# Walter William Rouse Ball

### Quick Info

Hampstead, London, England

Elmside, Cambridge, England

**Walter Rouse Ball**was an English mathematician best known for his popular books on the History of Mathematics and on Mathematical Recreations.

### Biography

**Walter Rouse Ball**was the only son of Walter Frederick Ball and his wife Mary Anne Rouse. Walter Frederick Ball was a rents and dividends man, born at St George Hanover Square, Middlesex in about 1824. Walter Frederick Ball married Mary Anne Rouse in 1849. She had been born in Marylebone, Middlesex in 1829. Walter Rouse Ball (known as Rouse Ball) was born at 81 New Bond Street, London, and had a younger sister Mary born at St George Hanover Square in about 1853.

Rouse Ball attended University College School in London. This school had been founded by University College, London, in 1830, just four years after the College was founded. The College was founded to provide an education for those with any or no religious beliefs. Oxford and Cambridge only took those who were members of the established Church of England. When Rouse Ball studied there the school was within the buildings of University College. It taught Classical Greek, Latin, French, German, Mathematics, Chemistry, and English. The fact that science was taught there was highly unusual for the time.

After studying at University College School and winning an Entrance Exhibition to University College, London, Rouse Ball entered the College in 1867. This was the standard route since really the school had been founded to provide a route into the College. There he studied mathematics, logic, and moral philosophy. The professor of mathematics was Thomas Archer Hirst who had replaced Augustus De Morgan in the year that Rouse Ball began his studies. His performance in mathematics was outstanding, and he was awarded the Gold Medal in that subject. He also studied philosophy under George Croom Robertson (1842-1892), the professor of philosophy of mind and logic. After graduating from University College in 1869 with honours in mathematics and philosophy, he matriculated at Trinity College, Cambridge, in 1870. His early interest in philosophy seems not to have lasted long. Edmund Taylor Whittaker writes [22]:-

To those who knew him only in the second half of his life, this early interest in philosophical studies seemed to have left but little residue. I never remember hearing him take an active part in philosophical discussion, or comment on philosophical books: and it is difficult to believe that the account of the Greek period in his History of Mathematics (long and valuable though it is) was the work of a mind fundamentally interested in philosophical questions.At Trinity he was taught by, among others, Henry Martin Taylor (1842-1927), William Davidson Niven, James Whitbread Lee Glaisher, and Horace Lamb. Four years later he was awarded a B.A. and placed Second Wrangler in the Mathematical Tripos (which means that he was ranked second in the list of those awarded First Class degrees). His achievements at Trinity had been exceptional and he had been widely expected to be First Wrangler but he was beaten by G C Calliphronas. The scene when the list was read was described by Donald MacAlister who became Senior Wrangler in January 1877 (see [2]):-

The great bell of St Mary's strikes. [The moderator] lifts his finger, and almost in a whisper, yet heard to the farthest corners of the hall, - says "Senior Wrangler - Calliphronas of Caius" -. A sudden gasp seemed to rise from the whole multitude, for nobody had heard of this man before, so to speak. Then a ringing cheer that lasts many minutes ... 2nd Wrangler, Ball of Trinity" - another big cheer, soon over though ...The Senior Wrangler was George Constantine Calliphronas (1852-1913) whose Greek father was the Rev Demetrius Panaghis Calliphronas, vicar of Walpole St Andrew, Wisbech. George Calliphronas was a junior fellow from 1875 to 1887 and became a master at Winchester. The day after the list of Wranglers was read, they received their M.A. degrees in ranked order with Calliphronas first, Rouse Ball second etc. Later in 1874, the year he sat the Tripos, Rouse Ball was first Smith's prizeman, and in the following year he was elected a fellow of Trinity College, Cambridge. Two years ahead of Rouse Ball at Trinity College was Alfred Kempe who, after taking the Mathematical tripos, chose the law as a profession and was called to the bar in 1873. Rouse Ball decided to follow the same route as Kempe (and many others) and make a career in law. E T Whittaker writes [22]:-

This, like the degree in Philosophy, is something of a puzzle: for he was a shy and reluctant speaker before any audience larger than a small committee.In 1876 he became a barrister when he was called to the Bar by the Inner Temple. However, he only had a short career as a barrister, which saw him practising as an equity draftsman and conveyancer, and writing

*The Student's Guide to the Bar*. In 1877 he returned to teaching mathematics when he acted as deputy to William Kingdom Clifford at University College London. Clifford's health had collapsed through overwork. Having now sampled the academic profession and the legal profession, Rouse Ball had no doubts where his interests and abilities were telling him he should make his career. His wish to become an academic was soon to become a reality.

