# George Ballard Mathews

### Quick Info

Canonbury, London, England

Liverpool, England

**George Mathews**was an English mathematician. Most of his research was on number theory but he also worked on analysis and geometry.

### Biography

**George Ballard Mathews**' father was George Mathews, a linen draper, born at Preston on Wye, Herefordshire on 26 September 1813 to the yeoman farmer William Mathews and his wife Elizabeth. His mother was Harriet Hannah Ballard, daughter of George Ballard (1784-1865), an under secretary at the Inland Revenue, and his wife Hannah Alcock (died 1851). Harriet was born in Shoreditch, Middlesex on 20 September 1826. George and Harriet Mathews were married at St Mary, Islington, on 8 October 1858. At the time of the 1861 UK Census, the family are living at 27 Canonbury Square, Islington, London. The head of the family is the widowed George Ballard, with his daughter Harriet H Mathews and her husband George Mathews, and one month old George Ballard Mathews. They have three servants, two female house servants and one man servant. George, the subject of this biography, was baptised at St Paul, Canonbury, Islington, on 8 May 1861. He had two younger siblings, Harriet Hannah Mathews and Arthur Mathews, twins born in July 1865 in Canonbury, Islington.

In 1866, following the death of George Ballard, the family moved to Herefordshire. At the time of the 1871 UK Census, the family are living at 36 Westbrook Villa, Richard's Castle, Herefordshire. There is George Mathews, now described as a landowner, his wife Harriet and their three children, all of whom are at school. They have two servants, a female domestic servant, and a male groom and gardener. In 1872 George Ballard

**Mathews entered Ludlow Grammar School in Ludlow, Shropshire. Living in Herefordshire and going to school in Shropshire sounds strange, but Richard's Castle is on the Herefordshire-Shropshire border and the school was less than 4 km from his home. Ludlow Grammar School was at this time a boys' school which had been founded in around 1200 making it one of England's oldest educational establishments. At Ludlow Grammar School [5]:-**

... his brilliant intellect soon asserted itself. Records of 1875 state that he was first in the top form with prizes in Mathematics, French, Drawing, Form Prize, and Parents' Prize. During the four years, 1874-78, he was captain of the school. From the Rev W C Sparrow, one of the most successful Headmasters of the school, he received instruction in Hebrew as well as in Greek and Latin.We note that the Rev W C Sparrow published articles in the

*Transactions of the Shropshire Archaeological Society*.

After graduating from Ludlow Grammar School Mathews went to University College, London where he studied mathematics taught by Olaus Henrici and also began to study Sanskrit. He spent the year 1878-79 at University College, still undecided whether to continue his studies in mathematics or in classics. In fact in 1879 St John's College, Cambridge offered him a senior scholarship in either mathematics or classics, leaving Mathews to make his choice of subjects.

He then studied at St John's College, Cambridge, entering on 30 April 1879, where he was coached by William Henry Besant (1828-1917). The most successful coach at Cambridge over many years had been Edward John Routh and, when Mathews matriculated at Cambridge, Routh had coached every Senior Wrangler in the Mathematical tripos since 1862. It was Mathews who broke Routh's run of 22 consecutive Senior Wrangler's when he graduated as Senior Wrangler in 1883. Mathews explains in [12] Besant's coaching method:-

Besant's method was rather odd but very effective with the right sort of man. At the cost of immense labour he had written out with his own hand, a set of "bookwork and rider" papers covering the whole range of the examination. The pupil, on each of his three weekly visits, found one of these papers awaiting him in the outside room, and proceeded to answer it as well as he could on the backs of old examination scripts. If he had not brought a pen of his own, he had to search among a lot of ancient quills until he could find one that was not hopelessly spoiled. Presently, the student would be politely summoned to an inner parlour, where his last exercise would be returned to him corrected and annotated, and if he had failed to answer any question he would be either shown a solution or given a hint how to proceed. Of course, it was not every pupil that was taken separately like this; some of them were taken in small batches (not exceeding five or six), but the general method was the same. It should be added that once every week each pupil took away with him a printed problem paper to be done at leisure in his own rooms. The results were marked, and the list was available for inspection.The year after graduating, 1884, Mathews was elected a Fellow of St John's College and awarded a Smith's Prize, and later in the same year he was appointed to the chair of mathematics at the University College of North Wales at Bangor, this being the year the university opened. Andrew Gray writes in his obituary of Mathews [10]:-

