Gresham College Lectures

Oxford’s Savilian Professors of Geometry: 400 Years On

May 06, 2022 Gresham College
Gresham College Lectures
Oxford’s Savilian Professors of Geometry: 400 Years On
Show Notes Transcript

England’s earliest chair of mathematics was that of Gresham College, founded in 1597, but who came next? 

The earliest University-based mathematics professorship was Oxford’s Savilian Chair of Geometry, founded in 1619. 

This illustrated lecture outlines the 400-year history of this Chair, from its beginnings to the present day, and features such figures as Henry Briggs, John Wallis, Edmond Halley, James Joseph Sylvester and G. H. Hardy.


A lecture by Robin Wilson

The transcript and downloadable versions of the lecture are available from the Gresham College website:
https://www.gresham.ac.uk/watch-now/savilian-professors

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- Well good afternoon, everybody. And welcome to this book launch of "Oxford's Savilian Professors of Geometry," both to those of you here at Barnard's Inn Hall, and those of you who are watching online. This book was published by Oxford University Press in January. Now I was wondering how many of these five professors, Savilian professors, can you recognize? If you can't recognize them all, you should probably stay here, because today you'll be meeting all 20 of them, covering a period of 400 years. So the authors for this edited book are all acknowledged as experts in the history of mathematics, and their chapters are illustrated by over 130 pictorial images, many of which you'll see today. Our journey begins as Henry Savile's founding of his Chairs of Geometry and Astronomy, as related by William Poole of New College, the Oxford College now associated with the Savilian chairs, and also of Oxford's history faculty. And also from the same faculty, are Philip Beeley and Benjamin Wardhaugh, who have written on John Wallis who was Savilian professor for over 50 years, as you'll see. Wallis' successor was Edmond Halley, or Halley, of Halley's Comet fame, the first of the succession of astronomers, as described by Allan Chapman of Wadham College, and Chris Hollings of Oxford's Mathematical Institute and The Queen's College. These then take us to the Victorian period, where three Savilian professors, Baden Powell, Henry Smith, and James Joseph Sylvester are introduced by Keith Hannabuss of Balliol College and Karen Parshall of the University of Virginia. Then moving on to the 20th century, we meet G.H. Hardy, and his successor, Edward Titchmarsh, while Frances Kirwan, the current Savilian professor of geometry has written about her doctoral supervisor, Michael Atiyah, and his successors. And Mark McCartney of the University of Ulster has interviewed her predecessor, Nigel Hitchin. Incidentally, Mark McCartney and Chris Hollings are currently editing a companion volume on Oxford's Sedleian professors of natural philosophy. So here are the first nine geometry professors, taking us through the 17th and 18th centuries, and into the 19th. And a few of them, such as Briggs, Wallis, and Halley, would become familiar names, as you'll see, while some others are largely forgotten. So how did the professorship start? Henry Savile was born in 1549, and had an eventful career, eventually becoming both provost of Eton College and warden of Merton College in Oxford. The author of an eight-volume history of St. Chrysostom, and other scholarly works, his first love was mathematics. And here you see his capacious chesta mathematica, his mathematical chest for his books and manuscripts, now in the Bodleian Library. And on the right is his magnificent memorial in the ante-chapel of Merton College, where he is flanked by Euclid and Ptolemy, whose writings he expounded at Oxford. While below, you can see some handwritten lecture notes on astronomy with Ptolemy's work on the left and Copernicus' then very recent work on the right. In 1619, Henry Savile founded his chairs of geometry and astronomy for persons of character and repute from any part of Christendom, well-skilled in mathematics and 26 years of age. For the geometry chair, John Aubrey has recorded, as you see here, that Savile first sent for Mr. Gunter from London to have been his professor of geometry. So he came and brought with him his sector and quadrant, shown on the left, and fell to resolving of triangles and doing a great many fine things. Said the grave knight, Savile."Do you call reading of geometry? This is showing of tricks, man." And so dismissed him with scorn, and sent for Henry Briggs from Cambridge. But Henry Briggs was, by then in London, as the first professor of geometry at Gresham College. Gresham College had been established to present free lectures to the general public, as it still does over 400 years later. And while at Gresham College, Briggs studied eclipses and navigation, and he later produced the map of North America that you can see on the right. He also became obsessed by the new and admirable logarithms of John Napier, shown here below on the left, designed to simplify calculations by replacing multiplication and divisions by the rather simpler additions and subtractions. And as Briggs enthused,"I never saw a