# Micaiah John Muller Hill

### Quick Info

Born
22 February 1856
Berhampur, Bengal (now Odisha), India
Died
11 January 1929
Golders Green, Middlesex, England

Summary
M J M Hill was professor at University College, London. He did important work on hydrodynamics and also on the teaching of mathematics, particularly on teaching Euclid's Elements.

### Biography

Micaiah John Muller Hill was the son of the Revd Samuel John Hill and Leonora Josephina Müller. Samuel John Hill (1825-1891) was a missionary who had been born in Berhampur India, the son of the missionary Micaiah Hill and Mary Beardmore. Samuel John Hill [22]:-
... was a missionary of rigid and exemplary character who felt it his duty to live continuously in, and for, India; and it fell to [the children's] mother, although of mixed Danish and Portuguese stock rooted in India, to take the children to Britain for their education. Family means were straitened and the divided home left a deep mark on [the children].
Samuel was back in England in 1837 when his family returned but then they went to Calcutta in 1842. Samuel was accepted as a missionary in Calcutta in 1852 and, in the following year, was ordained and married Leonora Müller (1833-1917) in Calcutta. Samuel and Leonora Hill then went to Berhampur where Micaiah John Muller Hill, the subject of this biography, was born. Their second child Samuel Charles Hill was born in Berhampur in 1857 but the family then returned to England where their next two children, William Kirkpatrick Hill and Mary Ellen Hill, were born in 1862 and 1864 respectively. Samuel and Leonora and their two youngest children returned to Berhampur, India where their fifth and last child George Francis Hill was born in 1867. Micaiah John Muller Hill remained in England, however, where he and his brother were educated at the Sons of Missionaries boarding school. In India Samuel John Hill opened a new Anglo-Vernacular School in Berhampur in 1868 and took charge of the Berhampur station two years later. In 1872 Leonora Hill's health became poor and she returned to London, England, with her three children, arriving on 8 August.

Let us record at this point some details of Micaiah John Muller Hill's brothers. Samuel Charles Hill was educated at the Sons of Missionaries School, Blackheath, England and became an historian of India writing a number of popular books. He was a Professor at Dacca College and then in charge of Imperial Record department and Imperial Library in Calcutta. William Kirkpatrick Hill studied at the University of London, and became a schoolmaster, journalist and author. He became Secretary of the Finance Committee of the University of London. George Francis Hill was also educated at the Sons of Missionaries School, Blackheath, studied classics at University College London, and  joined the Coins and Medals Department of the British Museum. He was knighted in 1933.

From now on let us refer to Micaiah John Muller Hill simply as Hill. As we noted above, he was educated at the Sons of Missionaries School, Blackheath, London. This school was founded as a small boarding school in Walthamstow in 1842 for the sons of Congregational and Baptist missionaries serving overseas. The school moved to a new building in Blackheath, London, in 1857 and it was in that building that Hill studied. The headmaster of the school at this time was Edward James Chinnock (1842-1911) who was a historian specialising in Greek who had studied at the University of London. Hill graduated from the Sons of Missionaries School in 1872 and, in October of that year, he entered University College, part of the University of London, to study mathematics. There he was taught by Olaus Henrici, the professor of mathematics, who was making many innovations in teaching at the College.

After only two years of study at University College, Hill graduated with a B.A. in 1874 being ranked the top student in Mathematical Honours. He continued to study for a Master's Degree and was awarded an M.A. in 1876, winning the Gold Medal in the examinations. Before the award of his M.A. degree from the University of London, Hill had matriculated as a scholar at Peterhouse, University of Cambridge, at the start of the Michaelmas term in 1875. In the Mathematical Tripos examinations of 1879 Hill was Fourth Wrangler. The Senior Wrangler that year was his fellow student at Peterhouse, Andrew James Campbell Allen (1856-1923), who became a tutor at Peterhouse, Principal of Chester Training College, and finally a Church of England vicar. The Second Wrangler was George Francis Walker (1855-1883) who after being a tutor at Queen's College, became Professor of Mathematics at Auckland, New Zealand in 1883 but drowned a few hours after arriving in Auckland. Although Hill was Fourth Wrangler, he was equal 1st Smith's Prizeman in 1879 showing his outstanding research potential. He had been examined for the Smith's Prize by James Clerk Maxwell.