In 1878 Trinity College, Cambridge, invited Rouse Ball to return as a lecturer in mathematics and, two years later, he was appointed as an assistant tutor. He is best known as an historian of mathematics but he also made a large contribution in many different posts within Trinity College. He was appointed Director of Mathematical Studies at Trinity in 1891, and became a tutor at Trinity in 1893 [22]:-

In 1893 he succeeded Glaisher as Tutor of Trinity: and he and Alice Ball ... soon won the reputation of being the best tutor and tutor's wife that had ever been. They built a house not far beyond the Trinity Fellows' Garden, in the new western suburb which had begun to rise when the compulsory celibacy of Fellows was abolished; and here they welcomed an entertained an endless succession of pupils. Their charm as host and hostess was beyond all power of description: both of them were, I think, shy and reserved by nature, but shyness was swallowed up in goodness of heart.In 1898 he was made a Senior Tutor and, in the same year, he became chairman of the College Council. He acted as moderator of the Mathematical Tripos on a number of occasions. He also held posts within the wider university administration including sitting on the University Financial Board. Outside the University of Cambridge he also undertook a number of important duties, including being representative of the University on the Borough Council and various other bodies. He was also a governor of Westminster School and of Perse School. A fellow governor of Westminster School wrote:-

Trinity College, Cambridge, has during the 40 years for which I have been a governor sent us some excellent representatives, but none better than the late Mr Rouse Ball. He was constant in attendance and an excellent colleague. He acted as auditor of our accounts and took our finances under his special charge. With these he was careful and prudent, but never hesitated to recommend judicious outlay.Rouse Ball married Alice Mary Gaid (1851-1919), daughter of William Snowdon Gaid, on 1 September 1885.

Rouse Ball wrote

*A short account of the history of mathematics*(1888) which provided a very readable and popular account of the subject [5]:-

... it contained a delightful account of what a young student of mathematics or most general readers interested in this science might wish to know.E T Whittaker offers high praise but also criticism [22]:-

The best parts - and they are very good - are those dealing with arithmetical and geometrical pastimes such as magic squares, mazes, and the knight's path on a chess-board. In the more subtle argumentative topics, such as the Paradoxes of Zeno and Hyper-Space, he is less successful, from the defect of philosophical quality in his mind. The three famous problems of antiquity - the duplication of the cube, the trisection of the angle, and the quadrature of the circle - he introduces by legends and discusses as isolated puzzles: this is hardly adequate, for to the Greeks the three problems were involved in a serious and far-reaching logical programme of research into the nature of things. But against these and all other criticisms may be set the fact that the copy which now lies before me is coming to pieces from constant use.The fourth edition of 1908 was reprinted in 1960. He was also the author of the very popular

*Mathematical Recreations and Essays*first published in 1892 which has run to fourteen editions (the last four being revised by H S M Coxeter). It would be impossible to describe the complete contents here but we will mention a few topics covered. Chapters on mechanical recreations, bees and their cells, and string figures were in Rouse Ball's original text but were omitted in Coxeter's revision. Topics such as colouring of maps, magic squares, chessboard problems and tessellations remained. It also contained many early examples of mathematical conjuring.

For more details see THIS LINK.

Ball also wrote

*The history of mathematics at Cambridge*(1889),

*Elementary algebra*(1890),

*An essay on Newton's "Principia"*(1893),

*A Primer of the History of Mathematics*(1895),

*Trinity College Cambridge*(1906),

*Cambridge papers*(1918), and

*An Introduction to String Figures. An Amusement for Everybody*(1920).

For more details see THIS LINK.

We also present short extracts from six of Rouse Ball's papers which are either on history or puzzles. See THIS LINK.

His work in history, however, was not confined to mathematics. He wrote a history of the First Trinity Boat Club, and histories of other university and college societies. From this we may deduce that he had a keen interest in rowing, and he also contributed to this sport by acting as treasurer of the University Boat Club. One of his close friends, Joseph John Thomson (1856-1940) who discovered the electron in 1897, was also an enthusiastic member of the University Boat Club. Rouse Ball was also a keen chess player and, when he was young, played for the Cambridge graduates team in the matches against Oxford graduates. Florian Cajori recounts his personal memories of Rouse Ball in [5]:-

It was at the Napier Tercentenary Celebration that the present writer was privileged to make the personal acquaintance of Ball and to enjoy the charm of his personality. Again later in 1914, at Cambridge, the writer was shown through Trinity College with its fine Library, enjoyed hospitality at the dining hall, and was also invited to Elmside, Ball's home. At that time Ball was saddened by the news of the death of Cambridge students who had early entered the war, some of whom he had known intimately.Shortly after World War I Rouse Ball founded the Conjuring Society at Cambridge. He described this in a letter to E T Whittaker written in 1924 (see [22]):-