book which pleased me better and made me more wonder." But Napier's tables were clumsy to use, and Briggs introduced his more practical logarithms to base 10. Producing first, the tables in the middle, and then in 1624, by which time he was in Oxford, he published the more extensive ones, the more extensive tables that you can see on the right. And these included the logarithms of no fewer them 30,000 numbers, which he calculated by hand to 14 decimal places. Certainly a prodigious feat of calculation. Briggs' gravestone, shown above, can still be seen in the ante-chapel at Merton College. Meanwhile, having failed to get Savile's geometry chair, Edward Gunter went to Gresham College as its professor of astronomy, while the Savilian astronomy chair was held by John Bainbridge, whom you see here. And his memorial, shown in the middle, is also in the ante-chapel of Merton College. Bainbridge wrote several notable works, including one on Ptolemy's planetary hypotheses. And this one on the right is "Canicularia," on ancient Egyptian astronomy. After Briggs and Bainbridge, the Oxford chairs were occupied by two people, Peter Turner in geometry, and John Greaves in astronomy. Greaves had actually previously been the Gresham professor of geometry here in London, and succeeding Turner in that position. Turner had held it earlier, following Briggs. Who were these people? Well, Turner was described by contemporary as a most exact Latinist and Grecian who was well skilled in Hebrew and Arabic, was a thorough paced mathematician, most curious critic, a politician statesman and whatnot. But his mathematical writings, if there were any have not survived. Primarily a university politician, he designed this weekly chart that presents the, presented the university's syllabus for the liberal arts. An ardent royalist in the civil war, then raging, Turner was later imprisoned and his loyalty to the royalist cause cost him his career. John Greaves on the right was a more impressive figure, who was proficient in many fields. He studied oriental languages and collected ancient manuscripts. He also acquired astrolabes and other mathematical instruments to take on his extensive travels in Europe and the Middle East. And while in Egypt, he entered the Great Pyramid of Cheops to measure its inner chambers. Described his experiences in his memorable book"Pyramido-Graphia" shown below on the right. But the English civil war was raging. And by 1649, the royalist professors had been replaced by supporters of the parliamentary cause. Peter Turner was succeeded by John Wallis, who had shown exceptional service as a codebreaker for the parliamentarians. But as Wallis admitted,"in the year 1649, I moved to Oxford"being then public professor of geometry of the foundation of Sir Henry Savile. And mathematics, which had before been a pleasing diversion was now to be my serious study." But although Wallis had little mathematical experience before his appointment, he soon made up for lost time as you'll see. And here on the left, you can see a 1678 engraving on him. And on the right is the magnificent portrait by Godfrey Miller that now hangs in Oxford's examination schools. Wallis held the geometry chair for 54 years, the longest tenure of any Savilian professor. And here on the left is his inaugural lecture given in the geometry schools in October 1649. While on the right are two items from his first important book. A treatise on conic sections of the ellipse parabola and hyperbola. His treatise on conic sections published in 1655. And it is here that we see the first appearance of the symbol that we now use for infinity. Just about see it at the end of that arrow. While before, while below is his use of Cavalieri's ideas to calculate areas. And the very next year, 1656, Wallis produced his best known work."The Arithmetic of Infinities" where he solved several area problems. And among the many achievements here was his infinite product for pie, which you can see above where the small rectangle you see there represents four over pie. And it was obtained using interpolation as carried out in his table below. But John Wallis was not an easy man to get on with. And he became involved in several disputes, such as those with the philosopher Thomas Hobbs, whose attempts to solve various classical problems, such as squaring the circle were described by Wallis in the work on the left, as inept. Hobbes then replied attacking Wallis in the acrimonious work on the right. And Wallis then retaliated and so on. And their rivalry continued for almost 25 years until Hobbes' death. Wallis' later publications included "A Treatise of Algebra" both historical and practical. It contained the earliest discussion of algebra's history, although from a very English point of view. He even accused Descartes of plagiarism. And on the right is his collected works, published in three volumes by the Oxford university press, which was then housed in the newly built Sheldonian theater, which you can see below. So after 54 years, Wallis died in 1703 and his successor was Edmond Halley, shown on the left in his youth and on the right, in his old age. He was an undergraduate at Queens college and below is his signature in the college