DE MORGAN MEDAL 2001

The De Morgan Medal for 2001 was awarded to Professor J.A. (Sandy) Green, Emeritus Professor of the University of Warwick; however, owing to illness he was unable to receive the award at the Annual General Meeting on 23 November 2001. With the active co-operation of the Mathematical Institute of the University of Oxford, it was arranged to present the award at a short LMS Meeting before the Institute’s regular Colloquium on Friday, 15 November 2002. Thus the President of the LMS made the presentation to Sandy Green after reading the citation for the award, which had appeared in the LMS Newsletter for July 2001. Happily, several members of Sandy’s family were present, including Mrs Margaret Green, one son, two daughters and one granddaughter; Sandy’s son (Alistair) acted as family photographer! An added bonus for the LMS was the large number of members who came forward to sign the LMS signature book, which dates from 1865. So the President became still more familiar with the phrase ‘On behalf of the London Mathematical Society I hereby admit you a member thereof’! After the LMS ceremony, Professor Terry Lyons introduced the Colloquium speaker, Professor Peter Sarnak (Princeton University and NYU), who spoke on ‘The spectrum of modular surfaces’. Following the lecture a reception was held in the Mathematical Institute in honour of Professors Sandy Green and Peter Sarnak. Later in the evening, a dinner was held at the high table of University College, where Dr Michael Collins presided as the Senior Fellow present. The London Mathematical Society is deeply indebted to Dr Nick Woodhouse, Chairman of the Mathematical Institute, Professor Terry Lyons, Chairman of the Colloquium, and Dr Michael Collins for their generous co-operation in making these arrangements, which gave great pleasure to Sandy Green and his family and to many LMS members.

Professor J.T. Stuart FRS President of the LMS 2000-2002

‘SO WORK THE HONEY BEES….BUILDING ROOFS OF GOLD’ The Story of Sophie Bryant

The first paper written by a woman member of the London Mathematical Society was published in 1884. The author, Sophie Bryant, had been elected to membership in 1882; she had been preceded first by Charlotte Angas Scott, an algebraic geometer, in 1881 and then by Christine Ladd Franklin, a mathematical logician, also in 1881. However, it appears that of the three earliest women members of the Society, Bryant was the only active member. Christine Ladd Franklin was an American and Charlotte Angas Scott later moved to Bryn Mawr in the USA.

Being the ‘first woman’ was not unusual for Bryant. She was the first woman to receive a DSc in England, her subject being mental and moral philosophy, she was one of the first three women to be appointed to a Royal Commission, the Bryce Commission on Secondary Education in 1894-95, and she was one of the first three women to be appointed to the Senate of London University. While on the Senate she advocated setting up a Day Training College for teachers which eventually became the Institute of Education. Later in 1904, when Trinity College Dublin opened its degrees to women, Bryant was one of the first to be awarded an honorary doctorate. She was also instrumental in setting up the Cambridge Training College for Women which eventually became Hughes Hall, the first postgraduate college in Cambridge. She was, it seems, one of the first women to own a bicycle.

It was fortunate for Bryant that she was able to learn mathematics and other subjects together with her five siblings in a very natural way from their father, the Rev WA Willock DD who was a keen educationalist. He had been a Fellow and Tutor of Trinity College Dublin and had gained high honours in mathematics and mental sciences.

When she was about thirteen her family moved to England and her private education continued until she attended Bedford College (at that time a ladies’ college similar to Queen’s College) where she was awarded the Arnott scholarship for science at in 1866. She sat the Cambridge Local Examination for Girls in 1867 and was the only one to be placed in the first class of the senior division. It was while she was sitting these examinations that she first encountered Frances Buss the Head Mistress and founder of North London Collegiate School (NLCS) founded in 1850, the year of Bryant’s birth.

In 1869 Bryant married Dr William Hicks Bryant, only to be widowed the following year when her husband, a surgeon and only 30 years old, died of cirrhosis.

After a short interval she returned to her studies. She arranged to meet Buss who, in 1875, invited her to teach mathematics at NLCS and encouraged her to take a training course as well. In 1878 London University opened its degrees to women. As Bryant had not had a conventional education she had to learn sufficient Latin to matriculate and biology before she could sit for her degree. In 1881 she took a BSc degree, first class in mental and moral science and second class in mathematics. In 1884 she received her science doctorate and the NLCS, where she had continued to teach, presented her with scarlet doctoral robes. The imposing portrait of Bryant which hangs in the entrance of the school shows her in these robes. Bryant was influential in improving the education system and introducing a scheme of enlightened and serious study. In 1885 Buss died and Bryant became the Head Mistress.

Bryant was interested in Irish politics, wrote books on Irish History and ancient Irish law, was an ardent Protestant Irish nationalist and helped found a Home Rule pressure group. She wrote on women’s suffrage in 1879 but later advocated postponement until women were better educated in politics. She enjoyed mountain climbing and she had climbed the Matterhorn twice. Her death in 1922 was both tragic and unexpected; she was lost on a mountain hike near Chamonix only four years after she had retired.

Bryant’s published paper for the LMS was ambitious. In The ideal geometrical form of natural cell structure she takes a logical and descriptive but not very mathematical (by today’s standards) look at the phenomenon of the honeycomb. This was not an unusual approach at that time; indeed abstract proofs, so essential to us in the twentieth century and beyond, were not as common as general discussion of mathematical phenomena. Bryant’s paper assumes Kepler’s Conjecture: that no packing of balls of the same radius in three dimensions has density greater than the face centred cubic packing, the cannonball packing. Although this has appeared obvious for centuries it was not finally proved until as recently as 1998 by Hales and Ferguson and then only with the aid of computers. Bryant explains how the complex and beautiful honeycomb shape could be produced by the natural activity of bees. All that was needed was for each bee to excavate his own cell at approximately the same rate as the others and use the excavated material to build up the walls of its cell. Bryant’s conclusion that elongated rhombic semi-dodecahedra are the natural form of honeycomb cells had been observed by Kepler. In the eighteenth century it was believed that the honeycomb was the most efficient possible, but this is now known not to be the case. In 1964 Fejes Tóth discovered in a paper entitled What the bees know and what they do not know, that there are more efficient cell shapes and that the most economical has yet to be determined.

