Young, Grace Chisholm (1868–1944)

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Young, Grace Chisholm (1868–1944)

English analytical mathematician and algebraic geometer. Name variations: Grace Chisholm. Born Grace Chisholm on March 15, 1868, in Haslemere, England; died in 1944 in England; daughter of Anna Louisa (Bell) Chisholm and Henry William Chisholm; educated by tutors; graduated from Cambridge University, 1892; graduated from the University of Göttingen, 1895; married William Henry Young, in June 1896, in London, England (died 1942); children: Francis (b. 1897), Cecily (b. 1900), Janet (b. 1901), Helen (b. 1903), Lawrence (b. 1904), Patrick (b. 1908).

Passed Cambridge University senior examination (1885); denied entry to Cambridge (1885); won scholarship to Girton College, Cambridge (April 1889); met William Henry Young (1889); graduated from University of Göttingen (1895), first female holder of a formal Ph.D. in Germany's history; returned to England (1895); moved to Switzerland (1897); with husband, published The First Book of Geometry (1905); with husband, published The Theory of Sets of Points (1906); published a paper on continuous non-differentiable functions (1915); awarded the Gamble Prize by Cambridge (1915); published a paper on derivates of a function (1916); delineation of the Denjoy-Saks-Young Theorem (1916); returned to England (1940).

Selected writings:

"Algebraisch-gruppentheoretische Untersuchungen zur sphärischen Trigonometrie," University of Göttingen: unpublished Ph.D. thesis, 1895; (with William Henry Young) The First Book of Geometry (London: Dent, 1905); (with William Henry Young) The Theory of Sets of Points (Cambridge: Cambridge University, 1906); "On Infinite Derivates," in Quarterly Journal of Pure and Applied Mathematics (privately published, 1915); "On the Derivates of a Function," in Proceedings of the London Mathematical Society (London: Hodgson and Son, 1916); "On the Solution Pair of Simultaneous Diophantine Equations Connected with the Nuptial Number of Plato," in Proceedings of the London Mathematical Society (London: Hodgson and Son, 1924).

In 1895, Grace Chisholm Young passed a stringent oral examination to become the first female recipient of a formal Ph.D. in Germany's history. The story of Young's struggle to secure an education is the story of many talented women of the 19th century who were excluded from and discriminated against by the educational system. At the time of Grace Chisholm's birth, higher education remained a male privilege. Women's education was designed to foster minimal literacy levels, as well as social and domestic skills.

Grace Chisholm Young was born in 1868, in Haslemere, England. Like the renowned scientists Ada Byron Lovelace and Mary Fairfax Somerville , she studied at home in her early years. Her mother Anna Bell Chisholm taught her music and mathematics. Her father Henry William Chisholm, however, did not take part in the formal education of his daughter. As Warden of the Standards, he was responsible for supervision of the British Department of Weights and Measures. Wrote Young:

Papa had his office at the Old Palace Yard, in the corner between the Houses of Parliament and Westminster Abbey. Baby [her nickname] loved the office and Mr. Chaney the chief clerk, and she always went there to see the Queen arrive in her grand carriage with her piebald horses and her gorgeous footmen. You saw the horses and the footmen and the coach but you hardly saw the dingy old Queen at all.

After 54 years of the public service, Henry Chisholm retired when Grace was still a girl. The social prominence of the Chisholm family was underlined by mementoes found in their home. Recalled Young:

She looked every day at the ugly but gorgeous Sèvre vase in the corner of the drawing-room with its golden inscription from the grateful republic of France, and she danced with delight round the beautiful silver punch bowl with its silver lions … a present from the Czar of all the Russians.

At home, Young was often in the company of her father. The pair spent hours in the carpentry shop, working on various projects. Henry doted on his youngest child, and Young remembered a visit which she and her father made to the Royal Mint in London:

The Master of the Mint took the little girl all round, and she always remembers watching the automatic balance making up its mind as to whether a threepenny bit was right, or too light, or too heavy, and when it was certain, tipping it into the appropriate receptacle. He also showed her a row of big black books, and told her they called them "Chisholms" and that they were in constant use for reference at the mint.

As a child, Young often suffered from nightmares and headaches. In her early teens, however, these afflictions seemed to have subsided. When her mother decided it was time Grace receive a formal education, a tutor was hired. Thus, for the first time in her life Young began prescribed studies.

The quality of instruction at home was such that Young passed the Cambridge University senior examination at the age of 17. Female students were still a novelty in the English university system, however, and Young was denied admission. Instead, the family envisioned a philanthropic career for their daughter, a suitable pastime for young women until the age of marriage. Grace, however, insisted on pursuing her studies. Her first choice was medicine, but her mother forbade it. With the support of her father, however, Young applied to Cambridge University. In April 1889, she won a scholarship to Girton College, an institution once patronized by Mary Fairfax Somerville. Girton College was the only institution of higher education for women in England. Formal degrees, however, were not available to graduates.

