Died: 18 January 1963 in Oxford, England

**Edward Titchmarsh** was known as Ted to his contemporaries. His grandfather was a grocer in Royston while Ted's father, Edward Harper Titchmarsh, became a Congregational minister in Newbury, Berkshire. Ted was the second of three children born to Edward and Caroline Titchmarsh. Ted's father moved to Sheffield, where again he was the Congregational minister, and it was in Sheffield that Ted attended King Edward VII School. He later wrote of his time at this school:-

The first occasion on which I distinguished myself was when I was in one of the fourth forms. The headmaster for some unknown reason made the whole upper school do an arithmetic paper, the same for all forms. The mathematical specialists in the sixth form came out top, and I came next. ... At this point one had to choose either classical or modern subjects: I was put on the classical side. I learnt enough Latin to pass and enough Greek to fail. It became clear that mathematics was my real subject and I began to specialise in it.

In December 1916, when he was seventeen years old, Titchmarsh won an Open Mathematical Scholarship to Balliol College, Oxford and he began his studies there in October 1917. By this time, of course, Britain had been involved in World War I for three years and Titchmarsh, by now eighteen years of age, was soon undertaking war service. After just one term at Oxford he joined the Royal Engineers and in August 1918 he was sent to France as a dispatch rider. Titchmarsh was fortunate to have arrived in France at a point when the tide of the war had changed. There had been major offensives by the German armies throughout June and July of 1918 but as Titchmarsh landed in France the Allied forces were making steady advances, driving the German troops out of France.

Titchmarsh carried out his duties as a dispatch rider first on horseback and then on a motorcycle. By October 1918 the Allies had recovered most of German occupied France and a part of Belgium. German morale collapsed, the German Kaiser William II abdicated on 9 November, and on 11 November the war ended with the signing of the Armistice between Germany and the Allies. However Titchmarsh served with the Royal Engineers for almost a further year before he was able to return to his interrupted studies in Oxford in October 1919.

At Oxford he was tutored by J W Russell. Mary Cartwright wrote (see [5] or [6]):-

At Russell's first lecture the room was packed to the doors, and Russell said: "Ah, there's my clever pupil Mr Titchmarsh - he knows it all, he can go away." Russell dictated his lectures word for word and examples were handed out - and then, if necessary, solutions to examples. Some of Titchmarsh's solutions replaced the official ones.

At Oxford Titchmarsh soon came under the influence of Hardy and he later wrote:-

From[Hardy]I learnt what mathematical analysis is, and at his suggestion I devoted myself to research in pure mathematics.

Hardy held a class which did not form part of the syllabus. The class met once a week on Monday evenings after dinner and it would begin with a talk and then continue until late in the evening with the members taking part in deep mathematical discussions. Titchmarsh attended this class, as did Mary Cartwright. Of course Titchmarsh and Hardy had a common passion, namely cricket, which must have served Titchmarsh well. His uncle was a professional cricketer and Titchmarsh often played in the regular cricket matches with Hardy.

Titchmarsh graduated with a First Class degree in 1922 and won mathematical scholarships for his outstanding work. He did not read for his doctorate but was appointed as a Senior Lecturer at University College London in 1923. This appointment in London did not see Titchmarsh end his association with Oxford. Far from it, he took the examinations for a Prize Fellowship at Magdalen College Oxford, also in 1923, and, having won the Fellowship, he held it for seven years. Not only did he lecture in London, where he supervised doctoral students, but he also began publishing high quality research papers on mathematical analysis. During the academic year 1928-29 Hardy was at Princeton, and it was Titchmarsh who took over the supervision of Mary Cartwright who was, at that time, one of Hardy's doctoral students at Oxford.

Despite having duties at both London and Oxford, Titchmarsh found time to visit his father who was by this time a Congregational minister in Essex. In 1925 he married Kathleen Blomfield, who was the daughter of his father's Church Secretary. They had three children, all daughters.

