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Martin Bridson Your Comments, and Also Contributions for Future Newsletters Number 15 • Spring 2016 We hope that you will enjoy this annual newsletter. We are interested to receive Martin Bridson your comments, and also contributions for future newsletters. Please contact A note of welcome the editor, Robin Wilson, c/o [email protected] On 1 October Prof. Martin Bridson, Whitehead Professor of Pure Mathematics and Fellow of Design & production by Baseline Arts Magdalen College, took over the reins as Head of the Mathematical Institute from Prof. Sam Howison. Martin writes: We are at a moment in the history of Oxford Mathematics that is so self-evidently special that we cannot help but marvel at it. Two years after moving into our splendid new home, it is still thrilling to enter the Andrew Wiles Building and sense the intellectual excitement all around us. Students and visiting mathematicians are inspired by the statement that it makes: mathematics is important, and you are part of this great enterprise. A different sense of recognition came with the results of the government’s 2014 Research Excellence assessments: Mathematical Sciences in Oxford was ranked first across the UK in all categories. Oxford’s reputation as a world centre for mathematics has never been stronger. ‘What then?’ sang Plato’s ghost, ‘What then?’. Sam Howison’s tenure as Head of Department Martin Bridson In 2001 we had 54 permanent faculty members; ended in September 2015. At a small reception, today we have 100, as well as many postdocs and Sam spoke graciously about those who had over 1000 students. We treasure our informality supported him, and passed me the baton. and the unique sense of community that grows Immediately after finishing my champagne I Oxford’s from our shared passion for mathematics and its received a sharp reminder of the constant need reputation propagation. But we’re a big family and we have for renewal in mathematics. Half a dozen of our to organise ourselves well if we are to maximise Statutory Professors are about to retire in quick as a world our contribution to mathematics and society. succession. This loss is daunting, but it presents us with an opportunity to reflect: what are the most centre for Conscious of this, the Department is prioritising exciting trends in world mathematics, and where mathematics its efforts to raise philanthropic funds for DPhil should we be providing leadership? With our studentships that are open to students of all emeriti remaining active, this process of renewal has never nationalities working in all areas of mathematics. can lift us to new heights. been This is central to our plans for the future, and I hope that many of you will see it as an In the 1960s the Mathematical Institute was stronger. opportunity to support the life of the Institute. headed by a Curator, and then for a long time we had a Chairman. The University now prefers the It has been a pleasure to see so many alumni and title Head of Department, and perhaps this is a friends at our recent public events. I hope to see hint about the challenges that come with growth. many more of you here during my time as Curator. n OXFORD MATHEMATICAL INSTITUTE NEWSLETTER . SPRING 2016 . ISSUE 15 / 1 Anniversaries Somerville. Although her mathematical Later in life Ada continued to pursue her pursuits were put on hold following her mathematical interests. Although she did marriage and the birth of three children, no further work on Babbage’s engines, she later went back to mathematics she and Babbage remained friends and and studied with the prominent British appear to have pursued recreational mathematician Augustus De Morgan. mathematics together: on one charming In a two-year correspondence course, document, for instance, we find an preserved in the Bodleian, we see her exploration of the problem concerning working through much of the same the Bridges of Königsberg. material as De Morgan’s students at UCL – limits, series, functions, differential The Oxford Ada Lovelace Symposium, equations, and the like. which took place on 9–10 December, saw a great variety of talks on subjects connected This background stood Ada in good with Ada, ranging from her contributions stead when she came to translate and to computing, to the literary influence on extend Menabrea’s article. Babbage’s her scientific thought, to a new (mixed) Analytical Engine was, in modern terms, a assessment of her mathematical abilities. general-purpose computer, programmed with punched cards, similar to those Thanks are due for the generosity of used at the time to control Jacquard the Clay Mathematics Institute and Ada Lovelace, aged 17 looms. In principle, it could calculate any the descendants of Ada Lovelace. The function. Ada’s paper presents it, not in presentations from the symposium may terms of ironmongery, but as what we be watched online at http://podcasts. Celebrating would now call an ‘abstract machine’, ox.ac.uk/series/ada-lovelace-symposium- describing the functions