Bryce McLeod received his early education at Aberdeen Grammar School, where his grandfather had been Head of Mathematics and Science. As was not uncommon in the Scottish education system at the time, he followed an accelerated path through the school and moved to the University of Aberdeen at the age of 16, receiving a First-Class BA degree in Mathematics & Natural Philosophy in 1950. He was awarded a scholarship to Oxford University, where he received a second First Class BA degree in 1952. His tutor there. TW Chaundy of Christ Church, was a specialist in differential equations and was influential in shaping Bryce's intellectual path; he coauthored the first of Bryce's 150-plus papers. Following a year as a Rotary Foundation Fellow in Vancouver and two years' National Service, Bryce returned to Oxford to complete a DPhil with Titchmarsh in 1958. He and Eunice married in 1956. After a spell of two years as a Lecturer in Mathematics at the University of Edinburgh, during which the first of their four children was born, Bryce returned to Wadham College, Oxford in 1960 and remained there until 1988, becoming a University Lecturer (with a much reduced college teaching load) in 1970.
Throughout this first stage of his career, Bryce had maintained regular contact with applied analysts in the US, in particular in Madison where he spent a number of sabbatical years and greatly expanded his range of contacts; indeed, his twins were born in Madison. He visited the US regularly and received many offers to cross the Atlantic. In 1988, faced with imminent mandatory retirement in the UK and feeling that (unlike today) applied analysis was not properly appreciated at Oxford, he moved to Pittsburgh, where he remained until 2007. He and Eunice had retained their house in the UK, however, and the migration reversed so that summers were often spent in Oxford, visiting the Oxford Centre for Industrial and Applied Mathematics (OCIAM) and the Oxford Centre for Nonlinear PDE (OxPDE), as well as elsewhere in Europe. When Bryce had retired from Pittsburgh they returned to live in Abingdon, while Bryce based himself in OxPDE for the remainder of his career.
Bryce was elected FRSE in 1974 and FRS in 1992. He received the Whittaker Prize of the Edinburgh Mathematical Society in 1965, the Keith Medal and Prize of the Royal Society of Edinburgh in 1987, and the Naylor Prize and Lectureship in Applied Mathematics of the London Mathematical Society in 2011.
Bryce considered himself a problem-solving mathematician rather than a builder of general theories. He liked to focus on a specific hard problem and to find something new to say about it that was at the same time rigorous, interesting and useful. He was, of course, fully au fait with modern techniques but he added to this a deep understanding in the style of the more classical tradition he had inherited from Chaundy, Titchmarsh and their predecessors. He solved problems with consummate skill across an extraordinary range of areas as diverse as fluid mechanics, general relativity, plasma physics, mathematical biology, superconductivity, Painlevé equations, coagulation processes, nonlinear diffusion and pantograph equations, among many others. He had long-lasting and productive collaborations with very many distinguished mathematicians, both applied analysts like himself and modellers whose differential equation had caught his interest: he was always interested to look at new problems unearthed by colleagues working in a more applications-focused way. His work was characterised by great lucidity of thought married to immense creativity and ingenuity of argument. Although he worked on many different problems some general themes did emerge. Prominent among these was the importance of the study of similarity solutions as indicators of more general behaviour, along with the development of a powerful suite of techniques for 'shooting' methods, especially with more than one shooting parameter. A McLeod seminar or lecture was a model of clarity: as the subject unfolded the board was filled from left to right with economical, spare notes in his characteristic hand, and the audience invariably left feeling they had witnessed a tour de force of applied analysis.
Many, many people throughout the mathematical community remember Bryce with great fondness: for his kindness and support for students and colleagues alike; for his intensely amused laughter or his rapt concentration on an explanation; for his zest for life and mathematics. Just as he was adventurous in the topics he worked on, so he and his family had many adventures along the way. For example, as they visited the US so often, Bryce and Eunice bought what Bryce termed a 'motor caravan' (in fact, a huge Winnebago) and took the family round that vast country on 'a blissful combination of vacation and mathematics'. The last words should be Bryce's: in an interview with John Ball, he was asked what advice he would give a young mathematician just starting their research career. The answer was simple: “Have fun”. Bryce certainly did that.