# Henry Martyn Taylor

### Quick Info

Born
6 June 1842
Bristol, England
Died
16 October 1927
Cambridge, England

Summary
Henry Martyn Taylor was an outstanding English mathematician who lost the sight of both eyes. He devised a Braille system to allow mathematical and other scientific works to become available to the blind.

### Biography

Henry Martyn Taylor was the son of James Taylor (1810-1898) and Eliza Johnson (1808-1902). James Taylor was born on 12 March 1810 in Dublin, Ireland. He studied at Erasmus Smyth's school in Dublin, and later was an Assistant Master at Sherborne School, 1834-37. After that, he opened a private school at Bristol. He married Eliza Johnson (1808-1902) on 27 March 1837 at Chard, Somerset, England. Eliza had been baptised on 14 December 1808 at St Nicholas (without), Dublin, Ireland. James and Eliza Taylor had five children: James Heber Taylor (1840-1914); Henry Martyn Taylor (1842-1927), the subject of this biography, Alice Mary Taylor (1844-1939); William Wilberforce Taylor (1848-1922); and Emily Jane Taylor (1853-1943). James Taylor matriculated at Trinity College, Cambridge in 1839 and was awarded a B.A. in 1843, being ordained a deacon in the same year. He was the headmaster of Kimbolton Grammar School for the four years 1843-47, then headmaster of the Queen Elizabeth Grammar School, Wakefield and Evening Lecturer at St Andrew's, Wakefield, 1847-75. Of the five children, the eldest two were born in Bristol, the youngest two in Wakefield and the middle child in Kimbolton.

The 1851 census shows the family living at 2 Almshouse Lane, Wakefield. James Taylor gives his occupation as "Clergyman, Schoolmaster and Evening Lecturer of Parish Church". In addition to the family, there are three boarders in the house, aged 10, 15 and 17, in addition to three servants and a nurse.

Henry Taylor attended the Queen Elizabeth Grammar School, Wakefield, the school of which his father was the headmaster. This school was founded by Royal Charter of Queen Elizabeth I in 1591 as a boys' school and still today (2021) is a boys' school. In fact when Henry Taylor attended the school it had just moved to a new site in Northgate, Wakefield, a site which it continues to occupy. Let us note one fact; James Taylor was the nineteenth headmaster of the school, all nineteen being ordained priests. He was, however, the last ordained headmaster of the school. At the time of the 1861 census, the family were living in a house which was part of the Queen Elizabeth Grammar School. Henry Taylor completed his schooling in 1861, was admitted as a sizar to Trinity College, Cambridge, on 9 February 1861 and matriculated at the College beginning his study of the mathematical tripos in the Michaelmas term (October) of 1861. He joined fellow student John William Strutt (later known as Lord Rayleigh) who also matriculated in Trinity College in the Michaelmas term of 1861 to study the mathematical tripos. Taylor became a scholar in 1863.

In the mathematical tripos of 1865 Taylor was third wrangler. The senior wrangler was John William Strutt and the second wrangler was Alfred Marshall (1842-1924) who went on the become a leading economist. It was announced that Strutt was the 1st Smith's Prizeman and Taylor was the 2nd Smith's Prizeman. Shortly before graduating, Taylor accepted the position of vice-principal of the Royal School of Naval Architecture and Marine Engineering. This School had only been founded a year earlier in 1864 to train naval architects. It was situated in South Kensington but in 1873 it moved to Greenwich becoming the Royal Naval College. Taylor was offered a fellowship by Trinity College, Cambridge, in 1866, which he accepted but continued to work at the Royal School of Naval Architecture until 1869 when he was offered an Assistant Tutorship on the staff at Trinity College. Among the pupils that Taylor taught at the Royal School was William Henry White (1845-1913) who went on to become Chief Constructor of the Admiralty and the designer of a great many British warships. Taylor remained close friends with White for the rest of his life. While Taylor had been a scholar at Trinity College he published the paper The method of inversion and when at the Royal School of Naval Architecture, he published the paper Geometrical explanation of the equations for the longitude of the node, and the inclination of the orbit both published in the Messenger of Mathematics in 1866. He joined the London Mathematical Society on 19 March 1866.