Some five years ago I founded a society of undergraduates interested in conjuring and such like shows: if members can conjure so much the better, but that is not essential. I took as our symbol the re-entrant pentacle, which, as you may perhaps know, was sometimes used as a sign by magicians in the middle ages and probably also in classical times. The Society prospers, and at the end of an academic year numbers something like 100 members. Nearly four years ago we received the unexpected 'compliment' of being asked to give a show in London before the leading professional conjurers. The invitation was embarrassing, but could not be declined: however, in fact, we gave a really good show. I was the more inclined to introduce a pentacle by the fact that, according to the historians, it was the symbol selected by Pythagoras as the badge of his school. This seems to be true, and hence to mathematicians it should have interest.After Rouse Ball's wife Alice died in December 1919, he never fully recovered. Outwardly, however, he was able to continue to be active and took great pleasure in the reunions that came about through the celebrations in September 1924 for the 600th anniversary of the founding of Trinity College (as Michaelhouse). However he was by this time suffering signs of heart problems and was less mobile, needing a stick to help him walk. He died at his home in Cambridge, Elmside, 49 Grange Road. His funeral was held in the chapel of Trinity College on Wednesday 8 April 1925. He was buried at the Ascension Parish Burial Ground in Plot 419 where his wife had been buried a little over five years earlier. Three years before his death he had established the Rouse Ball lectureship in mathematics at Cambridge with generous funding. In his will he set aside a sizable endowment to fund two professorships at Cambridge, the Rouse Ball professorship of English law and a Rouse Ball professorship of mathematics. At Trinity there is a memorial with a Latin inscription which, in translation, reads:-

In pious memory of Walter William Rouse Ball. He deserved well of both ancient universities and particularly of this College, which he helped while alive with his knowledge and advice, and after his death with his wealth. As Scholar, Fellow, Lecturer and Tutor, he always tried to further the well-being and reputation of the College so far as he was able.Ball's contributions are summed up in [1]:-

Generations of Trinity men benefited by his mathematical teaching; he was the historian of mathematics, of the College, and of the First Trinity Boat Club; and the University profited in various ways by his administrative ability.

### References (show)

- Obituary in
*The Times* - A Warwick,
*Masters of Theory: Cambridge and the Rise of Mathematical Physics*(University of Chicago Press, Chicago, 2003). - E M Blake, Review: A Primer of the History of Mathematics, by W W Rouse Ball,
*Science*, New Series**5**(113) (1897), 352-353. - W H Bussey, Review: Mathematical Recreations and Essays (Fifth Edition), by W W Rouse Ball,
*The American Mathematical Monthly***20**(2) (1913), 61. - F Cajori, Walter William Rouse Ball,
*Isis***8**(2) (1926), 321-324. - H S M Coxeter, Rouse Ball's unpublished notes on three fours,
*Scripta Math.***18**(1952), 85-86. - H T Davis, Review: Mathematical Recreations and Essays, by W W Rouse Ball and H S M Coxeter,
*National Mathematics Magazine***14**(6) (1940), 357-358. - W J G, Review: Mathematical Recreations and Essays, by W W Rouse Ball,
*The Mathematical Gazette***3**(54) (1905), 256-257. - D Johnson, Review: Mathematical Recreations and Essays (P, L, S), by W W Rouse Ball and H S M Coxeter,
*The Mathematics Teacher***81**(4) (1988), 325. - G V Morson, (Walter William) Rouse Ball (1850-1925),
*Oxford Dictionary of National Biography*(Oxford University Press, Oxford, 2004). See THIS LINK. - H F Munch, Review: Mathematical Recreations and Essays by W W Rouse Ball and H S M Coxeter,
*The High School Journal***26**(1/2) (1943), 44-45. - P Peak, Review: Mathematical Recreations & Essays (12th ed.), by W W Rouse Ball and H S M Coxeter,
*The Mathematics Teacher***69**(1) (1976), 86. - W D R, Review: Mathematical Recreations and Essays (Eleventh edition), by W W Rouse Ball and H S M Coxeter,
*The Mathematics Teacher***33**(1) (1940), 46. - Review: An Introduction to String Figures. An Amusement for Everybody by W W Rouse Ball, The Mathematical Gazette 10 (151) (1921), 255-256
- Review: Histoire des MathÃ©matiques, by W W Rouse Ball,
*The Mathematical Gazette***5**(80) (1909), 113-114. - J J Thomson, Walter William Rouse Ball,
*The Cambridge Review*(1925), 341-342. - Walter William Rouse Ball,
*The Times*(6 April 1925). - Walter William Rouse Ball,
*Nature***115**(1925), 808-809. - Walter William Rouse Ball,
*The Trinity Magazine***6**(June 1925), 53-54. - Walter William Rouse Ball,
*Trinity College Chapel, Cambridge*. http://trinitycollegechapel.com//about/memorials/brasses/rouse-ball/ - P F White, Review: Mathematical Recreations and Essays, by W W Rouse Ball and H S M Coxeter,
*The Mathematical Gazett*e**23**(256) (1939), 422. - E T Whittaker, W W Rouse Ball,
*The Mathematical Gazette***12**(178) (1925), 449-454.

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Written by J J O'Connor and E F Robertson

Last Update January 2015

Last Update January 2015