Andrew Hollingworth Frost, Biographical sketch.

Andrew H. Frost (Hull 1819 - Cambridge 1907)
His portrait in 1870, from the Church Mission Society archives

• 1819: Born in Hull, York (England), April 26th. Son of Charles Frost, solicitor and antiquary. Brother of Percival Frost born in 1817.
• 1838: Admitted Pensioner at St John's College, Cambridge, founded in 1511, one of the colleges of the University of Cambridge. Pensioner is the second of three ranks in which students were matriculated, the other ranks being Fellow-commoner and Sizar.
• 1842: B.A., Bachelor of Arts 11th Wrangler.
• 1844: Appointed Mathematical Master in the Manchester Free Grammar School, a famous school founded in 1515. Married Cora Dixon in Finchley, three years after the marriage of his brother Percival to Jennett Dixon, Cora's sister.
• 1846: M.A., Master of Arts, St John's College, Cambridge. Four years after the M.A. of his brother Percival, same college.
• 1847: Birth of his son, Percy Hollingworth.
• 1848: Death of his first wife, Cora aged 26, at the Cambridge house of his brother Percival. Ordained deacon in Lichfield, same year.
• 1849-1853: Priest and curate in England. Author of "The mathematical questions of the senate-house examination papers, 1838 to 1849 inclusive, arranged in order according to subjects" (Cambridge, 1849). Second marriage, to Margaret Atkinson, in Burton-on-Trent (1850).
• 1853-1869: CMS (Church Missionary Society) missionary in Nasik, India. Birth of his other sons Thomas (1854) and Horace (1855), and birth of his daughters, Jane Hollingworth (1857) and Catherine (1860). Death of his father (1862) who was at one time Vice-President of the British Association and several times President of the Hull Literary and Philosophical Society. Publication of "Invention of magic cubes" in The Quarterly Journal of Pure and Applied Mathematics (1866) in which his brother Percival was already a regular author: the first known perfect magic cube is published in this article of 1866.

Panchavati view, Godavari river, Nasik (Nashik), India

• 1869-1870: Secretary to the CMS.
• 1870-1874: Principal of the Church Missionary College, Islington, Middlesex. Publication of "General solution and extension of the problem of the 15 school girls" in The Quarterly Journal of Pure and Applied Mathematics (1870).
• 1875-1878: Rector of Thistleton, Rutland. Publication of his articles "On the knight's path" (1877), "On the General Properties of Nasik Squares" (1878),  "On the General Properties of Nasik Cubes" (1878) in The Quarterly Journal of Pure and Applied Mathematics. He built three glass models of different magic cubes:
• a magic cube of seven deposited at the South Kensington Museum, London,
• a magic cube of nine deposited at the St John's College Library, Cambridge,
• and a magic cube of eleven deposited at the home of his brother Percival, Fitzwilliam Street, Cambridge, who "will with pleasure shew to any who wish to see the curious properties investigated in this paper" (as written in the above article published in 1878). This cube is now at Royal Holloway University of London, but not on public display.

       
Frost's cube of eleven, Royal Holloway University of London. (Photos by John Williamson in 2013-2014, click on the images to enlarge them)
In the middle, the explanation sheet is the first of 154 handwritten sheets describing the cube.
On the right, a placard which has been kept alongside the cube



New photo of this cube by John Williamson in July 2015, with his comments:
"The cube has now been conserved and is in excellent condition. In order to protect it, it is now enclosed in a perspex cover. I am sure it will be good for another 100 years.
The cube is now held in the College archives along with other manuscripts and documents of A H Frost which were donated to Holloway College by his daughter Catherine Frost.
The cube and manuscripts are available to view on request to the College Archivist"

• 1878-1882: Curate of Croxton, Lincolnshire. Writer of the long article on Magic Squares for the 9th edition of the Encyclopaedia Britannica (1882) which was also used in later editions.

Beginning of the Frost's article in the Encyclopaedia Britannica
(here the 11th edition, 1911)

• 1884-1902: Teacher of Marathi and Gujarati under the Board of Indian Civil Service Studies. Gift received from W.A. Firth, author of a booklet of 19 pages, entitled "The magic square" (Belfast, 1887), who dedicated to him a cube of six, stored in a wooden box (1887). Publication of his article "On the construction of Nasik Squares of any order" in the Proceedings of the London Mathematical Society (1896). University teacher (from 1897). Death of his brother, Percival, aged 81 (1898), who had written several mathematical books (A Treatise on Solid Geometry, An Elementary Treatise on Curve Tracings,...) and who edited Newton's Principia. Death of his second wife, Margaret, aged 81 (1901).

     

Wooden box storing Firth's cube of six dedicated to Frost, Royal Holloway University of London. (Photos by John Williamson in 2013, click on the images to enlarge them)
The box is heavy and when opened up can be assembled to form the cube. It opens flat and one half shows 6 strips of wood, the 6 vertical planes of the cube.

• 1907: Died of heart failure in Cambridge, February 24th. Aged 88.
• 1933: His model of a magic cube of seven, kept at the South Kensington Museum (now the Science Museum), deaccessioned and given to Prof. William P. Milne at Leeds University.
• 1951: His model of a magic cube of nine, kept in a wooden box at the St John's College Library, transferred and deposited on loan at the Whipple Museum of the History of Science, Cambridge, and is still there today.

Frost's cube of nine, Whipple Museum of the History of Science, Cambridge.
Length 289mm; breadth 286mm; height 270mm. Turned square ebony base carries glass cube (edges covered with gold paper) which contains 7 glass plates. Each plate, together with the back and front of the cube carries 81 numbers, printed on paper, arranged in 9 rows of 9 columns.  Each position on the grid has two numbers, one facing in each direction.  These numbers run from 1 to 729.

• 1967: Death of Prof. William P. Milne who had the other Frost cube, since 1933.
  Where is this cube of seven, now? There is no trace of it at the Library Museum of Leeds University. If you have any information about this cube, send me a message!

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