There were two standard routes for Cambridge fellows at this time to set themselves up for a career after the fellowship ended. One was ordination and the other was a law career. Taylor chose to read for the Bar and was called to Lincoln's Inn in 1869. Although this qualified him to practiced law, it does not appear that he ever did so, but the legal training proved useful in his career at the university. We say that he does not appear to have practiced law since we have found no evidence that he did so, but we note that at the time of the 1871 census he was at his parents' home in Wakefield and gave his occupation as "Assistant tutor Trinity College. Barrister at Law in practice."

His mathematical interests were mainly in geometry and he published Inversion, with Special Reference to the Inversion of an Anchor Ring or Torus in the Proceedings of the London Mathematical Society in 1873. The paper begins:-
We premise that a straight line inverts into a circle passing through the pole, and vice versa; that a circle inverts into a circle, the two circles being subcontrary sections of a cone of the second degree passing through the pole; and that the angles between lines and surfaces at their points of intersection are the same as the angles between the inverse lines and surfaces at the inverse points. A normal is a straight line cutting a curve or a surface at right angles; it will therefore invert into a circle through the pole cutting the inverse curve or surface at the inverse point at right angles. Such a circle we will call a normal circle. We will now prove that, if two normals at any two points of a surface intersect and be equal, the normals at the inverse points of the inverse surface also will intersect and be equal.
In 1874 Taylor became a Tutor at Trinity College. In the same year his elder brother, James Heber Taylor, also came to live in Cambridge. James Heber Taylor had been a pupil at the Queen Elizabeth Grammar School in Wakefield, and had been awarded a Lady Betty Hastings Exhibition to Queen's College, Oxford, where he gained a first class in both classical and mathematical Moderations and a second class in Litterae Humaniores. He then went to Trinity College, Cambridge, where he studied both the Classical Tripos and the Mathematical Tripos with great success. He married Mary Elizabeth Pearce in August 1869 and after a while he became headmaster of Brewood School, Staffordshire. He came to live in Little Trinity House, 16 Jesus Lane, Cambridge in 1874 where he worked as a private tutor. We could also give details of Taylor's younger brother William Wilberforce Taylor who became a mathematician. He also studied at both Oxford University, where he matriculated in 1868, and at Cambridge University entering Trinity College in 1868 having obtained an exhibition. In the mathematical tripos examinations of 1872 he was ranked 7th wrangler. He became a teacher of mathematics and in 1881 he was teaching at Ripon, Yorkshire. On 10 January 1889 he joined the London Mathematical Society.

In 1876 Henry Taylor published a number of papers including On the generation of a developable surface through two given curves, On a certain multiple integral, On the lines of curvature of a surface, and On the relative values of the pieces in chess. Let us quote the first few sentences of the last mentioned of these papers:-
The object of this paper is to ascertain the relative values of the pieces on a chessboard. If a piece be placed on a square of a chessboard, the number of squares it commands depends in general on its position. If we calculate the average number of squares which any particular piece commands when placed in succession on every square of the board, it seems fair to assume that this gives a not very inexact measure of the value of the piece. For special reasons the above problem is stated in the following manner:- "A king and a piece of different colours are placed at random on two squares of a chessboard of $n^{2}$ squares; it is required the find the chance that the king is in check." The ordinary chessboard has an even number of squares; and as some of the results take different forms for odd and even values of n, the results are given merely for even values of n, and the results for the ordinary chessboard of 64 squares deduced from them.
The post of Tutor at Trinity College was a ten year appointment and when that expired in 1884 he was appointed as a lecturer at the College. Let us note that at the time of the 1891 census Taylor was living at the Rectory, Church Lane, Brington, Huntingdonshire. His sister Alice Mary Taylor had married the Rev Thomas James Sanderson and they had eleven children. The 1891 census records Henry Taylor, his mother Eliza Taylor, and his sister Emily Jane Taylor all living in the Rectory of All Saints Church Brington with the Rev Thomas James Sanderson, his wife (Henry Taylor's sister Alice Mary) and the youngest five of their children. The family had a cook and two housemaids also living at the Rectory. Although still employed as a lecturer at Trinity College, Henry Taylor gives his occupation as "barrister."

