**Bryce McLeod** was a Scottish mathematician who worked on linear and nonlinear partial and ordinary differential equations.

- The University of Aberdeen Bursary Competition was an important event for those in their final year at high school and McLeod had sat the examination and had been awarded a top bursay.
- At this time McLeod was aiming to become a school teacher.
- McLeod spent two years at Christ College, Oxford, working for his B.A. His tutor at the college was Theodore William Chaundy (1889-1966) who was also a University Reader in Mathematics.
- During the time McLeod was studying for his Oxford B.A., Chaundy taught the courses 'Elementary differential equations and Legendre's functions' and 'Partial differential equations.
- Parabolic equations' and McLeod became fascinated with the topic.
- McLeod was awarded a First Class B.A. by the University of Oxford in 1952.
- After obtaining his B.A. from Oxford, McLeod spent the year 1952-53 in Vancouver funded by a Rotary Foundation Fellowship from Aberdeen.
- However, although it wasn't a top place for mathematics, nevertheless McLeod had a great year there and made many good contacts.
- While still undertaking research, McLeod was appointed as a Junior Lecturer in Mathematics at Oxford in 1956, a position he held for two years.
- These papers mark the beginnings of a long publication list and we note that MathSciNet lists 156 published items for McLeod.
- In 1958, after completing the work for his D.Phil., McLeod was appointed as a lecturer in Mathematics at the University of Edinburgh.
- This was a move to a place that McLeod knew well since he had spent several summers and sabbaticals in the United States where he spent most time at the University of Wisconsin and the University of Pittsburgh.
- Since the early 1960s, McLeod has played an important role in this work.
- For example, in 1962 he devised a proof, far ahead of its time, that an infinite system of coagulation - fragmentation equations has non-trivial solutions; in 1971, his seminal paper with Tosio Kato on the asymptotic behaviour of functional differential equations broke completely new ground in what was then a new area; in 1977, with Paul Fife he established that solutions to reaction-diffusion equations converge to travelling waves (this now-classic paper has since been extended, in particular, by McLeod and others to an important integral equation from mathematical neuroscience); in 1979, he devised an ingenious proof that Krasovskii's conjecture concerning the maximum slope of a water wave is false; in the 1980s, his work with Stuart Hastings and others was among the first contributions to the rediscovery in modern times of the Painlevé transcendents; in fundamental work with Avner Friedman in 1985 he proved that for reaction-diffusion equations with certain nonlinearities, solutions blow up in finite time and in 1995, with Gero Friesecke, he showed that dynamics provides a mechanism which prevents the solution to a model of phase transformations from generating an infinitely fine microstructure.
- Bryce McLeod is an applied analyst with a terrific ability in problem solving.
- McLeod gave the Naylor Lecture at the London Mathematical Society Annual General Meeting on 16 November 2012.
- McLeod has written one book, Classical methods in ordinary differential equations.
- McLeod was the thesis advisor for many students at both Oxford and at Pittsburgh.
- In 1962 Ian Michael became McLeod's first research student.
- At one point in his Naylor lecture of 2012 Bryce emphasised the importance of asking questions.
- We have already mention that McLeod was awarded the Naylor Prize and Lectureship in Applied Mathematics by the London Mathematical Society in 2011.
- They had returned to Abingdon most summers during their twenty years in the United States and McLeod had maintained strong contacts with the Oxford Centre for Industrial and Applied Mathematics and the Oxford Centre for Nonlinear PDEs. McLeod spent the last years of his career at the latter Oxford Centre.
- Let us end with some tributes to McLeod.

Born 23 December 1929, Aberdeen, Scotland. Died 20 August 2014, Abingdon, near Oxford, England.

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Origin Scotland

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive