# George Neville Watson

### Quick Info

Westward Ho!, Devon, England

Leamington Spa, Warwickshire, England

**Neville Watson**studied at Cambridge, and then taught at Cambridge and University College London before becoming Professor at Birmingham. He is best known as the joint author with Whittaker of one of the standard text-books on Analysis.

### Biography

**Neville Watson**'s mother was Mary Justina Griffith (1860-1945), the eldest daughter of the rector of Ardley in Oxfordshire, Rev George Sandham Griffith (1831-1903) and Julia Robberd (1832-1904). Neville's father was George Wentworth Watson (born 1857 in Calcutta, India, died 1940) who, at the time of Neville's birth, was a schoolmaster at the United Services College, teaching mathematics and geography, but is more famous for his work as a genealogist. He played a large role in the publication of

*The Complete Peerage*, a 13-volume database of the British peerage, generally accepted as the greatest British achievement in the field of genealogy. The first edition was published in London between 1887 and 1898. George and Mary Watson were married in 1885 and had two children, the eldest being Neville and the younger his sister Muriel Mary Joyce Wentworth Watson (born about 1892).

Let us say a little about Westward Ho! where Neville was born. As a first comment, let us record that on the 1891 census his place of birth is given as Northam, Devon while on the 1901 census it is given as Westward Ho!. In fact Westward Ho! was the name of a new hotel opened in 1865, named after Charles Kingley's novel of that name which was set in nearby Bideford. Villas began to be built round the hotel and the United Services College, a secondary school preparing boys for a military or civil service overseas career, was founded there in 1874. Almost all the boys were boarders and this was the school in which Neville's father was teaching at the time of his birth. The school merged with another in 1906 and closed its premises in Westward Ho! The town of Northam is closer to Westward Ho! than Bideford, and certainly those living near the hotel would think of living near Northam before the village took the name of the hotel and became known as Westward Ho! In fact the 1891 census considers their house in Westward Ho! to be in the town of Northam. The census form shows that Neville and his parents had two servants, a nurse Clara Carter (age 23) and a general servant Mary Ann Hocking (age 20).

The Watson family moved from Westward Ho! to Kensington, London, and, certainly by the time of the 1901 census, they were living there with Neville's father described as a private tutor and as an employer. Again they have two servants, a housemaid and a cook. Neville was educated at St Paul's School in West Kensington, London, entering as a Foundation Scholar in 1898. While studying there, he held both the Campden Exhibition and the Keen Scholarship [25]:-

His sister's chief recollections are of long hours closeted with his father in his study and of occasions when he was so absorbed that he could pass his mother and sister in the street without recognising them.Kenneth Wardle writes [22]:-

At school he was not particularly sociable, being somewhat reserved, and while his fellows were playing games during their lunch hour Watson would be down at Addison Road station watching the trains and recording the numbers of the engines. This early interest developed later into an absorbing interest in railways. It was while still at school ... that he published his first mathematical paper, in the December 1903 number of 'The Gazette'; ... "A method for determining a very rapidly converging series for the square root of any positive integer."We note that certainly Watson's series converges rapidly, for example eight terms of his series for √2 gives it correct to 390 decimal places.

Winifred Cooke, writes of Watson's school days in [22]:-

He often remarked that he was eternally grateful that during his last three years at St Paul's School, where he was educated, there was an insufficient number of staff to teach him mathematics and consequently he was forced to do much on his own and so became prepared for university style of teaching.Despite this comment, he was very fortunate to have the outstanding teacher of mathematics Francis Macaulay. He mixed with equally outstanding pupils, for J E Littlewood, less than a year older than Watson, was also a pupil at the school. In 1904 Watson won the Smee Prize from St Paul's School for his essay "Properties of curves." This prize had been endowed "for original work of a scientific or practical nature."

Having won a scholarship to Trinity College, Cambridge, Watson matriculated there in 1904. At this time there were three young fellows of Trinity all of whom had a major influence on Watson's mathematics. They were E T Whittaker, E W Barnes, and G H Hardy. Perhaps the one from this trio who had the greatest influence on him at this time was Barnes, despite the fact that he was coming to the end of his career. Whittaker left Cambridge in 1906, two years after Watson arrived, and although his influence at this time was slight, he became an important collaborator and friend some years later.