In 1894 Taylor reached 25 years service at Trinity College, the maximum term allowed, and so retired at that time. We list a few more of his papers up to 1894: Note on the Equation of the Two Planes which can he drawn, through Two given Points to touch a Quadric (1879-80), Note on Euclid ii, 12, 13 (1880), (with R C Rowe) Note on a Geometrical Theorem (1881-82), On a six-point circle connected with a triangle (1882), and The Relations of the Intersections of a Circles with a Triangle (1883-84).

Another aspect of his work at Trinity College is described in [1]:-
The 1870s were an active time of academic reform in Cambridge. The old Elizabethan statutes had been partially modified by the first Victorian statutes in 1858; but a comprehensive change was made by the Universities of Oxford and Cambridge Act of 1877. Under that Act, each college framed its own statutes for submission to the Privy Council. Accordingly, Trinity proceeded with that duty in a long succession of meetings ... When decisions had been completed, the final drafting of the statutes was entrusted to three of the fellows: Prof Cayley, whose reputation as a draughtsman long survived his retirement from practice at the Bar: Rev Coutts Trotter, conspicuous for his share in the organisation of the University, especially in the domain of natural science: and H M Taylor, whose legal training proved of high value. Then, and for many years to come, Taylor had a prominent (if not foremost) part in giving effect to the necessary changes in the old system. Independent in thought, and scrupulously just, he maintained the even tenor of his views, devoted to progress yet mindful of the ancient ways, fair in constructive act, and straight in opposition. Those statutes are now under repeal; their actual initial working owed much to the prudent wisdom of a band of reformers, among whom Taylor held a not unworthy place.
Although as we have seen above, most of Taylor's publications were on geometry, his expertise ranged over a wide range of mathematics and he displayed this expertise in helping his friends. He proofread and helped improve a number of books written by his colleagues such as The Theory of Sound (1877) by John William Strutt who writes in the Preface:-
My best thanks are due to Mr H M Taylor of Trinity College, Cambridge, who has been good enough to read the proofs. By his kind assistance several errors and obscurities have been eliminated, and the volume generally rendered less imperfect than it would otherwise have been.
Horace Lamb had been tutored by Taylor at Trinity College and the two remained close friends throughout Taylor's life. Lamb published Treatise on the Mathematical Theory of the Motion of Fluids in 1879 and later editions were published under the title Hydrodynamics. Lamb dedicated the books to Taylor, writing in the Preface to the Fourth Edition (1916):-
It is again a satisfaction to me to inscribe on the fly-leaf the name of Mr H M Taylor, whose kindly encouragement first led me to write on the subject, and whose help in revision I had gratefully acknowledged on former occasions.
We also note that Lamb's admiration for Taylor led to him naming his third son, born in 1883, Henry Taylor Lamb.

Andrew Forsyth had also been tutored by Taylor and in the Preface to his book A Treatise on Differential Equations (1885) he wrote:-
I wish to express the very great obligations under which I lie to my friend and former tutor Mr H M Taylor, of Trinity College, Cambridge, for his kindness in the revision of the proof-sheets. He has caused the removal of obscurities and has made many valuable suggestions of which I have continually availed myself.
In the Preface to his Theory of Functions of a Complex Variable (1893), Andrew Forsyth writes:-
Mr H M Taylor, M.A., Fellow of Trinity College, Cambridge, had read the proofs with great care: the kind assistance he has given me in this way has proved of substantial service and usefulness in correcting the sheets. I desire to recognise most gratefully my sense of the value of the work which these gentlemen [Taylor and William Burnside] have done.
In the late 1880s Taylor began working on an edition of Euclid's Elements and Cambridge University Press began publishing it in separate volumes. The first three volumes were then published as Euclid's Elements of Geometry Books I-VI in 1893. It contains three Prefaces, the Preface to Books I-II is dated 1 October 1889, the Preface to Books III-IV is dated 8 January 1891, and the Preface to Books V-VI is dated 16 March 1893. The Preface to Books I-II begins:-
It was with extreme diffidence that I accepted an invitation from the Syndics of the Cambridge University Press to undertake for them a new edition of the 'Elements of Euclid'. Though I was deeply sensible of the honour, which the invitation conferred, I could not but recognise the great responsibility, which the acceptance of it would entail.

