David S Broomhead

Born: 13 November 1950 in Leeds, England
Died: 24 July 2014 in London, England

David Broomhead was born into a working class family. We give his own works about his family background below. After attending primary school, he took his eleven plus examination and, since he performed well in this examination, he was able to enter Aireborough Grammar School situated on the Yeadon-Guiseley border in Aireborough, West Yorkshire. This Grammar School only accepted pupils who had performed well in the eleven plus examination. He completed his secondary education at this Grammar School in 1969 and then spent a year in Uganda, where he both studied and taught in a school. Let us now quote David Broomhead's own description of his family and upbringing which he wrote in December 2007 [2]:-
Like many of my peers, I was brought up in a family where class was a tangible issue. However, given the volatile state of the class system, society was riddled with contradictions which were reflected in our lives. We were working class and therefore socialist, but we also 'knew our place'. It was drummed into me that the only way to better myself was through education, that is, by working hard at school, and yet, later, when at 15 I had to decide between leaving school to get a job and staying on to do A-level (and, actually, again when the possibility of attending university arose), it was not a foregone conclusion that I would be allowed to pursue my education. My grandfather, for example, a retired miner and a dyed-in-the-wool socialist - a man that I admired greatly for his blunt independence - said strongly that I should get out and get a job and believed that my parents were indulging me when they encouraged me to take my education as far as it would lead me. Somewhere during my time at grammar school, a transition had taken place. Without really realising it, I had ceased to study because it would help me transcend taking my lunch in a canteen, and I had become interested in just studying. Around the same time I conceived of the idea that our society was becoming a socialist meritocracy and that the class system within which my parents had lived was dead. I could do anything I wanted - including becoming a scientist and doing research - if I was prepared to work at it. Conversely, if I did nothing, then I could expect nothing more than a meaningless job and a meaningless existence. In the brashness of youth, I wanted my life to mean something.
Returning from Uganda, Broomhead matriculated at Merton College, Oxford, in 1970. He had decided that chemistry was the subject in which he wanted to specialise, so he took the required courses. However, Broomhead did not find much joy in the laboratory work and when he came to take Part III of the tripos, he signed up for a project on quantum mechanics with Peter W Atkins. Atkins had written a Ph.D. thesis on theoretical chemistry and was appointed to Oxford as a lecturer in physical chemistry in 1965. He published the two-volume book Molecular Quantum Mechanics in 1970, so Broomhead's project was very much in line with his current interests. After completing Part III, Broomhead remained at Oxford undertaking research with Atkins as his thesis advisor. He was awarded a DPhil in 1976 for his thesis Molecules in Electromagnetic Fields. On the classical theory of relaxation in nonlinear intramolecular modes. One important event in Broomhead's life which occurred while he was at Merton College, Oxford, was meeting Eleanor J Harries who was also studying chemistry. They were later married and had one son, Nathan Thomas Broomhead. Nathan studied mathematics and was awarded a Ph.D. in 2009 for a thesis on algebraic geometry entitled Dimer Models and Calabi-Yau Algebras.

After completing his thesis, David Broomhead spent a year as a postdoctoral student at the Atomic Energy Research Establishment at Harwell in Oxfordshire. After this he was awarded a NATO Postdoctoral Fellowship and a Science Research Council grant which enabled him to spend two years in the Department of Physics at the University of Kyoto working in the research group led by Kazuhisa Tomita [3]:-

It was here that he began to work seriously on applied nonlinear dynamics and chaos, topics that underpinned his research for the rest of his career.
While at the University of Kyoto, Broomhead wrote the paper The Self Interaction and Mutual Interaction of Limit Cycles. The Possibility of Chaotic Behaviour published in Progress of Theoretical Physics in 1979. In the paper he acknowledged the support he had from Kazuhisa Tomita and his group:-
I would like to thank Professor K Tomita and all the members of his research group, particularly Dr Y Aizawa, Mr H Daido and Mr I Tsuda, for all the helpful advice and interesting discussion that I have benefited from during the course of this work. Also I wish to thank the Science Research Council, Great Britain, for financial support.
Here is a part of Broomhead's introduction to this paper:-
The validity of the concept of "potential surface" and our ability to visualise mechanical motion on such a surface often permits detailed qualitative understanding of the global behaviour of Hamiltonian systems. This is in contrast with general dissipative systems, although, in this latter case, Lyapunov's direct method, the utilization of a generalization of the potential idea, can provide some information on the global behaviour. The present work is concerned with dissipative models which can be derived simply from a Hamiltonian form. For these models the use of the mechanical potential surface retains a validity and the energy may be used as a Lyapunov function. In this way a detailed visualization of the global behaviour is possible by analogy with the corresponding Hamiltonian system. Employing this approach a model is constructed having a bifurcation which involves the fusion of a pair of limit cycles. The structural instability in the region of this bifurcation is investigated by considering the response of the system to a small harmonic perturbation.
Returning to England, Broomhead took up a postdoctoral position working with George Rowlands in the Physics Department at the University of Warwick in 1980. Rowlands (born 1932) had taken up an appointment at Warwick in 1966 and was on the staff there when I [EFR] was a postgraduate student in mathematics. He had worked at the Atomic Energy Research Establishment at Harwell and at the UK Atomic Energy Authority at Culham before taking up the academic appointment at Warwick. Broomhead and Rowlands [3]:-
... became great friends and enjoyed a tremendously productive collaboration, not least because they solved the problem associated with Dave's funding within a few months and so had the best part of three years to work on whatever they liked. Dave also made fruitful connections to the Dynamical Systems group in Warwick's Department of Mathematics including Robert MacKay, David Rand and Christopher Zeeman.
Broomhead left the university environment in 1983 when he took up a position in the scientific civil service. He became Senior Principal Scientific Officer with the Signal Processing group at the Royal Signals and Radar Establishment in Great Malvern. He explained in [1] that he:-
... worked with mathematicians, physicists, signal processors and electrical engineers while in Malvern.
We list a few of the papers in wrote, in collaboration with his colleagues, while in Malvern: A Practical Comparison of the Systolic and Wavefront Array Processing Architectures (1985); Phase Spaces from Experimental Time (1989); A Parallel Architecture for Nonlinear Adaptive Filtering and Pattern Recognition (1989); A Systolic Array for Nonlinear Adaptive Filtering and Pattern Recognition (1990), and Signal Processing for Nonlinear Systems (1991).

