by Robin J. Wilson

© Oxford University Press 2004 All rights reserved

**Hirst, Thomas Archer** (1830-1892), mathematician, was born on 22 April 1830 in Heckmondwike, West Riding of Yorkshire, the youngest son of Thomas Hirst (1797-1842), wool-stapler, and his wife, Hannah, daughter of John Oates, wool merchant and shipowner. In 1828 his father retired from business and moved to Wakefield to educate his three surviving sons, and in 1840 Hirst entered the West Riding proprietary school where 'Mathematics was my favourite study' (Hirst, 799). In 1845 he was articled for five years to an engineering surveyor in Halifax, surveying for the West Yorkshire Railway, and meeting and working with John Tyndall, a close friend whom he greatly admired and who would have a major influence on his life.

On arriving in Halifax, Hirst began to record his experiences in a journal, which became a major chronicle of scientific life in the Victorian era. Covering over forty-five years and amounting to almost two million words, his diaries describe with clarity and perceptiveness the scientific circles in which he lived and the people he met--both in England and on the continent. Inspired by Tyndall, he embarked on a programme of self-improvement, enrolling at the Halifax Mechanics' Institute and reading widely in literature and the sciences. Meanwhile, in 1848, Tyndall had left Halifax with Edward Frankland to study for a doctorate in Marburg, Germany. Hirst visited them, and on completing his apprenticeship in 1850 returned there to study chemistry with Robert Bunsen, physics with Christian Gerling, and mathematics with Friedrich Stegmann. He was particularly interested in geometry, which became a lifelong passion, and within two years wrote a PhD dissertation on conjugate diameters of the triaxial ellipsoid.

With the successful completion of his dissertation in July 1852, Hirst decided to travel, first to Göttingen, where he conducted magnetic experiments with Wilhelm Weber and met Carl Friedrich Gauss, and then to Berlin, where he spent the winter semester attending the lectures of Lejeune Dirichlet, the analyst and number theorist, and the geometer Jakob Steiner. On returning to England in mid-1853 he secured a teaching job at Queenwood College in Hampshire, where practical work was encouraged, and he presented geometry in the context of surveying, rather than through rote learning of Euclid's *Elements.* Whenever he could he visited London to see Tyndall and attend the lectures of Michael Faraday and others at the Royal Institution.

In Marburg, Hirst had struck up an acquaintance with Anna Martin, the sister of the Irish naturalist John Martin (1812-1875), and he married her on 28 December 1854. Shortly after their wedding Anna began to exhibit signs of advancing tuberculosis. Hirst gave up his post to look after her, and they visited the spas of southern France vainly seeking a cure. In July 1857 Anna died. Hirst never fully recovered from the tragedy of her death, and did not marry again. He decided to devote his life to research rather than returning to teaching, and settled in Paris where he befriended some of the foremost French mathematicians of the day--Michel Chasles, Joseph Liouville, and Louis Poinsot. He read widely, translated many mathematical and scientific works into English, and investigated problems in geometry. In August 1858 he left for Italy to work with mathematicians in Rome, Naples, and Milan. He was able to live on his own resources, having inherited a substantial sum from his mother in 1849. In mid-1859 he returned to England, obtaining lodgings near Tyndall, who introduced him to the London scientific scene. He became acquainted with the mathematicians James Joseph Sylvester and Arthur Cayley, and attended lectures by Thomas Huxley and others. From 1860 to 1864 he taught mathematics at University College School.

Hirst quickly became a key figure in the London scientific establishment. In April 1861 he became a fellow of the Royal Society, and he was elected to its council in November 1864. He was a founder member of the X-club, a group that met monthly to debate the scientific issues of the day, untrammelled by religious dogmas; this club was to influence the organization and image of English science for the next twenty years. He was active in the formation of the London Mathematical Society in 1865, becoming its first vice-president and later (in 1872-4) its president. In 1866 he was admitted a fellow of the Royal Astronomical Society, and became general secretary of the British Association for the Advancement of Science, an onerous post which he held for four years. Meanwhile, he continued to travel widely throughout Europe, meeting mathematicians and attending meetings.

On 18 August 1865 Hirst was appointed professor of mathematical physics at University College, London, one of only seven physics professors in the country. Two years later he became professor of mathematics, replacing Augustus De Morgan who had resigned. However, his duties took up much time, and in 1870 he resigned his chair and became assistant registrar in the University of London in order to gain more time for his researches. One of his lasting contributions was to mathematics education. Long convinced that Euclid's *Elements* should be supplanted as the main geometry textbook in English schools, he helped to establish the Association for the Improvement of Geometrical Teaching (later, the Mathematical Association), and was its first president, for eight years.

In 1873 Hirst embarked on his final role when he became the first director of studies at the Royal Naval College in Greenwich. This position enabled him to stay in touch with the international mathematical community, entertaining such major figures as Felix Klein and Pafnuty Chebyshev. In 1878 he was elected to membership of the Cambridge Philosophical Society, and in 1883 the Royal Society awarded him its prestigious royal medal. He resigned his Greenwich post in 1883, due to ill health. As the 1880s continued, he increasingly withdrew from his various activities. In the winter of 1891-2 London was hit by one of the worst influenza epidemics of the century, and Hirst quickly succumbed. He died at his home, 7 Oxford and Cambridge Mansions, Marylebone, on 16 February 1892 and was buried in Highgate cemetery four days later.

Hirst's geometrical researches are largely forgotten today. Although his twenty papers were published in major journals, his work on such topics as equally attracting surfaces, the inversion of curves, and the correlation of planes, quickly went out of fashion as mathematics developed in other directions.

ROBIN J. WILSON

**Sources **

T. A. Hirst, journals, Royal Institution of Great Britain, London

W. H. Brock and R. M. MacLeod, *Natural knowledge in social context, the journals of Thomas Archer Hirst FRS* (1980) [booklet and microfiche]

H. J. Gardner and R. J. Wilson, 'Thomas Archer Hirst--mathematician Xtravagant', *American Mathematical Monthly,* 100 (1993), 435-41, 531-8, 619-25, 723-31, 827-34, 907-15

*DNB*

*The Times* (18 Feb 1892)

*Men and women of the time* (1891)

d. cert.

**Archives **

Royal Institution of Great Britain, London, journals | BL, letters from John Tyndall, Add. MS 63092

RAS, letters to RAS

UCL, corresp. relating to London Mathematical Society

**Likenesses **

Maull & Co., photograph, *c.1866,* UCL *[see illus.]*

photograph, *c.1866,* London Mathematical Society

photograph, *c.1866,* RS

portrait, Royal Naval College, Greenwich; repro. in *Journal of the London Mathematical Society* (1966)

**Wealth at death **

£14,640 15s. *5d.:* resworn probate, July 1892, *CGPLA Eng. & Wales*

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