. The National Portrait Gallery holds his portrait by John Arnison.

Sir Arnold Whittaker Wolfendale. 25 June 1927—21 December 2020

For over 50 years Arnold Wolfendale was an international leader in the fields of cosmic ray and gamma ray astronomy, making many seminal contributions. His extensive studies of the muon particle culminated in 1965 when, using an installation in the Kolar Gold Mine in India, he played a major role in the first detection of the neutrinos associated with muons produced in the atmosphere. His interests in the origin of high-energy cosmic rays were extensive and required the development of a better understanding of particle physics at energies beyond those accessible at accelerators. Recognizing that high-energy gamma rays can arise from cosmic ray interactions with the interstellar gas, he used early satellite data to argue for the galactic origin of intermediate-energy cosmic rays and for studies of the distribution of molecular hydrogen. His interests in astronomy, which he firmly held to be a branch of physics, drove him to develop a world-class activity in this area at Durham University. This achievement, in part, led to him being appointed Astronomer Royal in 1991. He used this position, and his roles as president of the Royal Astronomical Society, the Institute of Physics and the European Physical Society, to lobby tirelessly for more governmental support for science. He was an early advocate for improvements in the public understanding of science, leading by example. In his later years Arnold's interests extended to cosmology and horology, and he argued against a possible connection between cosmic rays and global warming. A brilliant communicator, Arnold gave a huge number of lectures each year to general audiences, almost to the end of his life.

Amyand David Buckingham. 28 January 1930—4 February 2021

David Buckingham was a chemical physicist and theoretical chemist who made fundamental contributions to the understanding of optical, electric and magnetic properties of molecules. Born in Australia, he was an undergraduate at the University of Sydney and the first PhD research student of John Pople (FRS 1961) at Cambridge, and there he made significant advances in the theory of intermolecular forces and nonlinear optics. He then moved to Oxford, where he and his group performed the first direct measurement of a molecular electric quadrupole moment. He was elected to the first chair of theoretical chemistry at the University of Bristol, where he wrote a particularly influential article on molecular moments, higher-order polarizabilities and intermolecular forces. His next appointment was at the University of Cambridge as the first holder of the 1968 Chair of Chemistry, and he was head of a distinguished department of theoretical chemistry for 28 years. With colleagues he pioneered experiment and theory on vibrational optical activity and developed a powerful model to predict the structures of weakly-bound molecules. A man of broad interests and achievements, he played first class cricket in the 1950s.

Graham Wood. 6 February 1934—4 November 2016

Graham Wood was a world-leading corrosion scientist who bridged both the aqueous (electrochemical) corrosion and high-temperature oxidation branches of the subject. His analytical predictions of depletion and enrichment profiles in substrate and scale during preferential oxidation have long been confirmed in practice. He also demonstrated that transient oxides can be vital solid lubricants in oxidative friction and wear processes. He elucidated ionic transport in amorphous anodic films, leading to precise models of pore initiation, development and closure, thus allowing the strict design of anodic films for practical application. He set up, and headed, the Corrosion and Protection Centre at the University of Manchester Institute of Science and Technology (UMIST) and was instrumental in initiating the Corrosion and Protection Centre Industrial Service, which, respectively, became the world's largest academic centre on the study of materials degradation and the world's largest corrosion consulting organization. While keeping active in research, he held increasingly senior administrative roles, where he established a specialist graduate school and helped prepare UMIST to full independence from the Victoria University of Manchester.

Alan Herbert Cowley. 29 January 1934—2 August 2020

Alan Cowley was one of the most creative main group chemists of his generation, and had a central role in what was often described as the renaissance of main group chemistry. Throughout his career Alan always had an eye for what was new. In his early years as an independent researcher, Alan made many fundamental contributions to the chemistry of phosphorus, not only in terms of the synthesis of new compounds but also in their study by employing novel analytical and computational methods. Starting in the 1980s he was at the forefront of emerging research into low-coordinate phosphorus chemistry and made seminal contributions in the areas of multiply bonded species, such as phosphenium ions and diphosphenes, as well as in the transition metal coordination chemistry of phosphinidenes. In the second half of his career, Alan also turned his attention to the study of single source precursors for important solid-state electronic materials, many of which were far superior to known examples. In all of the many areas in which Alan worked, he was a great collaborator with colleagues and researchers across the world, both in chemistry and in other disciplines. This was made all the easier by Alan's charm and easy-going nature, which was also manifest in the interactions he had with his many group members over a period of almost half a century. Alan was a gentleman in every sense and is much missed by friends, colleagues, collaborators and family.