In 1995 Broomhead was appointed as professor of applied mathematics at the University of Manchester Institute of Science and Technology (UMIST). In December 2005 he wrote about the worries he had when he took up this position [2]:-

Ten years ago, when I decided to move back to academia, my greatest concern was the prospect of lecturing to undergraduates. Clearly, the skills required to give a good seminar would not be the same as those required for a successful undergraduate lecture. I did enjoy giving seminars (and still do), but I anticipated a great gulf between this rather friendly - often intimate - exchange between well-educated peers, and the act of walking into a room full of students, picking up a stick of chalk, and proceeding to explain, intelligibly, some basic piece of mathematics. I remember the nerves on the first day that I did this: how seriously I questioned the wisdom of leaving a job where all I had to do was research; how bitterly I regretted my impetuosity as I walked along the corridor to that first lecture. To my great surprise, it wasn't so bad. The students were a cheerful bunch who seemed keen to learn, and when I had overcome the fear that I was telling them things which they would find obvious, I began to enjoy myself. As the term progressed, I began to identify my audience as individuals, banter was exchanged, some kind of bond was formed and I began to realise that I had missed something important in my previous occupation.
Kate Cooper writes about meeting Broomhead in 1999 in [5]:-
I trotted to Manchester to meet this warm, witty man who offered me a wide variety of teas, batting not an eyelid at my preference for builder's. I instantly loved him. His all-encompassing mind, his generosity of spirit, that sudden smile which started in his eyes when something amused him, the spread of papers across his room, his knowledge of Japanese pickles, his never-failing welcome to me - a lippy non-mathematician with crazy ideas about the importance of the practice of maths to society - and the immense professional respect other mathematicians had for him.
In 2004 UMIST merged with the University of Manchester so Broomhead became a professor in the University of Manchester. He continued in this role until his death ten years later. His contributions over this period are described in [3]:-
Working in a university environment allowed him greater interactions with younger scientists, and he enjoyed the process of supervising PhD students enormously. By all accounts the enjoyment was reciprocated. At Manchester he became increasingly interested in applications to biology, working initially on eye movement control with Richard Abadi and later, with Doug Kell, on large-scale models of metabolism and with Mike White's group on the dynamics of intracellular signalling cascades. In recent years he developed a deep interest in hybrid systems and asynchronous processes, leading a large, lively interdisciplinary group as head of Manchester's CICADA project.
Here is Broomhead's own description of his various roles at the University of Manchester [1]:-
I am Professor of Applied Mathematics in the School of Mathematics in the University of Manchester and an Associate Member of the Manchester Interdisciplinary Biocentre (MIB). I am director of the Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA) recently created within the University of Manchester and funded jointly by the University and with the aid of a £2m grant from EPSRC. I am also a member of the management team of the Manchester Centre for Integrated Systems Biology (MCISB). Within the School of Mathematics my interests are largely focussed around those of the Dynamical Systems Group and the Mathematical Biology Group.
In August 2002 Broomhead became the editor of Mathematics Today, a publication of the Institute of Mathematics and its Applications (IMA). Mathematics Today is a:-
... general interest mathematics publication providing articles, reports, reviews and news for mathematicians.
The February 2015 issue of Mathematics Today was dedicated to his memory. The editorial of this edition is reference [2] where it stated:-
Dave's last editorial was in April 2011, and between these dates [2002-2011] Dave helped recreate the magazine as a regularly enjoyable and informative read for members of the IMA. Dave brought the same enthusiasm and commitment to 'Mathematics Today' as he brought to his collaborations and friendships, his students and his academic thoughts. He influenced science policy in the UK and beyond through his work for the Research Councils and his internationally renowned scientific contributions.
Among the honours and awards Broomhead received, we mention the John Benjamin Memorial Prize which he was awarded (jointly with David Lowe and D A R (Andrew) Web) in 1989. This prize was established by Ralph Benjamin and his wife K R Benjamin as a memorial to their son Dr John Benjamin who died tragically in an accident in 1987:-
The prize is to be awarded annually to a scientist or engineer whose initiative and innovative original thinking has made a real difference to the ability to cope with some significant practical problem or problems or shows high promise of doing so.
Broomhead died suddenly at the age of 63. The Malvern Gazette contained the following notice on 8 August 2014:-
David (Dave) Broomhead passed away suddenly at The National Hospital, London on July 24th, 2014, aged 63 years. Beloved husband of Eleanor, loving father of Nathan and son of Elizabeth. He will be greatly missed by all who knew and loved him. Funeral Service will take place at Worcester Crematorium on August 8th, 2014 ...

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

July 2015
MacTutor History of Mathematics