Watson graduated as Senior Wrangler in 1907 (meaning that he was ranked in first position among those who were awarded First Class degrees), after choosing to take three years over Part I when many of his contemporaries were taking two. He completed the Mathematical Tripos in the following year in the second division of the First Class [25]:-

... although this result was attributable to illness it undoubtedly disappointed him.He wrote about the Tripos in [23]:-

In my undergraduate days, now slightly more than a quarter of a century distant, the order of merit in the Mathematical Tripos still existed though its abolition had been decided upon; and, in certain circles, the discussion of the form of candidates and the places which they were likely to obtain in the next Tripos was not without interest; though the contest was, I think, free from any betting element, some impression of the general attitude to the examination may be gained by comparing it with the attitude of the sporting press to a forthcoming race. I have always got the impression from my father (who was a contemporary of Professor Forsyth) that in his time, a quarter of a century before mine, this interest in Tripos results as sporting events was considerably stronger.While an undergraduate, he published three papers:

*The Expansion of Products of Hypergeometric Functions*(1907),

*A Series for the Square of the Hypergeometric Function*(1908) and

*The cubic transformation of the hypergeometric function*(1909). These papers were all published in the

*Quarterly Journal of Pure and Applied Mathematics*.

He won a prestigious Smith's Prize in 1909, becoming a Fellow of Trinity College in 1910 and living in the College's New Court. This was particularly pleasing to him for he had a great love of his College, and throughout his life he collected prints of the College and of previous Fellows. Later while holding the fellowship he lived at Neviles Court, Trinity College.

After election to his Trinity fellowship, Watson spent four further years in Cambridge before leaving to take up an assistant lectureship in University College, London. From 1918 until he retired in 1951 he was Mason Professor of Pure Mathematics at Birmingham University [22]:-

At that time one lecture room at Edmund Street in the centre of Birmingham sufficed for all lectures in both pure and applied mathematics at the University, and there was no Honours School of Mathematics. Promising students took one year of post-graduate work to qualify for the degree of M.A. or M.Sc. It was Watson who brought the Honours School into being, and so widened the scope of the work that it became necessary to have two separate departments, one for Pure Mathematics and a second which developed into the Department of Mathematical Physics under Professor R E Peierls [in 1937]. All this development took place at the same time that Watson was also carrying out an enormous amount of work outside the University.Winifred Adelaide Cooke who graduated from the University of Birmingham in 1926 writes [22]:-

I first met Professor Watson when I became one of his students at Birmingham University. How well I remember his shy and sensitive manner and his quick movements. He was a man of very strong likes and dislikes and his reactions were sometimes a little unorthodox. Many a time, when something or someone annoyed him during a lecture his piece of chalk would come flying over the heads of us students and someone would duck to avoid it. Beneath all this he had a very genuine interest in, and desire to help, all his students. In those early days he owned a small, open, three-wheeled car. The back seat was completely inaccessible unless you climbed over the car itself, and to be one of his passengers dashing across Birmingham was sometimes rather a hazardous affair, especially when he had to negotiate tram lines. ... He was always very much aware of students' difficulties during their first year at the University and did much to make the transition as smooth as possible.In 1925 he married Elfrida Gwenfil Lane (1898-1998) in Holbeach, Lincolnshire, the daughter of the farmer Thomas Wright Lane (born in North Eastham, Norfolk in around 1862, died 3 January 1932 on board the

*S.S. Ulysses*at Penang, Malay) and Sara Jane Lane (born in Bangor, Carnarvon around 1870). Elfrida was born in Holbeach on 3 November 1898 and had served as a Motor Driver in the Women's Royal Naval Service in 1918. They had one son who, following the family tradition, was named George.

Watson worked on a wide variety of topics, all within the area of complex variable theory, such as difference equations, differential equations, number theory and special functions. He is best known as a joint author with E T Whittaker of

*A Course of Modern Analysis*published in 1915. The first edition of the book has only Whittaker as an author. In 1922 Watson published

*The theory of Bessel functions*which was another masterpiece. Titchmarsh wrote of Watson's books (see for example [2]):-

Here one felt was mathematics really happening before one's eyes. ... the older mathematical books were full of mystery and wonder. With Professor Watson we reached the period when the mystery is dispelled though the wonder remains.For further information about Watson's three books, including extracts from reviews, see THIS LINK.

One piece of work undertaken by Watson deserves special mention. It involves the problem of wireless waves, which were quickly found to travel long distances despite the fact that theoretically they should not have been able to follow the curvature of the Earth. A mathematical model had been constructed where the Earth was represented by a partially conducting sphere surrounded by an infinite dielectric. Such a model had been used by Macdonald, Rayleigh, Poincaré, Sommerfeld and others. Although Watson was not interested in how best to model the situation, he was, however, very interested in using his expertise to determine mathematical solutions to the given model which others might then check against observations. He obtained solutions to the problem in 1918 which showed conclusively that the model was not a satisfactory one.

In 1902 Heaviside had predicted that there was an conducting layer in the atmosphere which allowed radio waves to follow the Earth's curvature. This layer in the atmosphere, now called the Heaviside layer, was only a conjecture in 1918 but it was suggested to Watson that, having shown the previous model to be wrong, he now looked at the model resulting from the postulated Heaviside layer. Watson showed that if the layer was about 100 km above the Earth's surface and it had a certain conductivity, then indeed the solutions obtained closely matched observations. That Heaviside, and Watson, were correct was confirmed in 1923 when the existence of the layer was proved experimentally when radio pulses were transmitted vertically upward and the returning pulses from the reflecting layer were received.