Patrick David Wall. 5 April 1925—8 August 2001

Patrick (Pat) Wall was a neurophysiologist and true pioneer in the science of pain. He discovered that the sensory information arising from receptors in our body, such as those for touch and heat, could be modified, or ‘gated’, in the spinal cord by other sensory inputs and also by information descending from the brain; this meant, as is now well recognized, that the final sensory experience is not necessarily predictable from the original pain-eliciting sensory input. He used this to explain the poor relationship between injury and pain, and to illustrate the fallacy of judging what someone ‘should’ be feeling from the sensory input alone. In 1969, together with his colleague, Ron Melzack, Pat proposed the ‘gate control theory of pain’ and the circuit diagram that summarized how central spinal cord circuits can modulate sensory inputs. Later on, he began to regret that ‘goddamned diagram’, which had come to dominate his life and work, but, like all great models, it paved the way for the future. Now, over 50 years after it was first published, molecular genetic dissection of dorsal horn neuronal circuitry has indisputably confirmed that sensory inputs are indeed ‘gated’ in the spinal cord dorsal horn. Through a career that started with a medical degree in Oxford, followed by almost 20 years at Yale and MIT in the USA, and continued at University College London, Pat Wall was a highly influential, critical, creative and original thinker who revolutionized our understanding of the relationship between injury and pain, and who also became a champion for all who suffered from chronic pain.

Thomas Arthur Steitz. 23 August 1940—9 October 2018

Thomas A. Steitz was among the foremost of the generation that was responsible for an explosion in our understanding of the structure and function of biological macromolecules. His research career was one of sustained excellence over six decades, and spanned the range from determining the structures of important metabolic enzymes to understanding the structural basis of how genetic information residing in our DNA is used to make the proteins they encode. This latter effort culminated in the structure of the ribosome, for which he shared the Nobel Prize in Chemistry in 2009.

Felix Jiri Weinberg. 2 April 1928 — 5 December 2012

Felix Weinberg's teenage years coincided with World War II. He spent much of the war in Nazi concentration camps, starting with Terezin in December 1942, followed by Auschwitz in December 1943, and finally Buchenwald, from which he was liberated on 11 April 1945. He joined Imperial College, London as a research assistant in 1951 and completed his PhD by 1954. He was appointed to a personal chair as professor of combustion physics in 1967, and he stayed at Imperial for his entire career. Weinberg was distinguished for his optical and electrical studies of flames and his pioneering development of innovative combustion methods. He invented a family of powerful optical tools in combustion, using both broad spectrum and laser light sources. His work on electrical diagnostics led to applications of electric fields to control combustion and to improved understanding of ionization and soot formation. He developed novel combustion devices that incorporated distinctive heat exchangers, thereby permitting the ignition and burning of very low calorific fuel–air mixtures. All of these works had a propelling influence on the global evolution of environmentally benign combustion furnaces. His wide-ranging service to academia, industry and scientific societies included visiting scholar appointments at universities around the world, consultancies for petroleum, chemical, aerospace and defence organizations, and active membership on committees and boards of governance for many scientific and professional bodies. He was author, co-author or editor of four books and well over 200 papers in the scientific literature.

Trevor Evans. 26 April 1927 — 10 October 2010

Trevor Evans was responsible for revealing the main physical processes which take place in natural diamond both in the upper mantle of the earth, where it is stabilized by high pressure and temperature, and as it is ejected by volcanic action to the surface. By measuring the activation energies required for graphitization, he clarified the reason for its very long life as a metastable crystal, valuable both as a gemstone and as an industrial abrasive. He learned how to make diamond specimens for examination in the transmission electron microscope, which enabled his discovery of dislocation loops and platelet precipitates in nitrogen-containing (type 1) stones. In a series of exacting laboratory experiments under geologically relevant conditions he pioneered the study of the emergence of nitrogen from solution to precipitation during the ejection process. In synthetic diamonds, using high-energy electron irradiation, he was able to reproduce the sequence of all the various types of nitrogen aggregation found in natural diamond. His work played a major role underpinning the characterization of gemstones, explaining many features of their colour. For many years he led diamond research in the UK, supported by De Beers. His work stimulated and has been confirmed by research in many other laboratories around the world.