register. And although we know him mainly is an astronomer, it was Savile's chair of geometry which he came to occupy and he occupied it for almost 40 years. Halley had various varied interests. While still a student, his sailed to Saint Helena to map the skies of the southern hemisphere to a greater accuracy than previously. Which secured him an international reputation and election to the Royal society at the age of just 22. It also led to King Charles II commanding Oxford university to award Halley an MA degree without examination. Halley's interest in magnetism led to him producing the magnificent chart of magnetic variation that you can see here on the left. Where he introduced the now familiar idea of joining points with equal values. Later in 1715, a solar eclipse in England led him to send the map on the right around the country in order to solicit local observations. The Savilian chair was actually Halley's first academic post. And to establish his credentials, what did he do? Well following a widely admired inaugural electron geometry, he secured his academic reputation by producing what became the definitive addition of the ancient text on conics by Apollonius. And it's front piece that you can see here on the right features the image first introduced by Savile, which shows the Greek philosopher Aristippus who having been shipwrecked on the Island of Rhodes was assured of the local inhabitants civilized nature when he discovered mathematical drawings in the sand. And in fact, there are several books published by Oxford University press, which have this picture. One by Savile, and this one by Halley. There's another one in between, and they all had different mathematical drawings depending on the contents of the book in hand. So Halley lived at this house in New College Lane on top of which he built an observatory, which a contemporary described as very convenient and indeed useful to the university, and what Henry Savile did expect from them. Indeed, these two adjacent buildings housed the two Savilian professors for some 200 years. In 1720, Halley was appointed astronomer royal. And for the last 20 years of his life, he spent much of his time at Greenwich while continuing to hold his Oxford position. That was allowable in those days. And his house, the one in white now marked with a plaque, you can see below it used to be marked with the plaque in the middle where Edmond was incorrectly spelled, but now that's been replaced by the one that you see on the right, which was unveiled about three years ago. And his house is currently used for housing the colleges undergraduates. Halley was of course an astronomer. In fact, the first of several astronomers to hold the Savilian chair of geometry. And his successor was Nathaniel Bliss, who also became astronomer Royal, but late in life, giving him only two years at Greenwich. The left hand image that you can see here, wrongly calls him professor of astronomy. Nathaniel Bliss, AM professor of astronomy in Oxford. Where does that come from? That engraving, it was engraved on a pewter mug during a rather, exciting dinner. Bliss talk his professorial duties very seriously and lectured on a range of topics. In fact, ranging from algebra and geometry to the use of logarithms and surveying instruments. Although one student actually the teenage, Jeremy Bentham, claimed that almost all Bliss' practical experiments in his lectures tended to go wrong. By this time Isaac Newton had died, but Oxford teaching was already becoming very influenced by his ideas. And here's a course of, of mathematical lectures and experiments based on Newtonian principles, all in great details there. And Bliss' teaching was along similar lines. Another Oxford Newtonian of the time was John Desaguliers, whom you can see shown at the top. His fine drawings and expositions of experimental philosophy helped to popularize Newtonian physics. And this is just one of several beautiful plates showing scientific diagrams. So that was Nathaniel Bliss. But we know rather little about the next two geometry professors. Joseph Betts, another astronomer was also interested in eclipses as his diagram of the 1764 solar eclipse shows. But he died after only one year in post. His successor, John Smith, occupied the chair for over 30 years. But he seems to have had few, if any, mathematical credentials. A physician for the new Radcliffe infirmary, he spent much of his time practicing medicine in Cheltenham while others carried out his Oxford lecturing duties. And here's his observations of the use and abuse of the Cheltenham waters. Proudly presenting him as Savilian professor of geometry in the university of Oxford. The last two from our first batch of geometry professors were active in mathematics, although again, mainly interested in astronomy. And in fact, both of these subsequently switched over to the Savile astronomy chair. But Abraham Robertson's geometry lectures, incidentally Abraham Robertson was one of the ones who filled in for John Smith when John Smith was looking at the waters of Cheltenham. But Robertson's geometry lectures were popular and he published on Euclid. And also as you see here on Conic sections as an introduction to the Newtonian