# Eric Harold Neville

### Quick Info

Bow, London, England

Reading, England

**E H Neville**was professor of mathematics at the University of Reading. He played an important role in mathematical education, particularly with the British Association for the Advancement of Science, with the Mathematical Association and with the International Commission on Mathematical Instruction. He wrote a number of important texts and many interesting articles.

### Biography

**E H Neville**was the son of Mynott Neville Jr (1854-1925) and his wife, Edith Batt (1862-1949). Mynott Neville Jr's occupation is given as 'analyst' in the 1891 census, as 'Tar Works Manager' in the 1901 census, and as 'Bookkeeper in Tar Works' in the 1911 census. Mynott Neville married Edith Batt in 1884 in Poplar, London, England. Edith was the daughter of the carpenter Joseph Batt and his wife Martha. Mynott and Edith Neville had four children: Bernard Mynott Neville (1887-1942); Eric Harold Neville (1889-1961), the subject of this biography; Maurice Raymond Neville (1894-1982); and Edith Hilda Neville (1896-1930). We note that Bernard Mynott Neville became a master at the William Ellis School, London. Maurice Raymond Neville studied mathematics at Peterhouse, Cambridge, was awarded an MC in 1918 for "conspicuous gallantry and devotion to duty as forward observation officer for his battery" and then worked for the General Electric Company.

Neville was educated at the William Ellis School at Gospel Oak, London. This school was founded in 1862 but was reconstituted in 1889 as a boys' secondary school under the headmaster Edward Boyce Cumberland who taught science and organised for the school to have an early physics laboratory. Cumberland was headmaster for nearly thirty years and had that role throughout Neville's time at the school. He was not, however, the greatest influence on Neville, for this was the mathematics and physics master Percy Nunn (1870-1944) [27]:-

Nunn was a brilliant teacher of science and mathematics, and a pioneer in these subjects of the 'new' methods which he was to advocate in general terms during the rest of his career. His lectures and demonstrations continued to be an inspiration to generations of apprentice science teachers.Nunn quickly saw that Neville had the potential to become a leading mathematician and he encouraged and inspired him. Neville graduated from the William Ellis School in 1907 and, later that year, entered Trinity College, Cambridge as a scholar. In addition to studying at Cambridge, he took the external University of London B.Sc. examinations in 1908 and was awarded First Class Honours.

Several others who would become leading mathematicians were studying the mathematical tripos at the University of Cambridge at the same time as Neville, for example both Louis Mordell and Percy John Daniell entered Trinity College in 1907 and William Berwick had entered Clare College, Cambridge, in 1906. Both Neville and Daniell were coached by Robert Alfred Herman (1861-1927). During his undergraduate years Neville became acquainted with G H Hardy and Bertrand Russell who were both fellows of Trinity College both of whom had a considerable influence on his career. The mathematical tripos examinations of 1909 were rather special since the candidates all knew that it was the last year in which Cambridge would rank the list of Wranglers. Daniell was the Senior Wrangler, Neville the Second Wrangler, Mordell the Third Wrangler, and Berwick the Fourth Wrangler.

In 1911 Neville was examined by Bertrand Russell for a Fellowship of Trinity and shortly after being awarded the fellowship he submitted an essay for a Smith's Prize and again was successful. Walter James Langford (1905-1996), who was taught by Neville at the University of Reading, writes [12]:-

His essay for this award was an original contribution in the field of differential geometry, a subject in which he retained a keen delight throughout his life and which led him to write two published works: a dissertation on moving axes, and a detailed and authoritative investigation into the foundations of analytical geometry.Percy Nunn, Neville's former teacher, reviewed the second of these published works and writes [18]:-

I could wish that the task of reviewing this important book had fallen into more competent hands; but I have had no difficulty in seeing that it is extraordinarily good, and feel that if my qualifications as a critic were higher its merits would appear to me still more conspicuous. It possesses, I think, all the qualities needed to give distinction to a work in this genre. An immense amount of laborious thinking must have gone to its making, yet it is never heavy or dull; it is based upon wide learning, but the learning is felt in the fibre, not exhibited for admiration; the diction is economical, lucid and precise; and the mathematical craftsmanship is of the highest order.For extracts from prefaces and reviews of these two works published by Neville in 1921 and 1922, see THIS LINK.

