by I. Grattan-Guinness

© Oxford University Press 2004 All rights reserved

**Young [née Chisholm], Grace Emily** (1868-1944), mathematician, was born in London on 15 March 1868, the youngest of four children of Henry Williams Chisholm (1809-1901) and his wife, Anna Louisa Bell (1824-1900). He was warden of the standards and chief clerk to the exchequer; the measures of length in Trafalgar Square were placed under his direction. Grace's elder brother Hugh Chisholm (1866-1924) gained eminence as editor of the eleventh and twelfth editions of the *Encyclopaedia Britannica* and as city editor of *The Times.*

The family moved to Haslemere in 1874 upon the father's retirement. After education at home from governesses, Grace won a scholarship to Girton College, Cambridge, in 1889, and four years later passed the mathematical tripos examinations. She performed even better by gaining a first class in the final honours school examination at Oxford University, which she had been allowed to take. Disliking the British system of mathematics education, she enrolled in a newly launched programme of higher education for women conducted at Göttingen under Felix Klein, director of the mathematics faculty. Two years later she was the first to complete the programme, with a dissertation on spherical trigonometry analysed in Klein's way in terms of the group of geometrical transformations under which configurations remain unchanged. Her results have been applied to astronomy.

Grace returned home to look after her elderly parents, and once more met William Henry (Will) Young (1863-1942), who had briefly coached her at Cambridge. She at first declined his proposal of marriage but they were married on 11 June 1896. Their first child, Frank, nicknamed Bimbo, was born in 1897. Grace drew her husband into research-level mathematics, which they pursued for the rest of their lives in continental Europe. At first they spent a year in Italy, working in geometry, but finding the topic somewhat uncongenial they returned to Göttingen in 1899 to seek Klein's advice on research topics. Klein proposed set theory, which was beginning to receive great attention from mathematicians at that time, and the couple devoted their research career to aspects of this topic. They lived in Göttingen until 1908, when they moved to Switzerland, spending seven years at Geneva, and then living near Lausanne. They existed largely on income from Young's savings as a coach, and from his salary as lecturer or professor in universities in England and India. While at Göttingen and then Geneva, Grace trained to be a medical doctor but did not take the examinations.

Two sons and three daughters were born to them at Göttingen; the eldest daughter, Rosalind Cecilia Hildegard (1900-1992), better known by her married name, Rosalind Tanner, also achieved a notable career in mathematics and its history. Bimbo's education inspired publications from his parents. They produced *A First Book of Geometry* in 1905, based on folding paper; it was translated into several languages. Then Grace wrote two little books explaining science for children: *Bimbo* (1906), and *Bimbo and the Frogs* (1907). Frank's death in action in February 1917 as an airman in the First World War was a devastating blow.

The Youngs' research work produced about 200 papers and two books. One joint book, *The Theory of Sets of Points* (1906), was the first comprehensive introduction to several aspects of set theory in English. Their attention centred on point set topology and its application to integration, and to properties of Fourier series and sets of orthogonal functions. It is clear from the couple's correspondence that, while his research-trained wife drew the coach into creative work, he had the stronger talent of the two. Most papers appeared under his name alone, and he wrote some of them entirely; however, she wrote up the majority and checked the details, and handled the proofs. As he put it in one of his letters:

I feel partly as if I were teaching you, and setting you problems which I could not quite do myself but could enable you to. [...] The fact is that our papers ought to be published under our joint names, but if this were done neither of us get the benefit of it. No. Mine the laurels now and the knowledge. Yours the knowledge only. Everything under my name now, and later when the loaves and fishes are no more procurable in that way, everything or much under your name. (Grattan-Guinness, 'Mathematical union', 141)

From the mid-1910s Grace produced some research papers of her own, mainly applying set theory to the differential calculus. An essay on 'infinite derivatives' won a Gamble prize at Cambridge University in 1915, stimulating some later research. Later she wrote some speculative papers on aspects of Greek mathematics.
Partly because of Grace's declining health, the Youngs' research work stopped rather abruptly in the mid-1920s, but during the early 1930s she wrote a long unpublished novel entitled 'The Crown of England', on Elizabethan society. During this period she also helped Young with secretarial duties in his post as president of the International Mathematical Union.

As Paris was falling in 1940 Grace managed, at great risk, to take back to England two children of her daughter Janet, but Young refused to accompany her, fearing punishment for his many praises of German academic achievements. He died in Switzerland in 1942; she died at Janet's house, 98 Park Road, Croydon, Surrey, on 29 March 1944, aged seventy-six.

I. GRATTAN-GUINNESS

**Sources **

I. Grattan-Guinness, 'A mathematical union', *Annals of Science,* 29 (1972), 105-86

G. H. Hardy, *Obits. FRS,* 4 (1942-4), 307-23 [obit. of William Henry Young]

I. Grattan-Guinness, 'University mathematics at the turn of the century', *Annals of Science,* 28 (1972), 369-84

I. Grattan-Guinness, 'Mathematical bibliography for W. H. and G. C. Young', *Historia Mathematica,* 2 (1975), 43-58

M. L. Cartwright, 'Grace Chisholm Young', *Journal of the London Mathematical Society,* 19 (1944), 185-92

**Archives **

U. Lpool L., corresp. and papers

**Likenesses **

photograph, repro. in Grattan-Guinness, 'Mathematical union'

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