philosophy. While his successor, Stephen Rigaud shown here in silhouette, wrote on a range of topics from Archimedes to steam navigation. So we now move to the second batch of geometry professors. We've now reached the 19th century. And we look next at the Victorian period, which is represented by three Savilian professors, before proceeding to the 20th century and beyond. So the 10th geometry professor was Baden Powell, who occupied the chair for over 30 years. And if his name seems familiar, it may be because one of his sons founded the boy scout movement. I think it was his sixth son by his third wife, but I'm not quite sure. And here you can see three images of Baden Powell, including the early photograph on the left, which was taken by, taken around 1850 Baden Powell's career took a common progression off time. Getting a first class degree, in his case at Oriel college. Followed by a college fellowship leading to ordination and a college church living. So Powell became a vicar in London where he spent his spare time researching into the polarization of light. And this led in turn to a fellowship of the Royal society and eventually to his Savilian appointment in Oxford. But Oxford mathematics at this time was at a very low ebb. With poor standards and small student numbers. And on his arrival, Paul was warned off giving an inaugural lecture because no one was likely to attend it.(audience laughs) So instead he produced two publications, a pamphlet that you can see on the left, on the present state and future prospects of mathematical and physical studies in the University of Oxford. Where he argued the importance of these studies as part of a liberal education. And on the right, a history of natural philosophy, which was designed to promote general scientific awareness. And in truth, Powell was not primarily a mathematician, but rather a popularizer of science. And here you can see him at London's Royal institution giving a public lecture in 1851 on the rotation of the earth. While here, the upper picture, both pictures are from Oxford's second meeting with the British association for the advancement of science, that started in 1831, I think in York. The second meeting was in Oxford. And Oxford's second meeting was in 1847 and here at the top, you can see it shows Baden Powell in Oxford's Radcliffe camera giving a two hour lecture on falling stars. And also attending the same meeting were John Couch Adams and Leverrier, the two recent discoverers of the planet Neptune. And the lower picture shows Adams lecturing on this achievement. Well Baden Powell was a supporter of Darwin's theory of evolution. But died in 1860, shortly after writing a controversial religious tape religious article that impressed Darwin but alarmed many others. And his successor in the Savilian chair was Henry Smith, whom you can see here. Henry Smith of Balliol college. The first real mathematician to hold the post for well over a century. And on the right is a lovely student caricature of him. A highly popular figure, Henry Smith spoke several languages and was well informed on a wide range of subjects. And he held several college and university positions. And one of his positions was as keeper of the university museum, which had been constructed in the 1850s. As you can see here on the left there, you can see the university museum being constructed in the mid 1850s. There it is complete. This was at the time, of a big scientific meeting. There you can see the keeper's house in the middle at the top. And he lived there with his sister. And the bust of him just next to there can be, can still be seen in the university museum. And there below is a, an engraving, a drawing of the university, the interior of the university museum. Henry Smith's mathematical research has covered a range of topics. From matrix algebra, where he introduced a so-called Smith form of a matrix, to the theory of integration, where he presented a form of Cantor's ternary set eight years before Cantor got there. But maybe his most important contributions were in number theory, the theory of numbers, and here is the first of six major articles on the subject that he wrote for the British association. Smith's work on number theory included the problem, of counting the ways in which we can reach a given number by adding perfect squares. For example, if we're given 11, you can write it as some of five squares by taking nine, two ones, and two zeros, Or you can take two fours and three ones, or any rearrangement of these. And Smith wrote a paper, counting the number of ways of getting of sums for five squares and also for seven squares. They, the problem had been solved for other numbers of squares, but five and seven were the two that no one had been able to do until he came along. So imagine his consternation then when some years later, the French academy of sciences posed the five squares problem as its special yearly prize competition. Smith wrote to the competition chair, a Charles Hermite you can see in the center pointing out his priority. Hermite was rightly greatly embarrassed and urged Smith to submit his solution in French.