sign in sign up
<<
Home , Arthur Cayley, Edmond Halley, Henry John Stephen Smith, James Joseph Sylvester, William Spottiswoode

Three Savilian Professors of Geometry dominated ’s mathematical scene during the : Baden Powell (1796–1860), (1826–83) and (1814–97). None was primarily a geometer, but each brought a different contribution to the role.

Oxford’s Victorian -line 1827 Baden Powell elected Savilian Professor 1828 Finals papers first Savilian Professors published 1831 Mathematical Scholarships founded 1832 Powell’s lecture on The Present State of Geometry and Future Prospects of Mathematics 1847 BAAS meeting in Oxford 1849 School of Natural Science approved The University Museum, constructed in the late 1850s, realised in brick and iron Oxford’s mid-century aspirations to improve the 1850–52 Royal Commission on Oxford University facilities for teaching mathematics and the sciences. 1853 First college science laboratory 1859–65 Smith’s Reports on the Theory of Numbers 1860 Opening of the University Museum Death of Baden Powell Henry Smith elected Savilian Professor 1861 The ‘Smith normal form’ of a 1867 Smith’s sums of squares 1868 Smith awarded Berlin Academy prize 1871 Non-Anglicans eligible to be members of Oxford University 1874 Smith appointed Keeper of the University Museum 1874–76 Henry Smith becomes President of the Mathematical Society 1875 Smith’s ‘Cantor set’ 1876 Ferdinand Lindemann visits Oxford Smith’s lecture On the Present State and Prospects of some Branches of 1881 French Academy announces Grand Prix competition 1883 Death of Henry Smith J J Sylvester elected Savilian Professor 1885 Sylvester’s inaugural lecture 1888 Oxford Mathematical Society founded 1894 William Esson elected Sylvester’s deputy 1895–97 Smith’s Collected Papers published 1897 Death of J J Sylvester William Esson elected Savilian Professor Oxford’s Victorian Savilian Professors of Geometry Baden Powell

Baden Powell was Savilian Professor of Geometry from 1827 to 1860. One of his sons was later to found the Boy Scout movement.

Early Oxford career Powell, the populariser

Powell was an accomplished public speaker and he set out on a crusade to educate people through his popular lectures and writings. When the British Association for the Advancement of Science was founded in 1831, he became an enthusiastic supporter.

The Association held its second meeting in Oxford in 1832 and returned in 1847, 1860 and 1894.

At the 1847 meeting Baden Powell gave a two-hour popular lecture on ‘Falling ’ to a large audience. A drawing of the A photograph of Powell taken by The highlight of the mathematical Revd. Baden Powell Nevil Story Maskelyne in the 1850s section’s proceedings was a lecture by on the Baden Powell graduated from Ever since the Honours School in recent discovery of Neptune, in the Oriel College in 1817 with First Mathematics had been introduced In order to promote scientific presence of its French independent Class Honours in Classics and in 1800 students had become more awareness among the general co-discoverer Urbain Le Verrier. Mathematics. He was primarily a exam-focused and less interested public, Baden Powell wrote Indeed, it was in Powell’s house , with a special interest in the subject as a whole. Powell this history of the physical and at this meeting that Adams and in optics, and was one of the first complained that, for examinations, mathematical sciences Le Verrier met for the first time. British scientists to embrace the ‘though a certain portion had “got wave theory of light. up” the four books of Euclid, not more than two or three could add In 1827 Stephen Rigaud, an Vulgar Fractions or tell the cause astronomer and historian of of day or the principle of a pump’. mathematics, migrated from the An examiner of the time told of a Savilian Chair of Geometry to student who reproduced a proof of that of , and Powell was Euclid perfectly, but in his diagrams elected as his successor. He began drew all the triangles as circles. his tenure with high hopes for the part that he could play in raising With great Powell set about the standard of mathematical changing things, but he lacked the education in Oxford. political ability to carry through more than a few modest changes. The new Savilian professor was His most successful innovation, shocked and dismayed by the low however, was to create scholarships esteem accorded to mathematics for the promotion of mathematical in the University. He was advised studies. These were founded in 1831, not to give an inaugural lecture as and were subsequently awarded to a he would almost surely not attract number of notable , an audience. such as William Spottiswoode (later President of the Royal Society) The British Association meeting of 1847 In 1832 he gave a public lecture and Bartholomew Price (Sedleian on The Present State and Future Professor of Natural Philosophy). Prospects of Mathematical and Physical Sciences in the University Baden Powell was the first of Oxford, in which he bemoaned prominent churchman to embrace the declining number of science ’s views on The students. Origin of Species, in a contribution to Essays and Reviews, published just before his death in 1860. Oxford’s Victorian Savilian Professors of Geometry Henry Smith in Oxford

Baden Powell had put Oxford mathematics back on the map, but it was Henry Smith who brought it international recognition.