Watson undertook a major project by examining in detail Ramanujan's notebooks, extending his results and supplying proofs. In fact he wrote twenty-five papers relating to results in Ramanujan's notebooks, and he spent many hours making a hand written copy in wonderful script of all the notebooks. He enjoyed numerical calculations and spent many happy hours doing numerical work on his calculating machine.

He was elected to the Royal Society of London in 1919. In 1946 he received the Sylvester Medal of the Royal Society:-

... in recognition of his distinguished contributions to pure mathematics in the field of mathematical analysis and in particular for his work on asymptotic expansion and on general transforms.Watson was also very active in his support for the London Mathematical Society. He served as its secretary from 1919 to 1933, its president from 1933 to 1935 and acted as an editor of the

*Proceedings*of the Society until 1946. The Society awarded him their De Morgan Medal in 1947. The Royal Society of Edinburgh elected him to an honorary fellowship.

A strong supporter of the Mathematical Association he played a very active role [22]:-

The Mathematical Association has every reason to feel proud that a mathematician so distinguished as Watson should associate himself closely with its activities. He was elected President for the two years 1932 and 1933, being the last to hold office for more than one year, and was noted in committee for his mastery of detail and precise pertinent comments on items on the agenda. His first Presidential Address was called "The Marquis and the Land Agent, a tale of the 18th century". It concerned Fagnano and Landen and elliptic arcs; but the title beguiled an unwary journalist into attending; he left early! The second address on "Scraps from some mathematical notebooks" was on Gauss and the entries in his day-book. Watson was a great believer in going to the original works of the great mathematicians, rather than to their interpreters, and he also had the great gift of clarifying the sometimes obscure material of others. As a Vice-President of the Association he was a regular attender at Council meetings almost to the end of his life.We learn something about Watson's beliefs when we look at his record of attendance at International Congresses of Mathematicians. He attended the 1912 Congress in Cambridge, England, but chose not to attend the 1920 and 1924 Congresses since they were not truly international with mathematicians from Germany, Austro-Hungary, Bulgaria and Turkey excluded. He attended the 1932 Congress in Zurich and wrote in [24] that he had:-

... deliberately abstained from attending the Congresses at Strassburg and Toronto in 1920 and 1924, for reasons which are now, happily, a matter of past history, and by my having been unavoidably prevented from going to Bologna in 1928; in fact my only previous experience of a Congress was gained at Cambridge in 1912.For a version of Watson's report on the 1932 ICM, see .

We find a little of Watson's personality described in [2]:-

He was the university's expert on the timetable; students with unusual combinations of subjects usually had to be referred to him for advice, and for many years after his retirement the dates of the academic year were governed by the "Watsonian cycle". ... He took great trouble with the style of his letters and his conversation and enjoyed finding a pungent phrase to express his points of view or his criticism ... he made no secret of his aversion to cars, telephones, and fountain pens. He loved trains - whose timetables were as familiar to him as those of the university lectures - and unusual stamps.Kenneth Wardle writes about Watson's personality in [22]:-

In manner and appearance (he always wore a wing collar) he recalled the professors of an earlier generation, and he was always very proud of his Fellowship at Trinity and delighted to entertain colleagues with remarks and tales from the High Table, around which, he was wont to say, one could always hear profound conversation on any subject under the sun. Yet the appearance belied the man, for, while he was somewhat difficult to get to know, when one did achieve this he was a very real friend, and there are many who will remember both his kindnesses and his assistance with their problems; he and his wife were most charming hosts to those whom they entertained at their house. ... He did not like telephones and regarded them as "an invention the devil". There was no Departmental Secretary during his time at Birmingham, and he carefully typed all examination papers from members of his staff himself, filling in the formulae most carefully with old-fashioned pen and nib. He preferred to discuss matters face to face with colleagues rather than write a letter and send it by internal post, and it may be that his long journeys on foot from one part of the University to another compensated for lack of other exercise, for he never seemed to suffer from ill-health. ... He took little exercise, apart from his walk to and from the station at Leamington and across Birmingham to catch the tram. Incidentally his pace of walking was such as to stretch his younger colleagues considerably, and pedestrians and traffic in the city appeared to split before his progress rather as the bow wave of a ship. At one time he drove a car, but he was never too happy with this, and forsook this method of transport when four-wheel brakes came into fashion.Watson died in 1965. Alan Champneys writes [12]:-

Upon his death, Robert Rankin of the University of Glasgow, who had been Watson's immediate successor as the Mason Professor in Birmingham, was initially given the task of organising Watson's unpublished work. To his horror, Watson's widow showed him a room in their house, devoid of furniture, knee deep in unpublished manuscripts. These included a massive, but incomplete further edition of the Whittaker and Watson textbook, a monograph on 'Three Decades of Midland Railway Locomotives' and a great deal of material relating to Ramanujan. The task of further editing Watson's papers was given to E T Whittaker's son, J M Whittaker, who was appointed by the Royal Society to write Watson's obituary in its Biographical Memoirs.