The invitation of the Syndics was in itself, to my mind, a sign of a widely felt conviction that the editions in common use were capable of improvement. Now improvement necessitates change, and every change made in a work, which has been a text book for centuries, must run the gauntlet of severe criticism, for while some will view every alteration with aversion, others will consider that every change demands an apology for the absence of more and greater changes.
He ended the Preface to Books V-VI as follows:-
I hereby acknowledge the great help I have received in this portion of my work from friends, and especially from Dr Forsyth and from my brother Mr J H Taylor. To the latter I am indebted for the Index to Books I-VI, which I hope may prove of some assistance to persons using this edition.
The review [10] of Euclid's Elements of Geometry Books III-IV begins:-
It is only of late years that the University of Cambridge has taken the wise step of giving greater scope to the teaching of geometry by not insisting on the actual proofs of propositions as presented in Euclid's text. All the definitions, axioms, and postulates, together with the sequence of propositions which he adopted, are retained, but in solving them "no proof will be accepted that assumes anything not proved in preceding propositions." The work under consideration is published in the "Pitt Press Mathematical Series," and it will be found to contain some important changes, both with regard to the proofs and method of arrangement. In the first few propositions of Book III the author has introduced several proofs which seem preferable to those generally adopted, while their order of sequence has been extensively changed. The alterations in the remaining propositions of this book have not been carried to any extent, but several outlines of alternative constructions have been inserted in cases where they may be most instructive.
Taylor continued to work on producing editions of further of Euclid's Books but tragedy struck him around the time he left his lectureship at Trinity College in 1894, when he rapidly lost the sight of both of his eyes. Although it is always a little difficult to know precisely what medical conditions afflicted people in past times, it would appear that Taylor suffered from detached retinas, a condition which causes total blindness. With much assistance from those around him, Taylor tried to carry on with mathematical research, something which he had always hoped to be able to spend more time on when retired from his lectureship. Some of his papers, which he dictated after becoming blind, are: On a Series of Cotrinodal Quartics (1896-97); On the Degeneration of a Cubic Curve (1896-97); On the Intersections of Two Cubics (1897-98); On the condition that five straight lines meet a sixth (1902); A problem of arrangements (1903); On a paperfolding puzzle (1904); On some geometrical dissections (1906); and On the order of the boats after a bumping race (1909). He also published the pamphlet Collisions at Sea: A Steamship's Lights Might Tell Her Course (1895) which is advertised as "by H M Taylor, M.A., Fellow of Trinity College, Cambridge, Barrister-at-Law, sometime Vice-Principal of the Royal School of Naval Architecture and Marine Engineering."

Taylor wrote Sir Isaac Newton - A Short Biography for Volume 19 of the 1911 Encyclopaedia Britannica. You can read a version of this article at THIS LINK.

