**James Murray**, the son of Peter and Sarah Murray, came from a family of plumbers. The family tradition would have seen James become a plumber but after contracting polio as a child, this was not a possibility. He said [14]:-

He spent three years at Dumfries Academy where the head of the mathematics department, Mr Ross, told him he would never make it as a mathematician! However James said that Mr Ross was an excellent mathematics teacher. Leaving Dumfries Academy, he entered the University of St Andrews where he began his university career studying chemistry. This was the result of Mr Ross's opinion of Murray's mathematical abilities. After one year he was bored with chemistry and changed to study physics. He said [14]:-I started in Moffat, a very rural and isolated part of Scotland, where there was only one non private school and you only attended until you were14. After that everyone left to get a job. However, there were two of us that went off to Dumfries Academy.

In 1950-51 Murray entered the Junior Honours class in mathematics. He won the class medal (first equal) and was awarded the Tullis Prize. In Honours Mathematics he studied the compulsory courses of geometry, algebra, analysis, statics and dynamics. He also took two special topic papers, namely fluid mechanics and partial differential equations. His most outstanding performance was in fluid dynamics. In 1953 Murray graduated from the University of St Andrews when he was awarded a B.Sc. with 1st class Honours in Mathematics. His performance was outstanding and he was awarded the Carstairs Medal for his performance in mathematics and the Miller Prize as the most distinguished graduate in science. It was not all work for Murray at university, however, for he won the University of St Andrews' first blue in table tennis and was captain of the university's billiard team. Any thoughts he had of getting a job in industry were soon changed after his experience of a summer internship at the end of his third year [14]:-However, I also found that to be boring. Alongside this I did keep up the mathematics and found I kept getting prizes and medals in it. This, of course, made me think that perhaps the teacher hadn't been right.

So, after taking his first degree, Murray remained at St Andrews to study for a Ph.D. having been awarded a Carnegie Research Scholarship. His thesis advisor was Ron Mitchell and he suggested to Murray a topic in boundary layer fluid dynamics. In these days the Air Ministry published a list of their top ten problems in fluids. Problem Number 6 at that time was flow into a pitot tube: was the speed of flow which was registered the correct speed of the aircraft? This was Murray's PhD problem. In 1954 Mitchell and Murray submitted the paperI did a summer internship in an aircraft industry, Fairey Aviation Company, near London. I worked in the theoretical division, but they had me doing the most boring jobs you could imagine. No wonder the company went bust! So, I decided against going into industry.

*Two Dimensional Flow with Constant Shear Past Cylinders with Various Cross Sections*to

*Zeitschrift für Angewandte Mathematik und Physik*. It was published in the following year. In the paper they give the following acknowledgement:-

A review of the paper states:-The authors are indebted to Dr D Borwein of the Mathematics Department, St Andrews University, for some helpful criticism during the preparation of this paper.

Having completed the work for his Ph.D. Murray was appointed as a Lecturer in Applied Mathematics, at King's College, Durham University in Newcastle upon Tyne in 1955. He had to wait for three years from his first matriculation as a research student before he was allowed to graduate with a Ph.D. by the University of St Andrews for his thesisFor the problem of two-dimensional flow with constant shear past cylinders, the author shows that the original Tsien's method of solution[(1943)]can be greatly simplified by using the natural co-ordinates where they exist. For examples, flows over elliptic and parabolic cylinders are calculated.

*Rotational Flow in Fluid Dynamics*in 1956

*.*It was the first Ph.D. in Applied Mathematics awarded by the University of St Andrews. In March of the same year he submitted (jointly with Ron Mitchell) the paper

*Flow with Variable Shear Past Circular Cylinders*to the

*Quarterly Journal of Mechanics an Applied Mathematics*. The paper, published in 1957, has the following abstract:-