On 15 March 1913 Neville married Alice Maud Emily Farnfield (1875-1956) in the Parish Church of Sidcup, Kent. Alice was the daughter of the schoolteacher Samuel Farnfield, who taught English, Science and Art, and his wife Sarah. Perhaps it is unfair to note that Alice's age on the marriage certificate is 34, where she is actually 35, while Neville's is 25 but he is actually 24. Eric and Alice Neville lived at 113 Chesterton Road, Cambridge, and they had one child, Eric Russell Neville, baptised on 27 September 1914 in the Chapel of St John the Evangelist in Sidcup. Sadly the child died in March 1915 and the Nevilles did not have any further children.

Neville went to India to deliver lectures in the first half of 1914. He had been asked by Hardy to make contact with Srinivasa Ramanujan. Neville writes [15]:-

Ramanujan's place in history was determined not when his first letter to Hardy showered fireworks in the Cambridge sky in 1913, for he resisted all immediate efforts to attract him to England, but when in Madras a year later he put into my hands the now famous Notebook and suggested that I should take it and examine it at my leisure. Only in a slight degree was the compliment personal to me; to Ramanujan then Hardy was a name on paper, and Walker and Littlehailes were parts of the governing machine, but I was a human being. Nevertheless, if Hardy could long remember with satisfaction that he could recognise at once what a treasure he had found, I too can be proud, for if I had failed to win the confidence of Ramanujan and his friends, Ramanujan would not have followed me to England. Nor could my failure have been remedied; before the autumn, that is, before any other visitor from Cambridge could have made contact with him, war was raging, and five years were to elapse before communication between India and England was again easy.Back in Cambridge in the summer of 1914 he seemed on the brink of a stellar research career when World War I broke out on 28 July and by 4 August Britain was at war. Neville's eyesight was too poor for active service but he did not want to leave it there, but wished to declare his opposition to war. This would have serious consequences as Bertrand Russell wrote in a letter (see [12]):-

[Neville's opposition to man killing man] was an obstacle, throughout his life, to academic advancement in spite of his brilliance, as many educational authorities think that a man is not fit to teach the young if he dislikes having them slaughtered. I was fond of him, particularly because of his gentleness.Neville worked in a London hospital throughout the war but his Trinity fellowship was not renewed, almost certainly because of his attitude to war. Langford writes [12]:-

One can only conjecture whether his Fellowship might have been renewed had he not declared his opinion, but the fact is that he moved from Cambridge never to return.In 1919 Neville accepted the position of Professor of Mathematics at University College, Reading. This College had been founded in 1892 as an extension college of the University of Oxford. By the time Neville was appointed it was already putting together an application for a Royal Charter to make it a university in its own right with the ability to award degrees. The application it made in 1920 was not successful and Neville worked hard helping to frame another application. Let us note at this stage that Neville did much to build mathematics at Reading and played important roles in UK mathematics throughout his career, but he would always look slightly out of place, for he could have been one of the leading research mathematicians of his day but after his Cambridge fellowship was not renewed, he chose not to engage in investigating current research problems. He seems to have felt out of place, beginning his address as president of the mathematics and physics section of the British Association for the Advancement of Science in 1950 as follows [14]:-

You are all mathematicians, but almost all of you are something more than mathematicians; you are astronomers, meteorologists, physicists, or whatever it may be. Few mathematicians who are nothing but mathematicians attend the meetings of our Association regularly, and in this Chair I am not only a fish out of water, but a very small fish at that: you should see the ones that got away!Certainly he played a major role in framing another application for a Royal Charter for University College, Reading. The application for the charter was made in 1925 and officially granted on 17 March 1926. University College, Reading, then became the University of Reading and was able to award degrees. Langford studied mathematics at Reading in the early 1920s and writes [12]:-

As a teacher he was an inspiring guide (though sometimes so far ahead as to be almost out of sight) but with the small classes of those days - there were never more than three of us in the honours group - a lecture could always become a seminar if we wished, and he delighted in the arguments which could develop. If his less able students sometimes found him difficult to follow, this was due, I believe, to the fact that his own mind worked so rapidly and his own knowledge was so immense that he just could not understand how anyone could find the work difficult.Neville applied his talents to mathematical education, particularly with the British Association for the Advancement of Science and with the Mathematical Association. It was Percy Nunn, someone passionately committed to reform mathematical education, who approached Neville, his former pupil, asking if he would chair a sub-committee of the General Teaching Committee of the Mathematical Association which was being set up to report on the teaching of geometry in schools. Neville agreed to take on the chairmanship of the committee which began work in 1922 [21]:-

