Obituary: John Elgin, Edinburgh-born mathematician and Emeritus Professor at Imperial College

John Elgin
John Elgin
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John Elgin: mathematician and Emeritus Professor at Imperial College London. Born: 15 October 1946 in Edinburgh. Died: 17 July 2017 in London.

John Elgin, who has died at the age of 70, was born into a working class family in Edinburgh’s Pleasance tenements and attended the local James Clark School, commonly known as Jimmy’s. He later claimed that they were never taught much except how to write letters applying for a job. If school left a bit to be desired, however, the Pleasance Trust Boys’ Club (one of many such all over Scotland keeping young lads off the streets in the 1950s) proved a godsend. Evenings spent playing sports, and weekend camping trips to Cockburnspath opened up new vistas and stirred a desire for something better.

Leaving school at 15 without any qualifications, he wrote that letter and was taken on as an apprentice by Parsons Peebles Turbines and, through them, was encouraged to take his ONC at night school. He soon found himself translated from the shop floor to a collar-and-tie job in the Drawing Office and the company, spotting further potential, subsequently funded his studies in Mechanical Engineering at Heriot-Watt, then going through its transition from College of Technology to University. Once there, however, he swapped Engineering for Physics – a subject he’d never studied before but which fascinated him. This proved the first of several changes of direction. He graduated with a First in Physics and, perhaps ungratefully, never returned to Parsons Peebles. Following a summer spent at CERN in Geneva, he was persuaded to apply to Cambridge for a PhD at DAMTP in 1970. Attached to Corpus Christi College and supported by a prestigious Carnegie Scholarship (always referred to as the gift of ‘Uncle Andrew’), he pursued thesis work on surface waves at vacuum-plasma interfaces under the supervision of Philip Clemmow – ‘the cleverest man never to hold a chair’ as John always thought of him.

In 1974 he began what was to be a life-long relationship with Imperial College, joining the Physics Department as a postdoctoral research fellow, working with Geoffrey New on theoretical nonlinear optics. He proved so able that in 1978 he was awarded a very competitive Research Council five-year Advanced Fellowship. But the lure of Mathematics proved strong, and in 1983 he made yet another switch, when he was recruited to the Maths Department as a lecturer under the ‘New Blood’ scheme. Promotion to Reader followed in 1991 then to Professor in 1995, followed by a stint as Section Head of Applied Mathematics (1998-2003) and then as Head of Department (2003-08). He also served on the advisory panels for the International Centre for Mathematical Sciences (ICMS) Edinburgh (2005-) and the Edinburgh Research Partnership (2006-).

John entered the research world at a time when revolutionary changes in our understanding of what are now called ‘nonlinear systems’ were making major leaps forward. Roughly speaking, linear systems are ones for which the evolution of some quantity (such as wave height) is proportional to the initial disturbance. In contrast, in a nonlinear system, if the initial disturbance is high enough, some completely different feature may occur. Such ideas go back to the observation of the “solitary wave” by John Scott Russell on the Union Canal in 1834, but were neglected until a revival by American and Russian mathematicians in the 1960s.

These ideas spread rapidly into many subjects, not least nonlinear optics, where John Elgin’s technically gifted but intuitive abilities led to a string of papers addressing the problem of energetic pulses of light propagating in nonlinear optical fibres. The pinnacle of this work was reached in 2007 with a joint paper with Viktor Enolski (Corncordia, Canada) and Alexander Its (Purdue, Indianapolis) on how to solve the so-called vector nonlinear Schrödinger equation. This is a masterly work of complex analysis, a topic at which John always excelled. During his prolific career, John authored or co-authored almost 100 scientific papers in Theoretical Physics and Applied Mathematics. Although Imperial was his home, he maintained strong links with Heriot-Watt, enjoying an honorary position there.

A popular lecturer, John had a rare ability to communicate with large classes in all the science and engineering disciplines, his dry, Scottish sense of humour enlivening a difficult subject and endearing him to generations of students. His steadfast refusal to put lecture notes up on line was frustrating to some - he believed it was more important to pay proper attention during the actual performance - but his office door was always open. A string of PhD students, now spread all over the world, were grateful for his rigorous but always encouraging tutorials.

Imperial College and mathematics were at the heart of John’s life, but marriage to his wife Kathy, an arts graduate, rescued him from a life of pure science. He plunged into the arts world with the same enthusiasm and curiosity he brought to research, enjoying a wide-ranging love of art, books, theatre and dance; equally happy at Edinburgh’s Lyceum, the Traverse or London’s Covent Garden. Together he and Kathy travelled widely to China, India, Uzbekistan (perhaps their most bizarre destination) and Vietnam. Italy was a favourite place, the pleasures of its food and wine undiminished by John’s complete inability to learn its (or any other) language.

Despite official ‘retirement’ at 65, he continued teaching at Imperial for another five years, seeing another batch of PhD students on their way and administering the Maths Department’s prestigious Chapman Fellowships. The determination that had got him through from an inauspicious start to the top of the academic tree kept him in action throughout his illness: few of his colleagues knew the seriousness of his condition. Only his premature death, from a progressive lung disease, has prevented a well-deserved retirement in Edinburgh, where he and Kathy had settled in the New Town – an unimaginably long way from the Pleasance.

John Gibbon
Chris Eilbeck