Early Oxford career Smith and Oxford University

Henry Smith gained First Class Honours in both Classics and Mathematics in 1849 after only seven terms in Oxford, and won the Senior Mathematical Scholarship. He was elected to the Mathematical Lectureship at Balliol College later in that year.

Besides teaching at Balliol he was also asked to run the College’s laboratory for the newly introduced Natural Science course. For this purpose he was sent to study chemistry with Nevil Story Maskelyne in the Old Ashmolean Museum.

A caricature of Smith by a student The University Museum in 1860

The widespread affection for The early 1870s brought a number In addition to his mathematical Henry Smith across the University of changes in Smith’s life. In 1874 work he played a key role in the Community can be gleaned from he was appointed Keeper of the various reforms that transformed the above caricature of him. As University Museum, and lived in Oxford into a modern university. a former student wrote after the Keeper’s house at the right of Smith’s death: this 1861 print. His sister, Eleanor, The University was undergoing ‘Alas!… that his flowing beard and kept house for him. An impressive some major changes, and Smith flying gown will be seen no more, scholar in her own right, she started served on the Royal Commission A photograph of Henry Smith, for his place cannot be filled.’ the ‘Women’s lectures’ in Oxford which set the framework for taken around 1850 by his friend and during the 1860s. this. He was also on the Royal collaborator Nevil Story Maskelyne Commission on Scientific Smith was also elected to a Education. Following Baden Powell’s sudden professorial fellowship at Corpus death in 1860, Smith was elected Christi College, which enabled Smith could persuade where the Savilian Professor of Geometry. him to give up the tutorial other Oxford reformers antagonised: Apparently the other, somewhat teaching he had continued to do ‘He could say the happy word which reluctant, candidate was George at Balliol, though he continued as quelled a rising storm’. Boole (of Boolean fame), an Honorary Fellow there. These His background in classics, but Smith soon justified the changes gave him more time to mathematics and chemistry gave him electors’ faith in him, in a spend on his research. an exceptionally broad perspective. of important research papers that applied the new concept of matrices to .

Henry Smith in old age Oxford’s Victorian Savilian Professors of Geometry Henry Smith’s mathematics

Henry Smith had an international reputation, and he was the only 19th-century British to win major scientific prizes from both France and Germany.

Smith’s mathematical research International prizes

Smith regularly invited Continental mathematicians, such as Charles Hermite and , to talk at the British Association meetings.