George Chrystal left the University of St Andrews in 1879 when appointed to the Chair of Mathematics at the University of Edinburgh. Hill was a candidate to fill the vacant St Andrews chair and he requested a testimonial from James Clerk Maxwell to support his candidacy. Hill was unsuccessful, Scott Lang being appointed to the St Andrews Chair.

Despite Hill's highly successful years at Cambridge, he lacked the experience needed for the St Andrews Chair so he returned to University College, London where he was appointed as assistant to Olaus Henrici. This position was short lived, however, for, in 1880, he was offered the Chair of Mathematics at the Mason Science College, Birmingham which he was pleased to accept. This College had been founded in 1875, five years before Hill was appointed; it went on the become Mason University College in 1898 and was incorporated into the University of Birmingham in 1900. In Birmingham, Hill lived in a boarding house. At the time of the 1881 census he was living as a boarder at 56 Wheeleys Road, Edgbaston, Birmingham. The house was owned by the widow Caroline Fearn and there were two other boarders living in the house who were both Stocks and Shares Brokers.

It was while Hill was in Birmingham that he published his first mathematical papers: Some properties of the equations of hydrodynamics (1881); Calculation of the Equation which determines the Anharmonic Ratios of the Roots of a Quintic (1882); On the motion of fluid, part of which is moving rotationally and part irrotationally [Abstract] (1883); On the Closed Link Polygons belonging to a system of Co-planar Forces having a Single Resultant (1883); On the motion of fluid, part of which is moving rotationally and part irrotationally (1884); and The Differential Equations of Cylindrical and Annular Vortices (1884).

In 1884, after four years in Birmingham, Hill returned to London when he was appointed Professor of Pure Mathematics at University College. Karl Pearson was appointed as Professor of Applied Mathematics in the same year. Hill and Karl Pearson would remain colleagues at University College for forty years. Louis Filon, who was a student at University College and later became a colleague of Hill's, writes [6]:-
The life of a professor in a University College in those days was very different from that to which we are now accustomed. Endowed Chairs were the exception and stipends largely consisted of professors' shares of fees, so that there was a strong inducement to make one's teaching popular rather than profound, a temptation fortunately resisted in most cases, certainly in the case of Hill. Assistants were few, and often paid by the professor. When Hill first took up his duties, the department of Mathematics boasted only a single assistant. The bulk of the routine work of undergraduate teaching, such the correction of students' exercises, fell upon the professor, and this work Hill, trained as he had been in a hard school, performed with unflagging energy and zeal, and an unselfish devotion which won him the affection and admiration of generation after generation of students.
Given the pressures on Hill in his new appointment, it is not surprising that he published little in the first few years after becoming a professor at University College. He did publish On the Incorrectness of the Rules for contracting the processes of finding the Square and Cube Roots of a Number Proceedings of the London Mathematical Society (1886) which, more than likely, was motivated by his teaching. He begins the paper as follows:-
The rule for contracting the process of finding the Square Root. The rule (see Todhunter's 'Algebra') is this:-

When $n+1$ figures of a square root have been obtained by the ordinary method, n more may be obtained by division only, supposing $2n+1$ to be the whole number.

It will be shown in this paper that the rule cannot always be extended to cases in which the 2n+1 figures are followed by other figures, as is usually assumed.
He began a new research topic with his next paper, however, namely On the c- and p-Discriminants of Ordinary Integrable Differential Equations of the First Order (1888). This was a major 34-page paper on singular solutions to differential equations which extended the work of Arthur Cayley in his paper On the theory of the singular solutions of differential equations of the first order (1873) and of Olaus Henrici in his paper On Series of Curves, especially on the Singularities of their Envelopes; with Applications to Polar Curves (1866). Hill published further important contribution to singular equations with On Node-and Cusp-Loci, which are enveloped by the Tangents at the Cusps (1890) and On the locus of singular points and lines which occur in connection the theory of the locus of ultimate intersections of a system of surfaces (1892). He did not neglect his research on hydrodynamics, however, and he published On some general equations which include the equations of hydrodynamics (1889) and Note on the Motion of a Fluid Ellipsoid under its Own Attraction (1891).