I first saw the late G B Mathews on June 4, 1884, at the Queen's Hotel, Chester, when the staff of the newly founded University College of North Wales was appointed. He was chosen for the Chair of Mathematics, and almost from that time we were linked together in friendship as well as in our offices as teachers of intimately related subjects in the same institution. I well remember his youthful and striking yet attractive appearance. He was the senior wrangler of the previous year, and came full of eager enthusiasm for the teaching of mathematics and for original mathematical work, and for ten years laboured hard in the hope of founding something like a school of mathematical study in North Wales. But alas! these hopes were dashed. Perhaps he was a little impatient, and I certainly did my best to counsel him to wait, and to find out the effect of the new Welsh university on the studies of the place, but without effect.He taught at the University College of North Wales in Bangor and in Cambridge for periods through his life. He resigned his chair at Bangor in 1896 to return to Cambridge, for the reasons which Andrew Gray gave in the above quote. Back at Cambridge, he was appointed as a Lecturer in Mathematics. During the following years he served on the Council of the London Mathematical Society from 1897 to 1904 and acted for the year 1904-95) as the Mathematical Secretary to the Philosophical Society. In 1911, however, he resigned from Cambridge and was appointed to a special lectureship in the North Wales College at Bangor. Back at Bangor, he acted as Professor during the two academic years 1917-19.

Most of Mathews' research was on number theory but he also wrote texts on Bessel functions and on projective geometry. In his work

*Theory of numbers*(1892) topics covered included Gauss's theory of quadratic forms and their development by mathematicians such as Dirichlet, Eisenstein and Smith. The book also discusses prime numbers and Riemann's memoir on primes but, since it was written two or three years before the prime number theorem was proved, this part of the work became dated rather quickly. It was published at his own expense by Deighton Bell, the Cambridge bookseller, and was intended to be Part I of a more comprehensive treatise, but no further parts appeared. A corrected reprint omitting the words Part I was published by the Chelsea Publishing Company in 1961.

For more information, including extracts from prefaces and reviews, about this book and others written by Mathews, see THIS LINK.

The book

*A treatise on Bessel functions and their applications to physics*(1895) was written by Mathews in collaboration with Andrew Gray who was the professor of physics at Bangor. It was the first major treatise on Bessel functions in English and covered topics such as applications of Bessel functions to electricity, hydrodynamics and diffraction. Here Mathews was luckier than with the number theory work, since even when Watson's treatise on Bessel functions was published in 1922, it did not cover the applications of Mathews' book which continued to be useful and well used.

Mathews also wrote

*Algebraic equations*(1907) which is a clear exposition of Galois theory, and

*Projective geometry*(1914). This latter book develops the subject of projective geometry without using the concept of distance and it bases projective geometry on a minimal set of axioms. The book also treats von Staudt's theory of complex elements as defined by real involutions. The book contains a wealth of information concerning the projective geometry of conics and quadrics.

In addition to his treatises and many papers on the classical theory of numbers, Mathews also wrote some articles for

*Encyclopaedia Britannica*, in particular writing the article on universal algebra and the one on number. He also wrote numerous articles for

*Nature*[5]:-

Ever since the mid-eighties Mathews was a frequent contributor to 'Nature' on mathematical topics. His articles and reviews, most of which appeared over the initials "G. B. M." were always written in a careful and scholarly style; they contained his considered opinion on the book or point concerned. His keen yet kindly criticism was undoubtedly of the greatest service to the many writers whose work passed through his hands. In conversation with the present writer he once expressed the opinion that some of his best work had appeared in 'Nature' reviews.Another role Mathews played in mathematics teaching and administration was as an examiner to the Universities of Ireland and to the University of Manchester. He is described by T A Broadbent in [1] as follows:-

Mathews was an accomplished classical scholar; and besides Latin and Greek he was proficient in Hebrew, Sanskrit and Arabic. He also possessed great musical knowledge and skill. His versatility led a colleague at Bangor to assert that Mathews could equally well fill four or more chairs at the college.Andrew Gray had personal knowledge of these talents by Mathews [10]:-

Mathews had a knowledge of Latin and Greek as minute and accurate as that generally possessed by professional classical scholars. He wrote pure and elegant Latin. I remember his amusing himself by turning into Latin prose an original philosophical dissertation which happened to come into his hands and arrested his attention. I remember also some Latin verses which he published anonymously and which were much praised by a very eminent scholar.Another of the many talents of this remarkable man was music [5]:-

He wrote also charming English essays in the style of Charles Lamb, of whom he was a great admirer. These I fear are lost, but one of them, "On a cock-loft," was a perfect gem, a charming piece of the most natural and simple prose, somewhat after the manner exemplified more recently by Kenneth Grahame in his "Golden Days." He gave much time to Arabic in later years, and it is to be hoped that his translations of Arabic poetry will ultimately be published. I have seen some of them, which certainly seemed very remarkable.