In June 1876 his guest in Oxford was the young Ferdinand Lindemann, with whom he discussed the Henry Smith’s Report on the Theory of Numbers possibility of showing that π is transcendental – that is, it is not a In addition to his diverse teaching responsibilities, Henry Smith began a root of any polynomial equation systematic study of Number Theory, an area rather neglected by British with integer coefficients. Five years mathematicians. The British Association for the Advancement of Science later this was proved by Lindemann, commissioned him to prepare a Report on the Theory of Numbers, a finally settling various questions comprehensive survey of the subject, which appeared in six instalments which had been raised in antiquity. between 1859 and 1865. Ferdinand Lindemann In 1869 the Berlin Academy of In the course of this work he also Sciences awarded Smith its Steiner SUMS OF SQUARES showed that in eight , prize for producing a geometric there is an exceptional lattice of construction (with algebraic In 1861 Smith showed that points different from the standard justification) for the other three any matrix with integer entries lattice of points with integer points of intersection of two quartic can be reduced by row and coordinates. This lattice, now curves when 13 of the 16 points are column operations to a diagonal known as E8, plays an important already known. form in which each diagonal role in the study of symmetry and entry divides its successors. This and was recently shown to In 1881, whilst recuperating from enabled him to give a complete give the optimal sphere packing in a fall, he noticed that the French solution of a problem studied eight dimensions. Academy of Sciences was offering in antiquity, giving precise its Grand Prix for solving the very conditions for when simultaneous In 1875 he published a paper problem of representing positive equations with integer coefficients on the theory of integration, in integers as sums of squares that have integer solutions. which his examples showed how he had published in 1867. He wrote to integrate some rather badly to Hermite to point this out and In 1867 a subtle application of behaved functions. One of these received an embarrassed reply, these same ideas enabled Smith examples was probably the first suggesting that he submit his earlier to solve another problem in Charles Hermite published example of a fractal. result (in French) for the prize. number theory. In 1621 it was It considered functions that were Smith complied, but he died in conjectured that every positive discontinuous at the points of what February 1883 before the prize integer can be written as the sum is now called a ‘Cantor set’, though was awarded. of four squares (sometimes in Cantor published a special case of several ways), a result proved by it only some years later. Two months later it was announced Lagrange in 1770. that the prize would be shared Smith was President of the by Smith and a young Prussian For example: London Mathematical Society student . 4 = 22 + 02 + 02 + 02 or 12 + 12 +12 +12 from 1874 to 1876. His wide- Journalists soon discovered that and 7 = 22 +12 +12 +12 ranging Presidential address Smith’s solution had been published On the Present State and many years before, and accused Similar questions may be asked Prospects of some Branches of Minkowski of plagiarism. Whether for sums of five, six, or seven Pure Mathematics surveyed, Minkowski knew of Smith’s paper is squares, and Smith used his among other things, work on unclear, but he went on to become earlier matrix theorem to obtain prime numbers by Riemann and one of the leading researchers solutions for all cases by Chebyshev, as well as Hermite’s in number theory, an admirer a uniform method. recent proof of the transcendence of Smith’s work, and his worthy of e. scientific successor. Hermann Minkowski Oxford’s Victorian Savilian Professors of Geometry James Joseph Sylvester

J J Sylvester was Savilian Professor of Geometry from 1883 to 1897. He was appointed at the age of 69.

Sylvester comes to Oxford Sylvester’s teaching

His inaugural lecture took place Whereas Henry Smith had been a in the existence and unity of that in December 1885, two years painstaking college tutor, Sylvester intellectual world which exists after his election, and had the could only lecture on his own within us, and is at least as real as snappy title of On the method researches, which was not popular that with which we are environed.’ of reciprocants as containing an in a place so wholly given over to exhaustive theory of the singularities examinations. His high-minded As a result, Sylvester’s lectures were of curves. This lecture, in which he teaching strategy, as outlined in his too remote from the examination paid warm respects to his Savilian inaugural lecture, was as follows: needs of students, and few students predecessors Henry Briggs, John ‘I think that I shall best discharge attended them: Wallis, and Henry my duty to the University by ‘Here in Oxford I am fortunate if Smith, was vintage Sylvester – even selecting for the material of I get an auditory of 6 persons… down to the recital of a sonnet of my work in the class-room any I begin to feel therefore very like his own composition, under the subject on which my thoughts the stalled Ox.’ inspiration of discovering that a may, for the time being, happen term involving b4d did not appear to be concentrated, not too alien However, some aspects of his where it might be expected to, in a to, or remote from, that which teaching were notable. He arranged table of reciprocative protomorphs. I am appointed to teach; and a grant from the University to It begins: thus, by example, give lessons in purchase from Germany a set of James Joseph Sylvester the difficult art of mathematical geometrical models for a course of TO A MISSING MEMBER thinking and reasoning – how to lectures ‘On surfaces, illustrated Henry Smith’s untimely death in Of a Family of Terms in an follow out familiar suggestions by plaster, string, and card-board 1883 created another vacancy for Algebraical Formula of analogy till they broaden and models’. He announced his lectures the Savilian Chair of Geometry. Lone and discarded one! deepen into a fertilising stream of for Tuesdays and Saturdays, Sylvester had spent seven years as divorced by fate, thought – how to discover errors commencing on Saturday October the first Mathematics Professor at From thy wished-for fellows – and repair them, guided by faith 23, 1886 at 4.30pm. the newly founded Johns Hopkins whither art flown? University in , USA. Where lingerest thou in thy Wishing to return to his home bereaved estate, country he decided to apply. Like some lost , or buried meteor stone?… As a Jew who had not been allowed to receive his degree from in the 1830s, he feared that his religion might still count against him. Also, he was already 69 and was a non-Oxford man. As he wrote to his friend, the Cambridge mathematician : ‘Do you think I am likely to be appointed? If the chances are considerably against me – it would be impolitic to offer – but perhaps even if impolitic it would be right on my part to do so by way of testing what I consider – although you may not perhaps agree with me – an important principle.’ Indeed, attempts had been made In his Laws of Verse Sylvester set to persuade him to withdraw on out his view of the mathematical account of his age. But, as the laws that govern the writing of greatest British mathematician poetry. His extensive annotations of his time, he was chosen appear in his copy, now in the unanimously by the seven electors. Mathematical Institute This plaster model, purchased by the University in 1886, illustrates the 27 lines on a . As well as his course, Sylvester gave a public lecture on these models Oxford’s Victorian Savilian Professors of Geometry Sylvester as Savilian Professor