Charles Burkill held the chair of pure mathematics at Liverpool from 1924 until 1929 when he took up a lectureship at Peterhouse, Cambridge. Titchmarsh was appointed to Burkill's chair at Liverpool, a post he held for two years before he succeeded to Hardy's Savilian chair at Oxford when Hardy moved to Cambridge. Wilson, in [9] recounts how the appointment came about:-

By chance, Titchmarsh was visiting Oxford to examine a doctorate and bumped into Ferrar who asked him whether he'd applied for Hardy's vacant Oxford Chair. Titchmarsh said no, but(encouraged by Ferrar)thought that he might. He sent in an application on a single sheet saying that he wished to apply for the geometry Chair but could not undertake to lecture on geometry as Hardy had done. Two days later he was appointed and the statutes were changed to say that the Savilian Professor of Geometry no longer had to lecture on geometry. Titchmarsh held the Savilian Chair of Geometry at Oxford for30years.

Ferrar wrote this about Titchmarsh's mathematical work [3]:-

Titchmarsh, from his earliest research days, displayed a power of analysis that marked him out as a mathematician whose reputation would be world wide. This power he carefully fostered and strengthened. Research papers and books flowed steadily from his pen...

All Titchmarsh's work was in analysis, in fact he refused to lecture on any other topic. His method of working was to concentrate on a topic until he tired of it, when he would write a book on that topic. He studied Fourier series and Fourier integrals writing Introduction to the *Theory of Fourier Integrals* (1937). Other topics to which he made major contributions included entire functions of a complex variable and, working with Hardy, integral equations.

He also did important work on the Riemann zeta function writing *The Zeta-Function of Riemann* (1930) which he brought up-to-date as *The Theory of the Riemann Zeta-Function* (1951) which [1]:-

... contained practically everything that was known on the subject.

His most popular book *The theory of functions* was published in 1932, and [1]:-

... a generation of mathematicians learned the theory of analytic functions and Lebesgue integration from it, and also learned(by observation)how to write mathematics.

From 1939 Titchmarsh concentrated on the theory of series expansions of eigenfunctions of differential equations, work which helped to resolve problems in quantum mechanics. However [1]:-

... he saw physics as a source of interesting mathematics problems; but his interest was exclusively in the mathematics, without any regard for its real applicability.

His work on this topic occupied him for the last 25 years of his life and he published much of it in *Eigenfunction Expansions Associated with Second-Order Differential Equations* (1946, 1958).

Titchmarsh was elected to the Royal Society in 1931 and received its Sylvester Medal in 1955:-

... in recognition of his distinguished researches on the Riemann zeta-function, analytic theory of numbers, Fourier analysis and eigenfunction expansions.

He received many other honours for his important contributions to mathematics. He served as President of the London Mathematical Society in 1945-47 and was awarded its De Morgan Medal in 1953 and its Berwick Prize. The University of Sheffield, which of course is situated in the town in which he attended school, awarded him an honorary doctorate in 1953.

Ferrar writes about Titchmarsh's lecturing style [3]:-

As a lecturer he was conscientious and careful, but in no way outstanding save on rare occasions. These occasions were when, with an audience of professional mathematicians, he was lecturing on his own current research; and then the lecture lit up with his own zeal for the subject.

Sir Michael Atiyah reminisces about Titchmarsh in [4]:-

He was a scholarly man who sat in his room and wrote beautiful books - impeccable, effectively written textbooks, from which many students have learnt their complex analysis. But he was a man of very few words; his influence was not due to personal contact but through his writing. When I first came to Oxford he was curator of the Mathematical Institute, so as a newly arrived member I had to go to him to get a key to my office. I was duly ushered into his big room, where he was sitting at his desk. I sat down and he handed over the key, and then I expected a word of welcome of some words of advice, but we just sat in silence. After five minutes, I left.

Outside mathematics, Titchmarsh had relatively few interests [3]:-

He was a retiring person and was not easy to know, but his shyness was relieved by a sense of humour which would suddenly transform him. He was very happy at home and he enjoyed listening to music and watching cricket, a game in which his father's family had been distinguished.

Charles Coulson, one of his colleagues, wrote a tribute to Titchmarsh:-

There were many things about Ted that I have always much admired - his utter humility, which never betrayed anything but the greatest simplicity; his complete integrity ... and his kindness to me when I arrived first; to his students(who worshipped him)and to everyone.

**Article by:** *J J O'Connor* and *E F Robertson*

**October 2003**

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Titchmarsh.html]