Mathews' knowledge of music, again, was fully as advanced as that of most professional musicians. His copies of Gauss and Bach were placed together on the same shelf, and he considered some of Sir Edward Elgar's compositions to be as fine as the work of Beethoven and Handel.Andrew Gray tells us about Mathews' personality in [9]:-

His mind was quick and his tongue sharp, and often his repartees in discussion were appropriate and caustic in a high degree. I remember his crushing reply to a person not remarkable for quickness of perception who raised a discussion on mass and weight, and advanced the statement that mass and density meant the same thing. "Not at all," said Mathews, "there is all the difference in the world between a massive intellect and a dense one!" ...Mathews was honoured, however, with election to the Royal Society of London in 1897. His certificate of election was read to the Society at its meeting of 5 March 1896. He was described as an eminent mathematician and a list of his 'works of merit in connection with mathematics' was attached. It was signed by an impressive list of proposers: E J Routh; W M Hicks; W Burnside; M J M Hill; E W Hobson; A B Kempe; A R Forsyth; A G Greenhill; J W L Glaisher; E B Elliott; W H Besant; J Larmor; P A MacMahon; A E H Love; J J Sylvester; J J Walker; Andrew Gray.

His life was a rather solitary one. He smoked and worked and read in his rooms when he would have been better in the open air; but he was not a mere recluse. He much enjoyed talking over current events with his friends. I remember that when he stayed with me in Strathspey in 1913 he was eloquent in appreciation of the character of Lord Kitchener, and talked with much vigour and information of all Kitchener's work for Egypt. Mathews was exceedingly sensitive, and almost morbidly afraid of appearing to put himself forward in any way, so that he hardly received the recognition which was his due.

You can see his nomination form at THIS LINK

We learn something of Mathews' attitude towards mathematics in [13]:-

We may venture to assert that the intellectual state of a country may be estimated fairly well by its attitude towards mathematics and its progress therein. In this respect England is much inferior to other and smaller nations. For instance, in England many private libraries have been either given to the nation or placed at the disposal of genuine students: very few of these are wholly or mainly mathematical. Contrast with this the Mittag-Leffler endowment .... The founders expressly emphasised the supreme importance of pure mathematics from a national point of view. Again, no one can dispute the practical efficiency of the American nation; compare their treatment of mathematical professors with ours. An American university teacher may be a specialist devoted to the most abstract and "unpractical" parts of his science; he is left perfectly free to pursue his researches; he is provided with a sufficient staff of assistants; the university library contains an ample store of mathematical books, and all other necessary equipment is supplied. Every seventh year the professor is relieved of his official duties; and the use which he generally makes of his respite may be illustrated by the "History of the Theory of Numbers" (now in course of publication), by Prof L E Dickson. His special subject is the highly abstract one of group-theory: but he spent his sabbatical year in ransacking the libraries of Europe, as well as of the United States, for works on the higher arithmetic. The result is an extraordinary display of laborious and accurate research: the first volume alone contains summaries, almost all of them based upon the author's personal examination, of thousands of papers. The value of the work, when complete, can scarcely be overestimated.Many articles by Mathews appeared in

*Nature*during 1920-22, but these were extremely difficult years for him for he was suffering from cancer and underwent a series of operations. He died in a Liverpool nursing home on 19 March 1922 and was cremated two days later.

### References (show)

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

See THIS LINK. - Anon, Review: Projective geometry, by G B Mathews,
*The Mathematics Teacher***7**(4) (1915), 176. - Anon, Review: A treatise on Bessel functions and their applications to physics, by Andrew Gray and G B Mathews (2nd edition),
*The Mathematical Gazette***18**(231) (1934), 356-357. - W E H Berwick, Obituary of Mathews,
*Proc. London Math. Soc.***21**, (1923), 46-50. - W E H Berwick, Obituary of George Ballard Mathews,
*Proc. Roy. Soc. London A***101**(1922), x - xiv. - W E H Berwick, Dr G B Mathews, F.R.S.,
*Nature***109**(2735) (1922), 450-451. - M BĂ´cher, Review: A treatise on Bessel functions and their applications to physics, by Andrew Gray and G B Mathews,
*Bull. Amer. Math. Soc.***2**(8) (1896), 255-265. - C, Review: Projective geometry, by G B Mathews,
*Science Progress in the Twentieth Century (1906-1916)***9**(36) (1915), 696-697. - A Gray, George Ballard Mathews, F.R.S.,
*The Mathematical Gazette***11**(160) (1922), 133-135. - A Gray, G B M,
*Nature***109**(2744) (1922), 712. - P A MacMahon, Review: Theory of numbers Part I, by G B Mathews,
*Nature***47**(1893), 289-290. - G B Mathews, Dr W H Besant, F.R.S.,
*Nature***99**(2485) (1917), 310-311. - G B Mathews, Mathematics and public opinion,
*Nature*109 (2738) (1922), 520-521. - W H Metzler, Review: The theory of determinants and their applications (2nd edition), by Robert Forsyth Scott and G B Mathews,
*The Mathematical Gazette***3**(51) (1905), 182-183.

### Additional Resources (show)

Other pages about George Mathews:

Other websites about George Mathews:

### Honours (show)

Honours awarded to George Mathews

### Cross-references (show)

Written by J J O'Connor and E F Robertson

Last Update November 1997

Last Update November 1997