of memory, CPU, celebrating-200-years-computer-visionary. registers, loops, and so on. What is truly Images and transcriptions of Ada’s Ada Lovelace remarkable to the modern computer mathematical writings will be released Christopher Hollings and Ursula scientist reading the paper is Ada’s online at www.claymath.org in 2016. n Martin high-level view, and how her speculation on the capabilities and potential of the The Ada Lovelace Symposium at the 10 December 2015 was the 200th machine mirrors present-day concerns. Mathematical Institute. anniversary of the birth of the computing pioneer Ada Lovelace. Various events took place in Oxford to mark this anniversary, including a two-day symposium at the Mathematical Institute and an exhibition at the Bodleian Library. Famous in her day as the daughter of the Romantic poet Lord Byron, Ada is noted amongst mathematicians and computer scientists for a paper published in 1843, which translated and extended a review (by an Italian engineer, Luigi Menabrea) of Charles Babbage’s ideas for a steam- powered computer, his unbuilt ‘Analytical Engine’. Ada’s substantial appendices contain an account of the principles of the machine, and a table displaying how it might compute Bernoulli numbers, often Unlucky 13 described as ‘the first computer program’. It has been pointed out to us that there was no issue Number 13 of this Newsletter; From an early age Ada showed both last year’s issue was Number 14. Was this due to superstition on the part of the Editor, interest and ability in mathematics or perhaps his inability to count? He justifies it on the grounds that issue Number 12 and science, and received tuition from was a double issue featuring the new building. a number of people, including Mary 2 / OXFORD MATHEMATICAL INSTITUTE NEWSLETTER . SPRING 2016 . ISSUE 15 Anniversaries Wallis’s formula for 4/π his favour was the esteem in which he of events in Europe was in part being was held in government circles for his decided by an Oxford mathematician codebreaking abilities. A more far-sighted labouring in his scarce free time in his mathematical appointment on false lodgings in New College Lane. grounds is difficult to imagine. Wallis’s appointment to the Savilian Chair, which Although Wallis was often conservative he held until his death fifty-four years in his use of mathematical notation he later, marked the beginning of an intense introduced two new symbols that we still period of activity which established use today, for ‘infinity’ and for ‘greater Oxford as the mathematical powerhouse than or equal to’. of the nation. Wallis’s last great mathematical work, A John Wallis’s Arithmetica Infinitorum Treatise of Algebra, Both Historical and (‘Arithmetick of Infinites’) appeared Practical, was published in 1685, in his John Wallis, by Sir Godfrey Kneller, Bt at a critical time for the development seventieth year. Of his vast output, it was of mathematics. Approaches using this work that was most widely read over geometrical indivisibles had previously the next hundred years, and was the first Celebrating been used to find areas under curves, substantial history of mathematics in the and were successful for any curve of the English language. form y = xn , where n is a positive integer, John Wallis but Wallis associated numerical values to Although Wallis’s main contribution Philip Beeley and Raymond Flood the indivisibles, allowing him to extend to learning was undoubtedly through the result to the case when n is fractional. his innovative and important work in 2016 marks the 400th anniversary the broad sphere of mathematics, he of the birth of John Wallis, who held The word ‘interpolation’ (in its excelled in other fields, too, including the Savilian Chair of Geometry for mathematical sense) was introduced classical scholarship and studies on 54 years. Oxford’s Wallis Chair of by Wallis in this work, and he would language. He also served for nearly half Mathematics is named after him. always be associated with supplanting a century as keeper of the archives, geometrical techniques to ‘quadratures’ one of the highest ranked officers in The introduction of John Wallis into with more rigorous arithmetical ones. It the University at that time, assiduously the University of Oxford was caused by was also here that Wallis produced his defending the institution’s ancient rights politics. During the early part of the Civil celebrated formula for what we would and privileges. Wars the University had been the Royalist call 4/π (and which he presented as headquarters, and in the subsequent pictured at the top of this page). Some measure of the impression that reckoning most college heads and fellows Wallis left on contemporaries may be were deposed. The Savilian professors Wallis’s fundamental engine of discovery seen in the remarkable full-length portrait were expelled in 1648 for Royalist was the exploration and recognition of him at the age of 86, by the court sympathies, and the Parliamentary of pattern.
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