### References (show)

- R A Rankin, Biography in
*Dictionary of Scientific Biography*(New York 1970-1990).

See THIS LINK. - Obituary in
*The Times* - Anon, Review: A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions (2nd edition), by E T Whittaker and G N Watson,
*The Mathematical Gazette***8**(124) (Jul., 1916), 306-307. - Anon, Review: A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions (2nd edition), by E T Whittaker and G N Watson,
*Science Progress (1916-1919)***11**(41) (1916), 160-161. - Anon, Review: A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions (3rd edition), by E T Whittaker and G N Watson,
*The American Mathematical Monthly***28**(4) (1921), 176. - Anon, Review: A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions (4th edition), by E T Whittaker and G N Watson,
*The Mathematical Gazette***14**(196) (1928), 245. - Anon, Review: A Treatise on the Theory of Bessel Functions, by G N Watson,
*The Mathematical Gazette***18**(231) (1934), 349-350. - H Bateman, Review: A Treatise on the Theory of Bessel Functions (2nd edition, by G N Watson,
*Science, New Series***101**(2614) (1945), 117-118. - H T Davis, Review: A Treatise on the Theory of Bessel Functions (2nd edition, by G N Watson,
*National Mathematics Magazin*e**19**(3) (1944), 153-154. - T A A Broadbent, Review: A Treatise on the Theory of Bessel Functions (2nd edition, by G N Watson,
*The Mathematical Gazette***29**(283) (1945), 37-38. - R D Carmichael, Review: A Treatise on the Theory of Bessel Functions, by G N Watson,
*Bull. Amer. Math. Soc.***30**(1924), 362-364. - A Champneys, Westward Ho! Musing on Mathematics and Mechanics,
*Mathematics TODAY*(February 2018), 18-22. - M C Gray, Review: A Treatise on the Theory of Bessel Functions (2nd edition, by G N Watson,
*Quarterly of Applied Mathematics***2**(4) (1945), 356. - P E B Jourdain, Review: A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions (2nd edition), by E T Whittaker and G N Watson,
*Mind***25**(100) (1916), 525-533. - E H Neville, Review: A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions (3rd edition), by E T Whittaker and G N Watson,
*The Mathematical Gazette***10**(152) (1921), 283. - Obituary,
*Yearbook of the Royal Society of Edinburgh Session*1964-65(1966), 37-39. - φ, Review: A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions (2nd edition), by E T Whittaker and G N Watson,
*The Monist***26**(4) (1916), 639-640. - M B Porter, Review: A Treatise on the Theory of Bessel Functions, by G N Watson,
*The American Mathematical Monthly***30**(6) (1923), 326-327. - R A Rankin, George Neville Watson,
*J. London Math. Soc.***41**(1966), 551-565. - I N Sneddon, George Neville Watson,
*Biographical Memoirs of Fellows of the Royal Society of London*(23 September 2004).

https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-36769

- F P W, Review: A Treatise on the Theory of Bessel Functions, by G N Watson,
*Science Progress in the Twentieth Century (1919-1933)***18**(70) (1923), 304-306. - K L Wardle and W A Cooke, Obituary: George Neville Watson. Honorary Member and Vice-President President 1932-3,
*The Mathematical Gazette***49**(369) (1965), 253-258. - G N Watson, Scraps from Some Mathematical Note-Books. Presidential Address to the Mathematical Association, 1934,
*The Mathematical Gazette***18**(227) (1934), 5-18. - G N Watson, The Congress at Zurich,
*The Mathematical Gazette***16**(221) (1932), 297-300. - J M Whittaker, George Neville Watson,
*Biographical Memoirs of Fellows of the Royal Society of London***12**(1966), 521-530. - D M Wrinch, Review: A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions (3rd edition), by E T Whittaker and G N Watson,
*Science Progress in the Twentieth Century (1919-1933)***15**(60) (1921), 658.

### Additional Resources (show)

Other pages about Neville Watson:

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### Honours (show)

### Cross-references (show)

- Other: Cambridge Individuals
- Other: EMS Members
- Other: Earliest Known Uses of Some of the Words of Mathematics (C)
- Other: Earliest Known Uses of Some of the Words of Mathematics (E)
- Other: Edinburgh Mathematical Society Lecturers 1883- 2023
- Other: Fellows of the Royal Society of Edinburgh
- Other: London Learned Societies
- Other: London Schools

Written by J J O'Connor and E F Robertson

Last Update September 2020

Last Update September 2020