Elizabeth Jane Gardner

(1957-1988)

Elizabeth Gardner was born on 23 August 1957, in Cheshire, where her father Douglas worked as a Chemical Engineer with ICI. Her mother Janette was also a scientist, having gained a PhD in Physical Chemistry at the University of Edinburgh. The family moved to Scotland the following year, on the expansion of BP Chemicals at Grangemouth.

Her interest in science extended beyond her school activities at St. Hilary's in Edinburgh, and from a remarkably early age; when she was two years old she was overheard pointing out to Granny: that's the Plough, and that's Orion...'. The fascination with astronomy, which has drawn so many towards science, continued through her school years, and found encouragement at home, with many a cold evening spent at the four inch reflector telescope which her parents gave her at the age of twelve. Around the same time she also became clear that experimental work was probably not going to be her strongest item: when she was fourteen, she and her brother Richard surveyed Blackford Hill using surrounding landmarks, and came to the conclusion that its summit was 360 feet below sea level!

Elizabeth applied to Cambridge and Edinburgh for undergraduate entry. Her application to Cambridge was unsuccessful and her interview there was followed by the suggestion 'Don't you think you'd be better at a Scottish University?' - remarkably sound and disinterested advice. She came to Edinburgh University in 1975 with the intention of studying fort he Astrophysics degree, but on learning that the Mathematical Physics courses were strongly recommended for that degree, she registered in her first year for the Mathematical Physics degree and continued in it for her four years as an undergraduate. She had an outstanding record, gaining more than 90% in every degree examination in every year. In her first year she was in the top three in all of her courses: Mathematics, Applied Mathematics and Physics. In her second year she was awarded the Class Medal as the top student in all three subjects. Again in her third year she was awarded the Class Medal, and graduated with First Class Honours, sharing the Tate Medal and Robert Schlapp Prize.

Elizabeth's quiet and reserved manner was well known, and never more noticeable than during formal interviews, but in scientific discussions she showed a vividly different side. This emerged early on during her DPhil studies, about half-way through her first year at Oxford, when she met with her supervisor, Dr I J R Aitchison, to talk about possible research projects. Until then her time had, as is usual, been mostly taken up with the graduate course work, in which she had naturally performed very well, though without making any special impact. but when, that day, the discussion with her turned to some problems in gauge theory, it became apparent that she was positively bursting with excitement: she was intensely eager to begin research work, for which indeed she proved to have a burning, though rarely visible, passion.

By the time she was in her third year as a graduate student she had acquired an unusual authority, and her opinion was much sought by those who knew her and recognized her quality. When a difficult point came up in coffee-time discussions, and people were stuck. they would turn to Elizabeth. Until asked a specific question, she would probably not have joined in the discussion but, when asked, she would often turn out to have thought about the problem already, and to have worked out the answer-which she would explain precisely, and economically. Otherwise, not having much taste for small talk or thinking out loud, she would simply say that she hadn`t thought about it, and didn't know.

Elizabeth had extremely high intellectual standards, both as regards the sort of problem she felt she wanted to work on, and as regards the style of the work itself. This was reflected in her personal dissatisfaction with the main work in her thesis, which concerned an attempt to learn about non-pertubrative aspects of non-Ahelian gauge theories. Naturally approximations had to be made - and they violated gauge invariance. Within the context of the approach adopted, her work was original and inventive, and marked by an easy-seeming technical competence. But she was not happy with an approximation which, she said, she could neither justify, nor control, nor improve upon systematically. In expressing these serious reservations about her own work, she showed how central to her inner self was the pursuit of the highest possible standards of scientific endeavor.

Although she fulfilled all the requirements, Elizabeth in fact never formally graduated from Oxford; she always said she could leave that until she was 90. After her DPhil at Oxford, Elizabeth spent two years as a postdoc in the theoretical group at Saclay with the support of a Royal Society Fellowship. It was here that she started to work on problems of field theory defined on random lattices. this work was motivated by the idea that field theories on random lattices have the advantage of being defined on lattices and set of keeping the continuous translational invariance. lt was this which, provided for her the bridge between field theory and the theory of disordered systems, on which she was going to devote all her future scientific work. Following this change of direction she contributed to several topics in the theory of disordered systems: in the localization problem for which a perturbative method was developed for the calculation of Lyapunov exponents, in the effect of disorder on the critical behavior of weakly disordered systems, and in stereological properties of random materials.

During this period Elizabeth also started to work on Spin glasses using both renormalization techniques and replica methods. Her first works on spin glasses were calculations on hierarchical lattices, on extensions of the Sherrington-Kirkpatrick model to p-spin interactions and on random energy models. Her deep understanding of the modern ideas developed in the theory of spin glasses allowed Elizabeth to become, very quickly, one of the leading experts on the thesis of neural networks.

She returned to the Physics Department at the University of Edinburgh in October 1984. This was because for the remainder of her brief research career, although she continued a close collaboration with colleagues at Saclay and latterly became overwhelmed with invitations elsewhere, to conferences, workshops and for scientific visits. She started with a two-year postdoctoral position supported by the Science and Engineering Research Council (SERC) for work in her DPhil area of theoretical particle physics. At the end of this period she applied unsuccessfully for a SERC Advanced Fellowship to study disordered systems and neural network models; one may speculate that again her modesty and diffidence at formal interviews was a crucial factor. It was clear to the Department however, that she was a scientist of outstanding potential, and a package of support was quickly put together, involving a short period under a contract for neural network studies from the Royal Signals and Radar Establishment at Malvern and a Dewar Fellowship from the University of Edinburgh. This enabled her to continue at Edinburgh, pending what was a successful second application.

Soon after her return to Edinburgh in 1984 it became clear that her scientific curiosity remained driven by the study of disordered systems. Her entry into the study of neural network models was remarkably incisive. At that time numerical simulations were being performed at Edinburgh to try to understand the storage capacity in the Hopfield net and the fraction of states perfectly stored in the model. That this quantity depends upon the ratio of the number of patterns stored to the number of nodes in the net can be readily understood on the basis of a simple 'signal and interference` argument, but the functional form obtained from numerical simulations cannot. Within three or four days of being first exposed to the problem Elizabeth came up with the exact result which explained the data perfectly. Shortly thereafter she became interested in the training algorithms which were being rediscovered and developed, and made the subject her own. There then followed a flood of papers of the highest scientific quality, elucidating the dynamics of network models, the effect of multispin interactions, the role of asymmetry and dilution, and above all the maximum storage capacity. For this last work she developed a beautiful technique exploring the phase space of the interactions themselves (the connection strengths in the network model). In her approach, in contrast to the usual statistical mechanics in which the spin variables are replicated to deal with the average over the quenched disorder, the statistical properties in the space of interactions is explored by replicating the interactions to deal with the average over the possible spin states.

Elizabeth bore her illness privately, with dignity and with remarkable strength of character. The first diagnosis of cancer was made in 1986; her colleagues at Edinburgh were aware of the physical changes resulting from the treatment, the flowering of her scientific talent and of her selfless support for her graduate students. The disease recurred in the subsequent two years and she succumbed to it on 18 June 1988, only nine months into her five year Advanced Fellowship. She had been interviewed for a lectureship in the Department of Physics at Edinburgh less than three weeks before. The seriousness of her illness was even then not fully known to her colleagues, and Elizabeth was pleased to be reassured that the University expected to be able to appoint her to a permanent position at the end of her Advanced Fellowship.

B. Derrida, I J R Atchison and DJ Wallace