The resulting report recommended dividing school geometry into stages: experimental, deductive, systematising, and advanced.One of the committee members later wrote (see Broadbent's contribution to [12]):-

It is perhaps not giving away a secret to say that T P Nunn and E H Neville were the two principally responsible for the Report, which has been a best-seller ever since.This began Neville's involvement with the Mathematical Association which lasted for the rest of his life. Neville contributed many articles to the Association's journal,

*The Mathematical Gazette*. These covered a wide range of topics in mathematics and its teaching, classroom notes as well as numerous reviews. For example:

*The Tracing of Conics*(1921),

*Partial Fractions Associated with Quadratic Factors*(1922),

*The Foci of the General Conic*(1925),

*The Cubic Equation as a Relation between Complex Variables*(1927),

*A Fallacy in Geometrical Conics*(1929),

*Bernoulli's Differential Equation*(1934),

*Cajori's Edition of Newton*(1935),

*Bieberbach's Trisection*(1936),

*Products of Vectors*(1940),

*A Simple Interpolation Formula*(1945),

*The Brocard Angle*(1947),

*The Equation of a Pascal Line*(1950),

*A New Proof of the Multinomial Theorem*(1954),

*Schur's Inequality and Watson's Identities*(1956),

*An Example of Tripolar Root-Squaring*(1961).

He edited

*The Mathematical Gazette*for a brief period but his long term commitment for the Mathematical Association was as its librarian, a task he undertook from 1923 to 1954. He was President of the Association in 1934 and gave his presidential address

*The Food of the Gods*in January 1935. The problem he chose to discuss is illustrated by these remarks [16]:-

Mathematics has been called by a vast number of fanciful names, and I daresay "the food of gods" is among these, but the application I have to make of the phrase is to a very definite problem, which impressed itself on me when I discovered some months ago, to my sincere surprise, that if I had sat for an entrance scholarship at Cambridge within the last year or two I should have had a fair prospect of success. Do not misunderstand me. I am not boasting childishly that knowing what I know now I ought to find the papers easy. I mean that my preparation at school a quarter of a century ago would have been adequate to this examination as it is now. On the other hand, I should have no hope whatever of a creditable degree on the same pretence. The schoolboy of those days was ready for the university of today, but his undergraduate contemporary would find a great many of the questions in a modern tripos literally incomprehensible. In other words, while a multitude of ideas have not only been developed in the most highly specialised mathematics during this generation but have permeated mathematical thought to the extent that every educated mathematician knows something of them, the schoolboy is not, as far as I can discover, expected to have a single idea with which his father was not familiar.Let us turn to Neville's contributions to the British Association for the Advancement of Science. He chaired the Association's Mathematical Tables Committee from 1931 to 1947. Jeffrey C P Miller wrote in the Preface to Neville's book

*Rectangular-polar conversion tables*(1956):-

Professor E H Neville played an active part in the formulation and execution of the table-making activities of the British Association Mathematical Tables Committee. He was chairman during its more active years from 1931 to 1947, when the series of B.A. Mathematical Tables, Volumes I-IX and Part-volumes A and B - inspired largely by Dr L J Comrie, Secretary of the Committee from 1929 to 1937 - was produced. The part played by the Chairman was visible only in his lively and well-phrased prefaces to several of the volumes. It is thus very fitting that the Royal Society Mathematical Tables - successors to the British Association Mathematical Tables should start with two volumes by Neville.The two volumes referred to in this quote are

*The Farey Series of Order 1025, Displaying Solutions of the Diophantine Equation bx - ay = 1*(1950) and

*Rectangular-polar conversion tables*(1956). For more information about these volumes, see THIS LINK.