In 1898, four years after he became blind, Taylor was elected a fellow of the Royal Society of London. Of course undertaking mathematical research became increasingly difficult since he could not read current research papers and books. He did, however, get much pleasure from reading Braille novels and it became a passion for him to develop a Braille system to allow mathematical and other scientific works to become available to the blind. Of course, developing the system was not enough for then scientific works had to be translated into Braille [7]:-
One Braille notation was devised by the eminent Cambridge mathematician, Henry Martyn Taylor, who was overtaken by blindness in 1894, when engaged in the preparation of an edition of Euclid for the Cambridge University Press. By means of his ingenious and well thought out Braille notation he was enabled to transcribe many advanced scientific and mathematical works, and in 1917, with the assistance of Mr Emblen, a blind member of the staff of the National Institute for the Blind, he perfected it. It was recognised as so comprehensive that it was soon adopted as the standard mathematical and chemical notation, and is universally used by English-speaking people.
Cambridge Borough Council had on it representatives of Cambridge University and Taylor served on the Borough Council in that capacity. Remarkably he served as mayor of Cambridge during 1900-01 and in the following years was Chair of the Finance Committee of the Borough Council. He also served as a borough magistrate. At the time of the 1901 census he was living in Trinity College, but by the 1911 census he, along with his brother William Wilberforce Taylor and his sister Emily Jane Taylor, were borders at the Nelson Hotel, Mudeford, Christchurch (at that time in Hampshire, but now in Dorset). He had a home, however, at The Yews, Newnham, Cambridge and he died at his home in October 1927. A memorial inscription, in Latin, is at Trinity College. An English translation reads:-
Sacred to the memory of Henry Martyn Taylor, Fellow of the College for sixty-one years and at one time Lecturer and Tutor. At the age of fifty-one he lost his sight; but undiscouraged and eagerly he kindled a torch of hope for those who shared his darkness. His invention of new symbols for Braille enabled them to compensate for the loss of their eyes with their fingers and to follow mathematics more clearly than they could have done by any light.  Although blind and almost sixty years old he became Mayor of Cambridge, and he dealt with College affairs assiduously to the last. He was born on 6th June 1842 and died on 16th October 1927, being by then Senior Fellow.
Let us end with Horace Lamb's description of Taylor's character [9]:-
Taylor was singularly modest and devoid of personal ambition. He did not seek positions of honour and responsibility, but if they came his way he applied himself conscientiously to the duties which he had undertaken. Throughout his life he was a loyal friend and a fair opponent, generous and just in his thoughts, as in his dealings. Before his blindness he had shared in the usual recreations of his time, "real" tennis, cricket, shooting, fishing, billiards, in all of which he was proficient. He was also fond of foreign travel and mountain excursions. But the privation when it came did not provoke a murmur, and he maintained the steady even temper characteristic of him. The last few years of his life were clouded by increasing infirmity, and he died on October 16, 1927. The funeral service in the Chapel of Trinity College drew together a large company of friends and former colleagues to pay the last tribute of affection and respect to a noble and lovable character.

### References (show)

1. A R Forsyth, Mr H M Taylor, F.R.S., Nature 129 (3027) (1927), 664-665.
2. A R Forsyth, Mr H M Taylor, F.R.S., The Times (17 October 1927).
3. H M Taylor, Blind Mathematicians dead; Senior Fellow of Trinity College, Cambridge - Kept up research with handicap, The New York Times (17 October 1927).
4. Henry M Taylor, Cambridge Mayors - past and present, Cambridge City Council (2014), 19.
5. Henry Martyn Taylor, FRS, Trinity College Chapel.
6. Henry Martyn Taylor to Oscar Browning: 19 letters, National Archives.
https://discovery.nationalarchives.gov.uk/details/r/042c0114-b4f4-4b67-9ed4-0aefd8216309
7. Henry Martyn Taylor and the blind student of mathematics, New Beacon 18 (210) (1934), 146-148.
8. H Lamb, rev. Alan Yoshioka, Taylor, Henry Martyn (1842-19270, mathematician, Oxford Dictionary of National Biography (Oxford University Press, Oxford, 2004).
9. H Lamb, Henry Martyn Taylor, Obituary Notices of Fellows Deceased, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 117 (778) (1928), xxix-xxxi.
10. Our Book Shelf, Euclid's Elements of Geometry Books III and IV, edited by H M Taylor, Nature 43 (1122) (1891) 607.
11. Photograph of the Month: Henry Martyn Taylor, mathematician, Trinity College Library (1 November 2016).
https://trinitycollegelibrarycambridge.wordpress.com/2016/11/01/photograph-of-the-month-10/
12. Printing by and for the blind, The Hospital (1 March 1913), 603-604.
13. H M Taylor, On the Relative Values of the Pieces in Chess, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science (5) 1 (3) (1876), 221-229.
14. H M Taylor, Sir Isaac Newton - A Short Biography, Encyclopaedia Britannica. Eleventh Edition (Cambridge University Press, Cambridge, 1910-11), 583-592.
15. E Wood, Pictures for the Blind. A great idea which has opened a new world to the sightless, Strand Magazine (Newnes, London, 1913).