On 21 December 1892, Hill married Minna Grace Tarbotton (known as Minnie) at St Saviour's Church, Paddington, London. Minnie (1861-1920), born in Nottingham, was the eldest of the three children of the surveyor and civil engineer Marriott Ogle Tarbotton (1834-1887) and his wife Emma Maria Stanfield (1832-1915). Micaiah and Minnie Hill had three children: Roderick Maxwell Hill (1894-1954); Geoffrey Terence Rowland Hill (1895-1955); and Elfrida Lilian Hill Gwendolen (1898-1971), known as Gwen. Let us say a little about the children. Roderick Hill became a fighter pilot during World War I, and was highly decorated for his bravery. Continuing a career in the Royal Airforce, he was Director-General of Research and Development at the Air Ministry at the start of World War II, and then Commander-in-Chief of Fighter Command. After the war he was Rector of Imperial College (1948-1954) and Vice-Chancellor of the University of London (1953-54). Geoffrey Hill also became a pilot, saw action in France during World War I and was awarded the military cross. He was wounded and returned to England to become a test pilot. After the war he worked as a test pilot and aeronautical engineer for Hanley Page Ltd. Gwen Hill became a radiologist. She married Reginald Hilton, who became a consultant physician at St Thomas's Hospital. Gwen became Director of the Radiotherapy Department at University College Hospital.

Let us return to Micaiah Hill's career. He was an active member of the London Mathematical Society, serving on the Council first in 1886 and then again for ten years from 1891 to 1901. He was Vice-President of the Society in 1894-95. In 1894 he was elected a fellow of the Royal Society of London. Now it is important to understand that Hill started out his research career making significant advances to hydrodynamics and he continued with this interest. His position, however, was Professor of Pure Mathematics at University College, so his teaching was in pure mathematics. Perhaps because of this his interests turned towards teaching and from around 1897 he began to publish papers on teaching mathematics. Louis Filon, who was taught by Hill, writes about Hill as a teacher in [6]:-
As a teacher he had, to an extraordinary degree, that infinite capacity for taking pains in which Carlyle saw the mark of genius; and he possessed that rare quality, which students so keenly appreciate, of never slurring over difficulties: time spent on making a demonstration perfect was always to him time well spent. And he showed great sympathy with the occasionally devious mental processes of beginners and would even, sometimes, adapt his demonstrations to them. The writer remembers, in his student days, sending up to him a solution which, alas! meandered through as many pages as it should have taken lines, arriving at the desired result by a singularly laborious and inelegant process. Hill read patiently and carefully every line, and in the end his only (and characteristic) comment was that it was a "very courageous " solution! Above all, he loved his students, a feeling which was universally and deeply reciprocated.
His interest in teaching led to him developing ideas about teaching geometry and to being very active in the Mathematical Association. His first publication, On the Fifth Book of Euclid's Elements was read to the Cambridge Philosophical Society in November 1897 and published in volume 16 of the Transactions of the Cambridge Philosophical Society in 1898. Hill writes in the Introduction:-
The objects of this paper are (I) To draw attention to the indirect character of the argument in the Fifth Book of Euclid's Elements. (II) To reconstruct the argument showing how the indirectness may be removed. (III) To develop the theory of ratio from the reconstructed argument.
In 1900 Hill published the book The Contents of the Fifth and Sixth Books of Euclid. The Preface begins:-
The object of this work is to remove the chief difficulties felt by those who desire to understand the Sixth Book of Euclid. It contains nothing beyond the capacity of those who have mastered the first four Books, and has been prepared for their use. It is the result of an experience of teaching the subject extending over nearly twenty years. The arrangement here adopted has been used by the Author in teaching for the past three years and has been more readily understood than the methods in ordinary use, which he had previously employed.

Hill was elected President of the London Branch of the Mathematical Association and gave the Presidential Address on The Theory of Proportion on 10 February 1912. His introduction is as follows [8]:-
I desire in the first place to express my thanks to the members of the London Branch of the Mathematical Association for the honour they have done me in electing me to the office of president. I esteem it a privilege to take part in the efforts the Association is making to bring about improvements in the methods of teaching Mathematics.