After spending a year at King's College in Newcastle, Murray, who had always wanted to go to the United States, went to Harvard University where he spent 1956-57 as a postdoctoral student supported by a Sir James Caird Travelling Scholarship. He remained at Harvard for two further years (1957-59) as Gordon MacKay Lecturer and Research Fellow in Applied Mathematics. During this time he was also a Tutor in Applied Mathematics at Leverett House, the largest Residential House at Harvard.Stream functions are obtained for two variable shear flows past a circular cylinder. The shear distributions in the free stream are of the ' linear' and ' boundary layer' type respectively. In both flows, the stagnation streamline is displaced in the free stream towards a region of higher Velocity. This is in agreement with the results obtained by the present authors(1)in the case of constant shear flow past a cylinder and with the experimental results of Young and Maas(2)for a pitot tube of circular cross-section in a low-speed shear flow. The displacements in both variable shear flows are comparable in magnitude to the values obtained in the constant shear case but are considerably smaller than the experimental values of Young and Maas.

Murray married Sheila Campbell in 1959; they had two children Mark and Sarah. Soon he was back in England because of what he described as "family pressure" [14]:-

The excessive teaching was too much, he could not do any research so he handed in his resignation after a year which greatly upset the Principal. He returned to the United States in 1963 and was appointed as Research Associate in Engineering and Applied Physics at Harvard. After a year he moved to the University of Michigan where he was appointed as Associate Professor of Engineering Mechanics. After a year at Michigan he was promoted to full Professor of Engineering Mechanics.I came back to England, to University College London and two years later was elected Mathematics Fellow in Hertford College, Oxford. I actually got the position by mistake. The college fellow in charge of the appointment was a physicist who said to me that any person who gets a strong recommendation from Goldstein, must be good. It turns out the Goldstein he was thinking of was not the same Goldstein that had written my reference!

Murray had continued to work on fluid dynamics and had published papers such as *Non-uniform shear flow past cylinders* (1957), *The flow of a conducting fluid past a magnetized cylinder* (1960), *The boundary layer on a flat plate in a stream with uniform shear* (1961), *Strong cylindrical shock waves in magnetogasdynamics* (1961), *On the mathematics of fluidization. I. Fundamental equations and wave propagation* (1965) and *On the mathematics of fluidization. II. Steady motion of fully developed bubbles* (1965). In 1965 he gave an Invited survey lecture *Mathematical aspects of bubble motion in fluidized beds* at the Symposium on Fluidized Particles run by the American Institute for Chemical Engineers in Houston, Texas.

It was while he was at the University of Michigan that Murray became interested in mathematical biology. He said [14]:-

In 1967 Murray was appointed as Professor of Mathematics at New York University but, after two years he returned to England where he was made a fellow and tutor at Corpus Christi College of the University of Oxford. He remained at Oxford for the remainder of his career, although he spent a number of months at various universities worldwide as a visiting professor.A professor of botany approached the department and asked if they could recommend anyone who could help him quantify how oxygen got into pea nodules. When the guy phoned me up he thought I was a graduate student and said he could offer me $5an hour! So, that was my introduction into mathematical biology: oxygen diffusion in pea nodules. After writing a few papers on it I found it quite interesting even though there was nothing too difficult about the mathematics as it was just singular perturbation analysis of the diffusion equation. I don't know how, but someone from anatomy heard about me and got in touch. His problem was on pilot ejection seat injuries. I got interested and the model consisted of a one-dimensional compressible material on one end of which we applied a force to simulate the chair lifting rapidly. This lead to a wave travelling up the rod, but the wave equation was nonlinear and so a shock developed.

From 1966 until 1973 Murray published papers both on fluid dynamics and on mathematical biology. For example *A theoretical study of the effect of impulse on the human torso* (1966), *A simple method for obtaining approximate solutions for a class of diffusion-kinetic enzyme problems* (Part I, 1968; Part II, 1968), and *On the molecular mechanism of facilitated oxygen diffusion by haemoglobin and myoglobin* (1971) are on mathematical biology while *A simple method for determining asymptotic forms of Navier-Stokes solutions for a class of large Reynolds number flows* (1967), *Singular perturbations of a class of nonlinear hyperbolic and parabolic equations* (1968) and *On Burgers' model equations for turbulenc*e (1973) are on fluid dynamics. After 1974 all of Murray's publications (around 200 from 1974 up to 2015) are on mathematical biology.