(audience laughs) Which of course Smith knew, but sadly Smith was unwell and he died before completing that task. And the prize was eventually shared between him posthumously and a young German Hermann Minkowski on the right, who had reached similar conclusions and who later became a well known mathematician in his own right. Henry Smith was succeeded as Savilian professor by James Joseph Sylvester, who held a number of positions in England before becoming the first professor of mathematics at the newly founded John's Hopkins university in America. But as a Jew, Sylvester had been barred from receiving his Cambridge degree in the 1830s, or from holding any academic post in Oxford or Cambridge. But in 1871, the rules changed. And so Sylvester writing from Baltimore, he successfully applied for the Savilian chair and he was appointed at the advanced age of 69. Earlier, Sylvester had worked with the Cambridge mathematician, Arthur Cayley, especially on a subject known as invariant theory. And the two became firm friends. But Sylvester soon became disillusioned with Oxford, as the research community that he developed in Baltimore did not exist in Oxford where the emphasis was almost entirely on undergraduate teaching. And as Sylvester complained in this letter to Cayley, he says, "I am bound by usage, and by the wants of the undergraduates reading for moderations to give a course or courses of lectures on pure synthetic geometry." Indeed as a professor of geometry, Sylvester had to give regular lectures on that subject. And one of his ideas was for a course of lectures on surfaces illustrated by plaster string and cardboard models. To be accompanied by three dimensional models, such as the one you can see on the right. He no doubt came across these models by Ludvig Brill of Germany. And here you can see a laboratory in, at Johns Hopkins university in Baltimore with lots of these models there, in the cupboards there. But unfortunately the models didn't arrive in time for his lecture course. So instead he lectured on Tuesdays and Saturday afternoons, that wouldn't be popular now. On projective reciprocates and their geometrical applications, a topic from invariant theory. Well the models eventually arrived and they still exist. They're actually housed in the Mathematical Institute in Oxford. But few undergraduates attended his lectures as they were of no help with their university examinations. However Sylvester did manage to promote mathematical awareness by founding the Oxford mathematical society. And this soon became the main forum for research activity in Oxford. Founded in 1888. Here you can see a list of the first members. It met for many years, right up to the 1970s On the right, you can see Sylvester as president and the secretary was Edwin Elliot, an algebraist who later became the first Waynflete professor of pure mathematics. And below them are the two vice presidents Bartholomew Price, Sedleian Professor of natural philosophy and sometime mentor to the Oxford mathematician, Charles Dodgson, better known as Lewis Carroll. And also you can see William Esson who became deputy professor when eyesight problems prevented Sylvester from carrying out his Oxford duties. It was around 1892 that Sylvester found he couldn't lecture anymore. He came to London and Esson continued as his deputy professor. Following a brilliant undergraduate career Esson had been appointed a fellow of Merton college shortly after graduation, and was responsible with Henry Smith and others for reintroducing the intercollegiate lecture scheme that would replace college based lectures. Up to that time, the professors lectured in their own colleges and the students went there. Otherwise students would have all their teaching done in their own colleges and it was through Esson and Smith and so on that the intercollegiate system that we know now came in. Most of Esson's academic contributions were not actually directly in mathematics, but were of its use, in particular in chemical kinetics. And after Sylvester's death in 1897, Esson was appointed his successor His period as Savilian professor was uneventful, and he died in 1916 during World War I. So as a result, his successor was not in post until after the war. And this was Godfrey Harold Hardy, the greatest British pure mathematician of the first half of the 20th century, with particular interest in analysis, mathematical analysis and in number theory. Although he's mainly remembered as a Cambridge man, he spent his happiest years in Oxford, as he said, producing in 11 years, no fewer them around a hundred papers, many with his longtime collaborator, J.E. Littlewood. And here you can see two pictures of Hardy. If you look at his mathematician's apology, which I'll show you in a minute, there's a long introduction by C.P. Snow who says that, in fact, he only knew of five photographs of Hardy. Hardy didn't like being photographed. Well, I know of at least 14, and here are two of them, neither of them I think, known to C.P. Snow. But why did Hardy leave Cambridge? After five years of close collaboration at Trinity college with a brilliant Indian genius, Srinivasa Ramanujan shown on the left the latter had fallen ill and returned home leaving Hardy devastated. Also disgusted by the pro-war attitudes of the Trinity fellows, especially