by J. C. Burkill, rev. I. Grattan-Guinness

© Oxford University Press 2004 All rights reserved

**Young, William Henry** (1863-1942), mathematician, was born in London on 20 October 1863, the eldest son of Henry Young, a grocer and a member of the Turners' and the Fishmongers' companies, and his wife, Hephzibah, daughter of John Jeal. He attended the City of London School and went up in 1881 as a scholar to Peterhouse, Cambridge. He took his degree as fourth wrangler in 1885, his friends having expected him to be higher in the list. In later years he related that he would not restrict the width of his interests (intellectual and athletic) by the intensive preparation necessary to become senior wrangler. Instead of sending in an essay for a Smith's prize as most young mathematicians did, he competed for and won a prize for theology.

Young was a fellow of Peterhouse from 1886 to 1892 but he held no permanent office in either the college or the university. He established himself as a very successful tripos coach and taught or examined in some public schools for a few years. On 11 June 1896 he married Grace Emily (1868-1944), daughter of Henry Williams Chisholm, warden of the standards; she was known thereafter as Grace Chisholm Young. They had three sons and three daughters, two of whom, Rosalind Cecilia Tanner and Laurence Chisholm Young, continued their parents' work in pure mathematics and received honorary degrees.

In 1897 Christian Felix Klein, under whom Grace had studied at Göttingen, travelled to Cambridge to receive an honorary degree and his visit set the seal on a resolution which he had urged at the Youngs' wedding, for them to acquire a wider outlook on mathematics. The Youngs moved to Göttingen for some months. They then lived in Italy with their first child for more than a year, and Young wrote his first papers, on multi-dimensional geometry; they developed the insights made in the book *Flatland* (1882) by Edwin Abbott, his old schoolteacher. After meeting Klein in Turin, the family returned in September 1899 to Göttingen, where they made their home until 1908. They then moved to Geneva, and from 1915 their permanent home was in or near Lausanne. Young mastered many languages, and he twice travelled round the world.

While the family lived on various investments Young took posts for part of the academic years: some teaching and coaching at Cambridge; special lecturer at the University of Liverpool from 1906 to 1913; Hardinge professor of mathematics at the University of Calcutta from 1913 to 1919; and finally professor at the University College of Wales at Aberystwyth from 1919 to 1923. For Calcutta he wrote, but did not finish, a long comparative report on university mathematics education in many countries. He did hardly any research until he was in his late thirties, but between 1900 and 1924 his activity was intense and he wrote three books and more than 200 papers. His wife collaborated officially in two of the books and a number of the papers, prepared many others for publication, and checked proofs, while continuing her own research. As joint researchers they constituted the first significant husband-and-wife team in mathematics, and they operated at the top level for a quarter of a century. One curious feature is that after Grace drew him into research from the coaching treadmill Young then displayed the stronger creative gift.

Towards the close of the nineteenth century it was broadly true that the processes of mathematical analysis could be carried out provided that continuous functions only were encountered: artificial restrictions had to be made to handle discontinuities. The time was ripe for new ideas to transform the subject, and Georg Cantor's point set topology provided the techniques needed. A group in Paris round Emile Borel and Jacques Hadamard took this as a speciality, and Henri Lebesgue made a spectacular contribution in 1902 with a definition of the integral which was more general than those developed hitherto.

Following Klein's advice the Youngs had transferred to this topic in 1900 after the foray in geometry, and in 1904 Young found definitions of measure and integration different in form from Lebesgue's, but equivalent in essentials. The anticipation by two years was a blow but Young recognized it magnanimously--'the Lebesgue integral' is his own phrase--and set himself wholeheartedly to develop the theory of integration. He made several contributions, notably his treatment of the Stieltjes integral and his method of monotone sequences. The Youngs' book *The Theory of Sets of Points* (1906) was the first textbook in English on the subject and is recognized as a classic; an extended posthumous edition appeared in 1972.

There are two other fields in which Young's powers are shown at their highest. In the first of these, the theory of Fourier series and other orthogonal series, he proved theorems of striking simplicity and beauty. Moreover, he initiated many lines of thought which were worked out more fully by younger men, notably G. H. Hardy and J. E. Littlewood. The second field--and therein lay what was probably his most fundamental work--was the differential calculus of functions of more than one variable. This is well expounded in his Cambridge tract (1910), but perhaps the best tribute to it is that the Belgian analyst Charles de la Vallée Poussin rewrote part of his *Cours d'analyse infinitésimale* in 1912 in accordance with Young's treatment.

The immediate and abiding impression which Young gave was one of restless vitality; it was shown in his gait, his gestures, and his words. His appearance was striking: in early married life he grew a beard, red in contrast with his dark hair, and he wore it very long in later years. Many stories were current about him, all turning on his mental and physical energy. Young did not meet the recognition he deserved, due in part to his late start, and in part to a certain conservative hostility to the modern theory of real functions--a theory which few Englishmen in the early years of the twentieth century understood. Even when his profundity and originality were better appreciated, he was passed over in elections to chairs in favour of men who might be expected to be less exacting colleagues.

Young gained the ScD at Cambridge in 1903, was an honorary doctor of the universities of Calcutta, Geneva, and Strasbourg, an honorary fellow of Peterhouse (1939), fellow (1907) and Sylvester medallist (1928) of the Royal Society, De Morgan medallist (1917) and president (1922-4) of the London Mathematical Society, and president of the International Union of Mathematicians (1929-36). In this latter post he tried hard to raise the international community spirit among mathematicians, to build upon the reconciliation with Germans at the International Congress at Bologna in 1928, but he met with much apathy.

The fall of France in 1940 found Young at Lausanne, and he remained in Switzerland, unhappy and restive, until his sudden death at Château Corcelles, Chavornay, Canton de Vaud, on 7 July 1942.

J. C. BURKILL, *rev.* 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

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

G. H. Hardy, 'William Henry Young', *Journal of the London Mathematical Society,* 17 (1942), 218-37

*Nature,* 150 (1942), 227-8

*G. E. Young and W. H. Young, selected papers,* ed. S. D. Chatterji and H. Wetelscheid (Lausanne, 2000)

personal knowledge (1959)

private information (1959)

private information (2004)

**Archives **

U. Lpool, corresp. and papers | CUL, corresp. with Lord Hardinge, memo relating to university education in Calcutta

**Likenesses **

W. Stoneman, photograph, 1920, NPG *[see illus.]*

W. Stoneman, photograph, 1933, NPG

photograph, RS

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

**Wealth at death **

nil: probate, 2 July 1943, *CGPLA Eng. & Wales*

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