In what position does the work of the Association now stand? Is it in fact in the position described by Sir J J Thomson in his address to the Association of Public School Science Masters? He is reported to have said that he had come to the conclusion that if you have intelligent masters and small classes it does not matter much what theory of education you adopt and if you have not these, well, it does not much matter either.

That seems to me to be a counsel of despair. I prefer to take my stand by the side of Professor Hobson, who said two notable things in his recent address on "The Democratisation of Mathematical Education."

The first was that the business of this Association was "the progressive adaptation of methods and matter of teaching to meet the needs of those who lacked any exceptional capacity."

The second was that "Education in Mathematics must be pronounced a failure if it did not rise beyond the purely practical aspect to the domain of principle. The most important educational aspect of the subject was an instrument for training boys and girls to think accurately and independently."
C L T Griffith, who was Professor of Mathematics at the Engineering College, Madras, India, had been a student of Hill's at University College London. Griffith tried to gain recognition of the abilities of Srinivasa Ramanujan and wrote to Hill on 12 November 1912 sending some of Ramanujan's work and a copy of his 1911 paper on Bernoulli numbers. Hill replied to Griffith on 3 December 1912 [24]:-
I am sorry that the twenty years, which have passed since you were with me, prevent me from remembering anything about you but your name. As soon as I can get more time I will look into Mr Ramanujan's paper about the Bernoulli's Numbers, but I cannot do this during term time. One thing however is clear. Mr Ramanujan has fallen into the pitfalls of the very difficult subject of Divergent series.
Hill did read Ramanujan's paper about the Bernoulli numbers quickly and wrote to Griffith again on 7 December 1912. He makes some correct observations, complains about a lack of "logical completeness" but failed to understand Ramanujan's divergent series. See [20] for an interesting discussion of Hill's involvement with Ramanujan's work.

Hill's wife Minnie died on 10 January 1920 at their home, 39 West Heath Drive, Hampstead, Middlesex. He retired three years later but stayed on a further year to allow a successor to be appointed [6]:-
When he retired in 1924 from the Chair of Mathematics, his friends asked him in what way he would wish them to commemorate his long connection with University College; and he then, remembering the financial struggle of his early years, expressed the desire that any subscriptions received should be devoted to establishing a Loan Fund by means of which the difficulties of students in straitened circumstances might be temporarily relieved, while their spirit of independence was to be preserved by an undertaking of eventual repayment, so soon as they felt able to do so. It was done according to his wishes, and, indeed, no more fitting memorial could have been found of a life spent in the unselfish service of studious youth. Hill was one of those who fought for the establishment in London of a real teaching University; and from the re-constitution of the University in 1900 until 1926, when ill-health compelled his retirement, he was a member of its Senate, in which his balanced judgment, ever-courteous modesty, and, above all, his transparent honesty of purpose and that moral atmosphere which radiated from him and impressed all, even the bitterest opponents of his policy, who came into contact with him, soon gained for him a position of ascendancy.
His health deteriorated and he began to rapidly lose his sight. He was elected President of the Mathematical Association and gave two presidential addresses. The first On the Teaching of Mathematics was given in 1927 and the second The Logical Eye and the Mathematical Eye. Their Outlook on Euclid's Theory of Proportion given in January 1928. We must note that by the time he gave this second address he was totally blind; one cannot help us seeing irony in his title.

Louis Filon writes [6]:-
Almost to the day of his death he continued at work, contending with surprising success against well-nigh insuperable obstacles, and planning a book on the foundations of Geometry. The end came swiftly and comparatively painlessly on January 11th, 1929.
He was cremated on 14 January 1929 at Golders Green crematorium.

Hill had served on the senate of the University of London from 1900 to 1926, and as vice-chancellor from 1909 to 1911. Let us end with H H Bellot's tribute to Hill in these roles [2]:-
... it was said that by his death the college lost one of the most commanding personalities among its members. No one who sat with him on the many boards and committees concerned with university and college administration could forget the power of his influence, and yet, it was added, he never allowed the administrator or the teacher to eclipse the scholar.