in their treatment of the young lecturer Bertrand Russell shown in the middle Hardy needed a change of scene. Administrative tasks had become increasing irksome and his work with Littlewood shown on the right, was going through a bad patch. So Hardy applied to Oxford and duly took up the Savilian chair in early 1920. As I mentioned earlier, these positions had for some years been linked to New College, and here's a 1920s view of the college. Hardy's rooms were in the block, the new block top of the picture. A true college man, Hardy enjoyed the atmosphere of the senior common room and was often the life and soul of the party, getting all his colleagues to play all sorts of clever games, which some of them enjoyed, some of them enjoyed. Hardy's inaugural lecture was given in May, 1920 on some famous problems from number theory. And in particular, he'd become interested in what's called Waring's problem, some famous problems of the theory of numbers and in particular Waring's problem. It had long been known that every number can be written as the sum of four perfect squares, or is the sum of nine cubes or 19 fourth powers. But can you carry on in this way, can similar statements be made about higher powers? And if so, how many of those higher powers are needed? Well together with Littlewood, Hardy published no fewer than eight papers on the subject. Indeed in total, these two Hardy and Littlewood wrote almost a hundred joint papers causing a contemporary to remark,"there are only three English mathematicians, Hardy, Littlewood and Hardy-Littlewood."(audience laughs) And this picture taken in Cambridge seems to be the only one of them together. Well Hardy disliked tutorial teaching, but he loved lecturing. And as a professor of geometry, he gave at least one course of geometry lectures every year, as well as giving a range of other things. Number theory, he gave a course of mathematics for philosophers and all sorts of other topics. And he also much enjoyed supervising research students. In the 1920s, doctoral degrees were being introduced in Oxford. And Hardy had several students who later became well known. These included his Savilian successor, E.C. Titchmarsh whom we'll meet in a moment and Edward Wright with whom he wrote a celebrated book on number theory and who later became vice chancellor of the University of Aberdeen. Hardy was also a strong supporter of women's education. And you can see him here with his doctoral student, Mary Cartwright. Who later became Mistress of Girton College in Cambridge, and was the first woman to become president of the London Mathematical Society. As you can see, one of Hardy's main recreations was cricket. And here we see him leading out a cricket team consisting mainly of his research students, during the 1926 British association meeting in Oxford. Hardy described this photograph as mathematicians versus the rest of the world. A firm internationalist, Hardy worked with others to rehabilitate continental mathematicians after the war. In particular, he was active in the Rockefeller foundation scheme for enabling international scientists to work abroad. And he hosted some of these in Oxford. In particular these included the Hungarian mathematician George Pólya shown here, who visited England for six months with Hardy followed by six months in Cambridge with Littlewood. And an outcome, or an outcome of these was their co-authored book on "Inequalities". But in addition to his 300 papers, Hardy also wrote several books, including a very influential course on pure mathematics and also his well known retrospective,"A Mathematician's Apology" written in 1940, where he describes himself as a mathematician towards the end of his life. And "A Mathematician's Apology" should really be read by all students of mathematics. It is highly recommended whether you agree with what he says or not, it is something that everyone should read. He also co-edited Ramanujan's"Collected Papers". Ramanujan, as I said had gone back to India and tragically died in 1920 at the age of just 32. While in Oxford, Hardy became president of the London Mathematical Society and also of other societies. And here is the top of his, the beginning of his presidential address to the mathematical association on what is geometry. In which he insisted that, "I do not claim to know any geometry, but I do claim to understand quite clearly what geometry is," an interesting distinction. In 1931 Cambridge's Sadleirian chair, very prestigious chair became vacant and Hardy decided to return there not least because he could then live at Trinity college forever rather than having to give up his new college rooms upon retirement. So over he moved to Cambridge and his Oxford chair was taken by his former research student, Edward Titchmarsh. Who heard about the position only by chance, happening to bump into an Oxford mathematical colleague in the street. He said, oh, have you applied? The deadlines tomorrow.