Murray gave the *Introductory Remarks* at the 'Theories of biological pattern formation', a Royal Society of London conference held on 25 and 26 March 1981. These remarks give an interesting account of Murray's interest in Mathematical biology - an extract is available at THIS LINK.

Murray has published three single authored books *Asymptotic Analysis* (1974), *Lectures on Nonlinear Differential Equation Models in Biology* (1977), *Mathematical biology* (1989), and, in addition, one multi-author work *The mathematics of marriage: dynamic nonlinear models* (2002), with John M Gottman, Catherine C Swanson, Rebecca Tyson and Kristin R Swanson. He has also been the editor (along with S Brenner and L Wolpert) of the Proceedings of *Theories of Biological Pattern Formation* (1981), the editor (along with W Jäger) of the Proceedings of *Modelling of Patterns in Space and Time* (1984), and the editor (along with H G Othmer, P K Maini) of the Proceedings of *Experimental and Theoretical Advances in Biological Pattern Formation* (1993). We give extracts from reviews of various editions of Murray's four books at THIS LINK.

At Oxford, Murray was a Reader in Mathematics from 1972 to 1986, and Professor of Mathematical Biology from 1986. He was Director of the Centre for Mathematical Biology at Oxford from 1983. In 1992 Murray retired both from his chair of Mathematical Biology and from the Directorship of the Centre for Mathematical Biology. When he retired, Oxford made him an Emeritus Fellow at Corpus Christi College and an Emeritus Professor of Mathematical Biology. However, from 1987 Murray had, in addition to the Oxford positions, held appointments at the University of Washington in the United States. He was Robert F Philip Professor there from 1987 to 1994 and, in addition, Professor of Applied Mathematics, Adjunct Professor of Zoology. From 1997 to 2000 he was Boeing Professor at the University of Washington and, in 2000, he was made Emeritus Professor of Applied Mathematics at the University of Washington. In 2010, now in his eightieth year, Murray became a Senior Scholar in Applied and Computational Mathematics at Princeton University and a Visiting Professor in Ecology and Evolutionary Biology at Princeton. He continues to undertake research at Princeton.

During his long career, Murray has held numerous positions as Visiting Professor. These include: the National Tsing Hua University, Taiwan; the University of Florence; Massachusetts Institute of Technology; the University of Iowa; the University of Utah, Salt Lake City; the California Institute of Technology; the University of British Columbia, Vancouver; the University of Heidelberg; the University of Guelph; the Southern Methodist University, Dallas; the Los Alamos National Laboratory; the Neurosciences Institute, Rockefeller University, New York; the Institut de Biologie Théorique, Université d'Angers; and the University of Paris (IX-Dauphine).

For his outstanding contributions to mathematical biology, Murray has received many honours and awards. These include election as a Fellow of the Royal Society of Edinburgh (1979), as a Fellow of the Royal Society of London (1985). He was awarded the London Mathematical Society's Naylor Prize in Applied Mathematics (1989), became a Membre de l'Insitut de France (Foreign member Académie des sciences) (2000), was elected an Honorary Fellow, Corpus Christi College, University of Oxford (2001), *Lectio doctoralis*, University of Milan (2004), and was awarded the Akiro Okubo Prize (2005). The University of Washington created a donor endowed chair in perpetuity: the James D Murray Chair of Applied Mathematics in Neuropathology in 2006. He was made an Honorary Member of the Edinburgh Mathematical Society in 2008, received the Royal Society's Bakerian Medal and Prize Lecture (2009), Institute of Mathematics and its Applications, Gold Medal (2009), European Academy of Sciences' Leonardo da Vinci Medal (2011), and the William Benter Prize in Applied Mathematic (2012). He has received honorary degrees from the University of St Andrews (1994), the University of Strathclyde (1999), the University of Milan (2004), the University of Waterloo (2006) and the University of Dundee (2011).

**Article by:** *J J O'Connor* and *E F Robertson*