As a way of encouraging more research activity, Sylvester founded the Oxford Mathematical Society. But his age was beginning to take its toll…

Oxford research Women’s education and his retirement

Coming from Baltimore, where activity; and the latest proof of this Like his predecessor, Henry Smith, SYLVESTER AND he had built up a mathematics is the formation, during the last Sylvester kept in regular touch WOMEN’S EDUCATION research community, Sylvester term at Oxford, of a Mathematical with international colleagues. He was surprised and disappointed Society, which promises, we hear wrote to David Hilbert and Felix Sylvester was always a great to find no such community in without surprise, to do much for Klein, and invited to Oxford the supporter of women’s education, Oxford: all that seemed to matter the advancement of mathematical Danish mathematician Julius helping mathematicians such as was examinations. In a letter to science there.’ Petersen, with whom he worked the American Christine Ladd. Daniel Gilman, President of Johns on some . Among women mathematicians Hopkins University, he wrote: At its first meeting on 9 June 1888, that he particularly admired was ‘Entre nous this university except Sylvester was elected President. But he realised that his the Russian Sonya Kowalevskaya, as a school of taste and elegant light There were two Vice-Presidents – mathematical interests were whom he referred to in one of literature is a magnificent sham. William Esson, later to be Sylvester’s becoming increasingly out of date. his sonnets. It seems to me that Mathematical successor in the Savilian Chair, and As he wrote to Arthur Cayley: science here is doomed and must Bartholomew Price, the Sedleian ‘I expect Poincarre [the French eventually fall off like a withered Professor of Natural Philosophy. mathematician Henri Poincaré] branch from a tree which derives The secretary was E B Elliott, soon tomorrow and he will have rooms no nutriment from its roots.’ to be the first Waynflete Professor of in College. I rather dread the Pure Mathematics. The Society met encounter as there is so little in In order to encourage his six per year, with about three the way of Mathematics upon colleagues to take an interest in or four papers read at each meeting, which I can hope to talk to him.’ creative mathematics, he founded and for many years was the only the Oxford Mathematical Society. forum in Oxford for discussion Meanwhile his body was gradually As Arthur Cayley remarked: of research-level mathematics. weakening, and eventually his ‘Wherever Dr Sylvester goes, The list of original members is eyesight deteriorated to such there is sure to be mathematical shown below. an extent that a deputy had to be appointed to carry out his lecturing tasks. This was William Esson, an established Oxford figure who succeeded him after his death in 1897. But it would not be until after the First World War that a true research ethos came into being in Oxford mathematics, with the arrival of G H Hardy.

Above: Sonya Kowalevskaya Below: Mary Somerville

The most famous woman of 19th-century British science, and a keen advocate of women’s mathematics education, was Mary Somerville, after whom the Oxford college was named.

It was not until 1920 that women were admitted to Oxford degrees and full University membership. William Esson

These posters were written by Robin Wilson and Keith Hannabuss, with the assistance of Raymond Flood, Adrian Rice and Dyrol Lumbard. The material on Sylvester is adapted from material written by the late John Fauvel.