Bryant read another paper for the LMS entitled Logarithms in general logic, but it was not printed by the Society. However, a note of the Proceedings of 1885-86 records that a ‘long discussion ensued’ in which Sylvester (who was at that time President), Bryant and two others members took part. She was ambitious too in other papers that she wrote. In a paper published in 1884 in ‘Mind’, The double effect of mental stimuli; a contrast of types, Bryant attempts to analyse the effect of a mental event. She considers both a reflex action which does not cause a change in consciousness but clearly is a mental event, and contrasts it with a conscious mental event. She grapples with what is a contemporary problem: the understanding of consciousness. Unfortunately her arguments are too diffuse to shed much light on the problem. Extra paragraph In 1885 she published a paper in the Journal of the Anthropological Institute entitled, “Experiments in testing the characters of school children”. This study, undertaken at the suggestion of Francis Galton, produced an early account of the use of open-ended psychometric tests to deduce personality types. Bryant claimed that her results agreed with the observations of teachers familiar with the children but did not provide any supporting evidence. In spite of incomplete analysis, this was a pioneering study.

Although Bryant’s direct contribution to scholarship may not have been substantial, her influence as a teacher and educationalist was immense. Many of the next generation of teachers and headmistresses succeeded as a direct result of her endeavours; and her work continues to spread throughout subsequent generations. Patricia Rothman University College London

MENTORING FOR EUROPEAN WOMEN IN MATHEMATICS

A new EU-funded website for women in mathematics to find mentors is now live (http://ewm. brookes.ac.uk). Please have a look and consider signing up as a mentor (both female and male mentors are welcome). If you are a female postgraduate student, postdoctoral student, or have recently started your career as a lecturer you may also wish to sign up to get a mentor. Please draw this to the attention of other colleagues if you think they would be interested in the scheme. Dr Cathy Hobbs Oxford Brookes University

A BRIEF HISTORY OF THE DE MORGAN MEDAL

Most mathematicians would recognise the name Augustus De Morgan, if only through an acquaintance with ‘De Morgan’s Laws’ in logic and set theory. But to LMS members, the name has an extra significance because of the key role he played in the Society’s foundation. When the LMS held its inaugural meeting on 16 January 1865, he was its first President, and was to remain an enthusiastic member during its formative years. Not long after his death in 1871, a meeting was held to discuss an appropriate testimonial in his memory. One of the resolutions of the resulting “De Morgan Memorial Committee” was the proposal “to establish a De Morgan medal, to be awarded annually by the [London] Mathematical Society to the writer of the most original mathematical treatise”. Although the decision to commemorate De Morgan with the award of an LMS medal had not been initiated by the Society itself, its members quickly endorsed the idea. But the inauguration of the commemorative medal was to take far longer than anticipated, for a variety of reasons. For example, it took several years to agree on a precise design. Eventually it was decided that one side of the medal should feature De Morgan’s “Zodiac of Syllogism”. This was a drawing of which De Morgan had been especially proud, incorporating notation used in his work on symbolic logic with the initials ADM to form a symmetrical pattern, which he had used as his personal motif. For the medal’s reverse, it was agreed that a profile of De Morgan would be appropriate, and this was taken from a posthumous bust sculpted by the artist Thomas Woolner, which is housed today in the University of London Library.

By 1882, subscriptions from LMS members had raised sufficient funds to enable the Society to endow the award of a medal, worth £10, at intervals of three years. (In 1942, this initial endowment was augmented by a bequest of £250 to the Society by the applied mathematician Sir Joseph Larmor.) The medal was to be made of 22-carat gold, but it would appear from the Society’s records that this was not the only metal used. Minutes from June 1920 reveal that the Council agreed that “the De Morgan Medallist in future be given the choice either to receive the medal in bronze only, or in gold only, or in both as hitherto usual”. Actual evidence of this practice came to light in the summer of 2002, when the Society obtained William Burnside’s 1899 De Morgan Medal cast in bronze. The first medal was awarded at the Society’s annual general meeting on 13th November 1884. After much discussion, it had been agreed “that there should not be any special competition for the medal but that it should be granted by the Council of the L. Math. Society for distinguished services in the advancement of Math. Science”. Given this criterion, it is perhaps not surprising that the inaugural medal went to the man who was arguably Britain’s finest pure mathematician of the time, Arthur Cayley. Subsequent medallists included the algebraist James Joseph Sylvester, the analyst G.H. Hardy, and the philosopher Bertrand Russell. Although it was originally intended “that the Medal be open to Mathematicians of any country”, the majority of its 40 recipients have in fact been British. Despite the award of the fourth medal to the German Felix Klein, in the medal’s early days it was more common for foreign nominees (who included Weierstrass, Hermite, Poincaré and Veblen) to be unsuccessful. More recently, those recipients such as Mordell, Besicovitch, Mahler and Roth, who were born overseas, all spent the majority, if not all, of their careers in the United Kingdom. But irrespective of nationality (at birth or otherwise), it is the calibre of De Morgan medallists over the past 118 years that has resulted in its becoming arguably the highest honour available to mathematicians in Britain, whether they be British or not.

Adrian Rice


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