(audience laughs) And also Titchmarsh stipulated that if appointed, he could not undertake to lecture on geometry. And his application was only a page long and so done rather roughly. But anyway, he was appointed. And the requirement to have to lecture on geometry was duly dropped. And the Savilian professor of geometry can now come from any area of pure mathematics. Here are two letters sent to Titchmarsh. The first on the left from the university registry, is his appointment letter as Savilian professor. Which I obtained a picture of from the Titchmarsh family. On the right is a letter sent to him on a problem in analysis by G.H. Hardy. Dear Titchmarsh, and then he goes straight into the problem, no preamble. Like Hardy, Titchmarsh published several influential books in addition to his many research papers. The first was a short monograph on the Riemann zeta function which he later expanded into a major book. Another was his "Theory of Functions" on real and complex analysis, which I studied for many long hours when I was taking finals. And this book was once described as the rebellion of a young, widely read professor against a narrow range to which mathematical analysis was then so often confined. It didn't excite me quite as much as it did the writer of that, but even so it helps me take my finals. But Titchmarsh's method of writing books was rather unusual. He would research a topic for a few years. And then sign off by writing a book on it. And then he moved on to a completely different area and repeated the process. But in January of 1963, Titchmarsh died suddenly and unexpectedly, and his place was taken by Michael Atiyah, or later Sir Michael Atiyah. Larger than life in personality, he occupied the chair for five years and he was a genuine geometer with a wide interest also in other areas. Atiyah worked with many distinguished mathematicians from around the world. Here are three of his collaborators whose names will be known to mathematicians, Friedrich Hertzberg from Germany, Isadore Singer from the U.S. and Raoul Bott, a U.S. citizen of Austrian Hungarian descent. And all of them visited him in Oxford, sometimes for extended periods of time. Work with Hertzberg led to the development of of an area of mathematics known as K-theory, and also with, with Singer to the so-called Atiyah-Singer index theorem. For which they were jointly awarded the prestigious Abel prize, an equivalent if you like of the Nobel prize in 2004 by King Herald of Norway as shown below. Many years earlier in 1966, Atiyah had received a Fields Medal. The International Award for Mathematicians under the age of 40, and the top picture recalls the three Fields Medalists who coincided for a while at Oxford. Two others Simon Donaldson and Daniel Quillen. Michael Atiyah was Knighted in 1983, and received the Order of Merit in 1992. He finally left Oxford in 1990 to become simultaneously Master of Trinity college Cambridge, Director of the new Isaac Newton Institute there oh, and also president of the Royal society. In 1969, Atiyah's place as Savilian professor had been taken by the topologist and Ioan James who was in post for over 25 years. Following in the footsteps of his Oxford doctoral supervisor Henry Whitehead, he quickly achieved an international reputation for his work topology, and he wrote and edited many influential books and papers on the subject. And this bust of him at the top is in Oxford's mathematical institute. Incidentally his supervisor, Henry Whitehead that you can see top right, he was also a pig farmer who claimed to get the mathematical inspiration for his theorems by scratching the backs of his pigs. He was always in the Mathematical Institute in the morning, then at lunchtime he went back to the farm, scratched the backs of his pigs and wrote his mathematical papers.(audience laughs) I always said that the Oxford mathematical Institute should have a permanent pig there, but that hasn't been taken up. On Ioan James' retirement in 1995, Richard Taylor was appointed. Two years earlier, Andrew Wiles, who you can see below had presented a proof of Fermat's Last theorem that the equation X to the N plus Y to the N is Z to the N, has no positive solutions if N is at least three. But unfortunately there turned out to be a gap in the proof. And it was Richard Taylor who collaborated with Wiles to fill this gap. But unfortunately, Richard Taylor stayed in Oxford for only a year leaving to take up an appointment at Harvard university. So we come finally to the most recent Savilian professors, Nigel Hitchin and Frances Kirwan. I won't say much about them except to remark that Nigel held the position for 20 years and was interviewed for the book. And that Frances who wrote the chapter on Michael Atiyah, her doctoral supervisor and who also wrote the books forward is still in post having now held it for almost five years. And very appropriately Frances was recently awarded the Royal society's very prestigious Sylvester Medal, named of course after one of her Savilian predecessors. So to conclude, our book on the "Savilian Professors of Geometry" is now available from Oxford University press, and can be ordered from them online. But for more general information about mathematics in Oxford over the past 800 years and not just the Savilian professors, please see the book "Oxford Figures" edited by John Fauvel, Raymond Flood and myself, with this edition published in 2013. And finally, may I thank you for listening. Thank you.(audience applauds)