While serving on the Mathematical Tables Committee, Neville met Dorothy Wrinch who had produced works such as

*Tables of Bessel function*(1924). Wrinch was married to the mathematician John William Nicholson (1881-1955) but he had a problem with alcohol which led to them separating in 1930. Marjorie Senechal writes in [24]:-

[Dorothy Wrinch] and Neville served together on the Mathematical Tables Committee. Their thirty-one year love affair, if that's what it was, began in her annus horribilis, 1930, the year of John's implosion. She never loved Neville as he loved her, but he would be the one, perhaps the only one, for whom she didn't wear a mask of gaiety. Her letters to Erice, as she almost always spelled his name, are filled with fears, frustrations, and worries; his with love and advice. ... Time and again Neville set his own work aside to give her a hand: "The author offers her thanks to E H Neville for his advice and criticism;" "Reproduced by kind permission of Prof E H Neville, University of Reading, England, who kindly constructed this model."We must not get a false impression from this quote: Neville was happily married to Alice [12]:-

... and she was the complete foil to the idiosyncrasies of his genius. As host and hostess, they were unsurpassed in my experience and many others share this opinion ...We should also mention his work for the International Commission on Mathematical Instruction [21]:-

The high regard in which he was held by the British pedagogical community was reflected in his election in 1932 as a member of the Central Committee of International Commission on Mathematical Instruction, on which he served with Hadamard as President and Fehr as Secretary General. He was re-elected in 1936.Neville was a member of the London Mathematical Society from 1913 and he was a member of the Council from 1926 to 1931. On 17 June 1943 he gave the lecture 'Jacobian elliptic functions' to the Society and it was published as [17]. We quote its first paragraph, in part as an illustration of Neville's style:-

On the fringes of philosophy, mathematics is deplorably Arician: the aspirant to a throne must slay the reigning monarch. If elsewhere our subject is more civilised, this is not to say that individually we are crushed under the weight of all the knowledge that our predecessors have acquired; we do not refute their arguments, but we do not share their enthusiasms. Nor do we expect our own favourite studies to have peculiar longevity merely because they are ours. The calculus of extension has almost as few admirers today as the Greek classification of quadratic surds, and Dupin's cyclides are following Robert Tucker's circles into oblivion. But the flux is not quite universal; there are some theories and some theorems, we are sure, which must always be as important as they are to us. We cannot doubt that in the most distant future every student of mathematics will be familiar with some form of Rolle's theorem, with Cauchy's theorem, with Pascal's theorem, with Fejer's form of Fourier's theorem, with Lagrange's equations, with a theory of incommensurables into which the Greek theory is in some sense incorporated, and with the properties of the circular functions. Thirty-five years ago my contemporaries would have included in any such list the elements of the theory of the Jacobian elliptic functions; it never crossed our minds that the time would come when the ordinary mathematical undergraduate was to know less of these functions than we did. We were wrong, but it was not the accepted estimate of the functions that was mistaken. If interest in the functions has lapsed and facility with them is an old-fashioned virtue, reasons are not hard to find, but they are reasons which should not be allowed to persist.His attempt to restore an interest in elliptic functions had begun earlier [5]:-

... a painful illness and prolonged convalescence in 1940 gave Neville time to write a long-meditated volume on Jacobian elliptic functions ...His 1943 lecture gave a preview of the volume which was published in 1944. For more information about the book, see THIS LINK.

In fact, after the success of this volume, he was persuaded to write a more elementary treatment. Although the primer was written by 1950, for some reason Neville never published it and after his death the manuscript was found among his papers. It was eventually published in 1971, ten years after his death; for more information about

*Elliptic functions: a primer*, see THIS LINK.

For Neville's interests outside mathematics we quote from [5]:-

Books indeed were his passion. He had an admirable mathematical library, full of rare and choice items; the collection of texts on elliptic functions is almost certainly complete. But his tastes were catholic; books of all kinds filled every corner of his house, and first editions of his favourite authors, such as Lewis Carroll and H G Wells were eagerly sought. Your bedside reading could be anything from Bayle's 'Dictionary' to the latest Agatha Christie.Neville's wife Alice died in 1956 [12]:-

Neville was a strong swimmer and received an award from the Royal Humane Society for his gallant rescue of a child from the flooded Cam on a winter's day. Weak eyesight prevented him from playing games, but he would watch and discuss cricket and football as keenly as he would watch and discuss Molière or Shaw; and at bridge a casual manner masked a devastating brilliance. ... Neville's logical skill made him a dangerous opponent in an argument, but a natural tolerance prevented him from dogmatising or attempting to impose his own firmly-held opinions and beliefs on others.

No one can ever estimate the effect which Mrs Neville's death had upon E H, but those of us who knew him closely have the feeling that he never reconciled himself fully to her passing. ... E H, himself, was taken ill in the early days of August 1961 and passed away in hospital in Reading, being unconscious for most of the time.