It was at Girton that Young first met her future husband, William Henry Young. If initial impressions are a forecast of the future, their romance hardly seemed fated. Young recalled the first time she set eyes on William, staring down from a friend's window.

She heard faintly the scrunch of the gravel and turned her head quickly to look. What she saw however was entirely unexpected. This dreaded Mr. Young, this great mathematical gun, was a boy, hardly older than herself.

William Young had a fearsome reputation. He was a meticulous tutor who demanded the utmost of his students, and Grace determined to avoid him. As fate would have it, however, her own tutor was soon absent, and William replaced him. No indication of a budding romance emerged at this time.

Though contemporary Cambridge was reputed to be at the forefront of British mathematics, Young did not find it so. Instead, an air of conservatism permeated the institution, suffocating new ideas. Young blamed Arthur Cayley, the senior mathematician:

The atmosphere around him was stifling to the young mathematician. Cayley unconscious himself of the effect he was having on his entourage sat, like the figure of Buddha on its pedestal, dead weight on the mathematical school of Cambridge.

She sought permission to attend one of Professor Cayley's lectures. Though Girton College granted her request, she still had to secure the personal consent of Cayley. She and a friend approached Cayley as he left home to deliver a lecture. He graciously asked them to accompany him, wrote Young:

[We] darted after him. It was a most amusing race. [We] were too afraid of losing sight of the swift moving professor to look at one another, or laugh. The flapping black gown sped ahead, across Trumpington Street, round a corner and, as [we] hurried after, [we] beheld the trail of a gown whisking up a flight of stairs in a large building on the right. Up the stairs [we] flew and passed through an open door into a small lecture room. Professor Cayley, having already divested himself of his cap, was fumbling about the blackboard with chalk and sponge. At the long table Mr. Berry was seated with another man in academicals, and the mathematical dons of Girton and Newnham were present in their everyday attire with hats.

In 1892, Young passed the Cambridge Tripos with the equivalent of a first. On a dare, she also wrote the Oxford University examination, and received the highest score of any student that year, graduating with first class honors. Graduate degrees were not offered to women, however, and she was unable to continue her academic career in Britain. Young decided to study abroad.

The University of Göttingen was the finest mathematical institution in Europe. Luminaries such as Carl Friedrich Gauss had spent their careers at Göttingen, and had elevated the university to international fame. The renowned mathematicians David Hilbert and Felix Klein also taught at Göttingen. Klein, widely known for his innovative research, is still remembered for the Klein bottle, a four-dimensional figure with no interior surfaces. Professor Klein became Young's academic supervisor, friend, and supporter. In a letter to a friend, Young described Klein's attitude toward women seeking higher education:

[H]e will not countenance the admission of any woman who had not already done good work, and cannot bring him proof of the same in the form of degrees or their equivalent, or letters from professors of standing and further he will not take any steps till he has assured himself by a personal interview of the solidity of her claim. Prof. Klein's view is moderate. There are members of the Faculty here who are eagerly in favour of the admission of women and others who disapprove altogether.

Certain steps had to be taken, in the opinion of university officials, to accommodate their female student. They were determined to shelter her from the attention of male students. If she arrived early for a lecture, she was forced to wait in Klein's office "to avoid the students who loaf and lark in the corridors for a quarter hour after the nominal hour for the lecture to begin," wrote Young. "Klein, instead of beginning with 'Gentlemen!' began 'Listeners!' with a quaint smile: he forgot once or twice and dropped into 'Gentlemen' again, but afterwards he corrected himself with another smile." The research which Grace Chisholm Young undertook at Göttingen centered on spherical triangles and their relationship to algebraic groups. Much of her original work was later incorporated into Klein's book Elementary Mathematics from an Advanced Standpoint.

The question of whether she would receive a formal Ph.D. instead of an honorary one, as had Sophia Kovalevskaya , remained open to debate. Felix Klein supported her. He argued that the right to grant a doctorate was the sole privilege of the Faculty of Mathematics, and that the university's charter did not specify the gender of doctoral recipients. At age 27, Grace Chisholm Young became the first woman in the history of Germany to receive a formal doctorate in any field. Graduating magna cum laude, she recalled that after her oral examination she "used the occasion to execute a war dance of triumph. Then the professors came congratulating and beaming."

Upon her return to England, Young sent a copy of her dissertation to her former tutor. Impressed, William Young suggested joint authorship of a work on astronomy. What began as professional collaboration soon blossomed into romance. They married in London in June 1896 and spent their first year at Cambridge, where William was teaching and where their first child was born. Young undertook independent research, since academic positions were not open to women.