### References (show)

- Anon, Review: Prolegomena to Analytical Geometry in Anisotropic Euclidean Space of Three Dimensions, by Eric Harold Neville,
*Nature***112**(1923), 582-583. - Anon, Review:
*Biometrika***47**(1/2) (1960), 216. - M A
*Mathematical Reviews*MR0012658**(7,53g).** - P T Bateman, Review: The Farey Series of Order 1025, Displaying Solutions of the Diophantine Equation bx - ay = 1, by Eric Harold Neville,
*Bull. Amer. Math. Soc.***57**(4) (1951), 325-326. - T A A Broadbent, Eric Harold Neville,
*Journal of the London Mathematical Society***37**(1962), 479-482. - I W Busbridge, Review: Elliptic functions: a primer, by Eric Harold Neville,
*The Mathematical Gazette***56**(398) (1972), 355-356. - E T Copson, Review: Elliptic Functions (2nd edition), by Eric Harold Neville,
*The Mathematical Gazette***36**(315) (1952), 59-60. - E Cunningham, Review: The Fourth Dimension, by Eric Harold Neville,
*The Mathematical Gazette***11**(159) (1922), 127. - Eric Harold Neville,
*The Times*(23 August 1961). - A Fletcher, Review:
*The Mathematical Gazette***41**(337) (1957), 234. - P Franklin, Review: Jacobian Elliptic Functions, by Eric Harold Neville,
*Science, New Series***101**(2624) (1945), 378. - W J Langford, T A A Broadbent, R L Goodstein and E H N, Obituary: Professor Eric Harold Neville, M.A., B.Sc.,
*The Mathematical Gazette*48 (364) (1964), 131-145. - D H Lehmer, Review: The Farey Series of Order 1025, Displaying Solutions of the Diophantine Equation bx - ay = 1, by Eric Harold Neville,
*Mathematical reviews*MR0041934**(13,24e).** - E H Neville, Mathematical Notation,
*The Mathematical Gazette***48**(364) (1964), 145-163. - E H Neville,
*The Farey Series of Order 1025, Displaying Solutions of the Diophantine Equation bx - ay = 1*(Cambridge University Press, 1950). - E H Neville, The Food of the Gods. Presidential Address to the Mathematical Association, January 1935,
*The Mathematical Gazette***19**(232) (1935), 5-17. - E H Neville, Jacobian elliptic functions,
*J. London Math. Soc.*(1)**18**(3) (1943), 177-192. - T P Nunn, Review: Prolegomena to Analytical Geometry in Anisotropic Euclidean Space of Three Dimensions, by Eric Harold Neville,
*The Mathematical Gazette***12**(168) (1924), 27-30. - R Rado, Review: The Farey Series of Order 1025, Displaying Solutions of the Diophantine Equation bx - ay = 1, by Eric Harold Neville,
*The Mathematical Gazette***36**(315) (1952), 60-61. - A Rice, Neville, Eric Harold,
*Oxford Dictionary of National Biography*(12 July 2018).

https://doi.org/10.1093/ref:odnb/108385 - Eric Harold Neville,
*History of the ICMI, The First Century of the International Commission on Mathematical Instruction (1908-2008)*,*International Commission on Mathematical Instruction.*

https://www.icmihistory.unito.it/portrait/neville.php - D Roegel, A reconstruction of Neville's Farey series of order 1025 (1950), Research Report (21 December 2011).

https://hal.inria.fr/hal-00654447/document - W Seidel, Review: Prolegomena to Analytical Geometry in Anisotropic Euclidean Space of Three Dimensions, by Eric Harold Neville,
*Bull. Amer. Math. Soc.***52**(7) (1046), 604-607. - M Senechal,
*I Died for Beauty: A Biography of Dorothy Wrinch*(Oxford University Press, Oxford, 2012). - K D Tocher, Review:
*Journal of the Royal Statistical Society. Series A (General)***119**(3) (1956), 346. - J Todd, Review:
*Mathematical Reviews*MR0077245**(17,1011a)**. - J W Tibble, Sir Percy Nunn: 1870-1944,
*British Journal of Educational Studies***10**(1) (1961), 58-75. - P F W, Review: Multilinear Functions of Direction and their Uses in Differential Geometry, by Eric Harold Neville,
*Science Progress in the Twentieth Century (1919-1933)***17**(68) (1923), 657-658.

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Written by J J O'Connor and E F Robertson

Last Update September 2021

Last Update September 2021