In the opinion of the Youngs, the conservative environment of Cambridge was far from conducive to learning. Too much attention was paid to academic performance and too little emphasis was placed on original research. It was also becoming increasingly apparent that William could not secure a permanent position at the university. Therefore, in 1897, the couple relocated to Switzerland, where they hoped prospects for William's career would be brighter.

From their base in Switzerland, the family followed William as he filled temporary appointments and sought a tenured position. Even with a family to care for, Young still found time to continue her research. The Youngs' collaboration was long and fruitful. Grace deferred to William on the question of authorship, largely due to career considerations. William wrote to her:

The fact is that our papers ought to be published under our joint names, but if this is done neither of us get the benefit of it. 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.

At times during their long partnership, Young acted as researcher and scribe, while at other junctures, William performed the task. In either case, William Young would have accomplished considerably less without his wife's assistance.

Grace Chisholm Young was involved in every aspect of her children's education. Her dissatisfaction with available texts lead her to write Bimbo, a book designed to teach her son (nicknamed Bimbo) biology. In 1905, Young and her husband completed The First Book of Geometry, an innovative children's work on elementary geometry. Again in collaboration, they published The Theory of Sets of Points in 1906. The book was the first of its kind. It pointed out the mistakes which could be avoided in the fields of projective geometry, variable calculus, astronomy, and differential equations when cluster sets and prime sets were employed. Prior to its publication, set point theory had been avoided by mathematicians. The work, however, changed the minds of many.

The brilliance of Grace Chisholm Young as an analytical mathematician is underlined by the independent group of papers which she published between 1914 and 1916. In 1915, her work on continuous non-differential function secured her the Gamble Prize from Cambridge University. Another paper, "On the Derivates of a Function," was published in 1916 and delineated what has since become known as the Denjoy-Saks-Young Theorem. This theorem explained the three possible dispositions of the function f(x) and proved its measurability.

The Youngs' oldest son Frank blossomed into a promising scientist. Tragedy struck, however, when he was killed on the Western Front during World War I. Janet Young became a physician, as her mother herself had intended to do. Another daughter, Cecily Young , joined Cambridge University as a mathematician, fulfilling another of her mother's ambitions.

World War II caused separation for the Young family. William, long sympathetic to Germany, feared a return to England. Thus, Young returned alone. She never saw her husband again. In the summer of 1942, William Young died suddenly at the age of 75. He had never secured a tenured academic appointment. In 1944, Grace suffered a heart attack and died. At the time, Girton College was considering the award of an honorary fellowship.

The interests of Grace Chisholm Young were many and varied. Included among them were medicine, languages, and music. Indeed, Young completed all the requirements for a medical doctorate, save the internship. Thus her medical ministration were limited to the family. She spoke six languages and was an ardent and accomplished musician.

The combined output of Grace Chisholm Young and her husband resulted in the publication of roughly 220 articles and several books. They were an admirable and productive scientific team, and it is difficult to determine who contributed more to the partnership. Young independently published over a dozen mathematical treatises.

In Through the Looking Glass, the mathematician and writer Lewis Carroll wrote:" Ittakes all the running you can do to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!" Carroll's metaphor is apt when applied to women in the sciences. Women such as Young not only had to over come the normal hurdles of scientific research, but the barriers of sexism as well. The commonly held belief was that science was antithetical to the ideal and the role of women. Even William Young, a liberal by the standards of the age, wrote to his wife that "at present you can't undertake a public career. You have your children."

William Young's statement illustrates one of the many obstacles faced by women of the period. Grace Chisholm Young enjoyed the challenges of motherhood. However, she wished for more. It is difficult not to speculate how Young would have fared in a career of her own, free of the constraints of the day and of the society which produced her. But one fact is clear. She would have accomplished far more than many of her male colleagues, if she'd had the opportunity.


Cartwright, M.L. "Grace Chisholm Young," in Journal of the London Mathematical Society. London: C.F. Hodgson and Son, 1944.

Collingwood, E.F., and A.J. Lohwater. The Theory of Cluster Sets. Cambridge: Cambridge University Press, 1966.

Grinstein, Louise S., and Paul J. Campbell, eds. Women in Mathematics. NY: Greenwood Press, 1987.

Herzenberg, Caroline L. Women Scientists from Antiquity to the Present. West Cornwall, CT: Locust Hill, 1986.

Klein, Felix. Elementary Mathematics from an Advanced Standpoint. NY: Dover, 1945.

Rebière, Alphonse. Les Femmes dans la Science. Paris: Nony, 1897.

suggested reading:

Grattan-Guinness, Ivor. "A Mathematical Union: William Henry and Grace Chisholm Young," in Annals of Science. London: Taylor and Francis, 1972.

Hugh A. Stewart , M.A., Guelph, Ontario, Canada.