March 15, 1868 - March 29, 1944

Grace Chisholm Young was born on March 15, 1868, near London, England. She was the youngest of three surviving children. Her father was Warden of the Standards in the British government, in charge of the department of weights and measures. Her brother was sent to grammar school, a prestigious boarding school, and then earned a top scholarship to Oxford, but in the custom of the times in England, Grace and her sister were taught at home by their mother and a governess.

Her family encouraged her to become involved in social work among the London poor but Chisholm wanted to continue her studies. She passed the senior examination for entrance into Cambridge University at the age of 17, but it was not until Girton College at Cambridge offered her a scholarship four years later that she was allowed to go. Girton, opened in 1869, was the first school in England dedicated to educating women at the university level. Chisholm entered Girton in 1889 to study mathematics. One of her classmates and special friends was Isabel Maddison. At the end of their first year, when the Mays list came out, Maddison was top of the Second class with Grace next below her. That same year, also, Phillippa Fawcett became the first woman to score above the (male) Senior Wrangler on Part I of the Mathematical Tripos. Women could not earn formal degrees at Cambridge at that time, but in 1892 Chisholm passed her final examinations (Mathematics Tripos Part I) and scored the equivalent of a first-class degree. She also took (unofficially, on a challenge, with Isabel Maddison) the exam for the Final Honours School in mathematics at the University of Oxford on which she out-performed all the Oxford students. Mary Cartwright writes that she believed "they were the first women to sit for the Final Honours School of Mathematics, and that they did it to refute a suggestion from one of their coaches that it was more difficult for a woman to obtain a first at Oxford than at Cambridge." Chisholm then remained at Cambridge for an additional year to compete Part II of the Mathematical Tripos, "a most unusual thing for a woman to do in those days" according to Cartwright.

Chisholm wanted to continue in mathematics but women were not yet admitted to graduate schools in England so she went to Göttingen in Germany to study with Felix Klein. This was one of the major mathematical centers in the world. The decision to admit her had to be approved by the Berlin Ministry of Culture. Also admitted at the same time to study mathematics was Mary Frances Winston from the United States. During her first year Chisholm gave a lecture in Klein's seminar which Grattan-Guinness describes by quoting from one of her letters [10]:

The lecture came off yesterday, and if it is a success to interest one twelfth of one's audience I may be said to have achieved one. As to the other eleven I do not know what they thought about it, but May Winston says they were all quite wide awake, which is something that cannot be said for all the preceding lectures. I never felt the pulse of an audience so little, and I was much too nervous to have made any alterations if I had been more aware of how they were taking it. I noticed once that Mr. Woods was wrinkling his eyebrows over one of my figures, and trying to work out a result I had stated as clearly evident. If I had been speaking English I should have stopped and explained more fully, but I had not the nerve to do it then. You see I did not read a written paper, but I just spoke it extempore after two rehearsals, one in the school and one here. I got into one or two hopeless muddles with the German tongue, but I think I was mostly intelligible, and these people are so used to our limping speech that I was sure of sympathy in my attempt.It took a little over an hour to deliver and there were a good many interruptions, which is always a good sign. Once I had written some equations down and Professor Klein asked me to verify them as there seemed to be discrepancy. Now I did not feel equal to doing any brain work then and there, and for one moment I had a pang of despair; but Dr. Ritter got up and explained that I had rubbed out a minus sign by mistake and I blessed him; that showed he was attending.

Another time Professor Klein asked for an explanation of certain facts, a thing he is very fond of doing. I had been more frightened than anything of his questions, it is so difficult to think on an occasion like that, and although the same thing happens to nearly every one I always think it looks foolish not to be able to answer. The Gods willed on this occasion that my brain should work, and I gave the explanation to my own astonishment, and I fancy, to his too.

In 1895 Grace Chisholm earned her Ph.D., magna cum laude, at the age of 27 with a thesis entitled "Algebraisch-gruppentheoretische Untersuchungen zur sphärischen Trigonometrie" (Algebraic Groups of Spherical Trigonometry.) Again government approval had to be obtained to allow her to take the examination, which consisted of probing questions, in German, by several professors on conic sections, geometry, differential equations, physics, astronomy, and the area of her dissertation. She thus became the first woman to officially receive a Ph.D. in Germany. As Sylvia Wiegand writes in [4]

Although Sofia Kovalevskaia had been awarded a doctorate in mathematics in absentia from Göttingen in 1874 after submitting a thesis, the rules for doctoral degrees had become stricter, and Grace was required to take courses and pass a difficult examination showing broader knowledge as well as prepare a thesis in order to receive her degree.

The following year she married William Henry Young, who had been one of her tutors at Girton College. William Young was also a mathematician. They left England soon after their marriage to study mathematics in Europe. In 1898 the couple visited Klein in Göttingen and he encouraged them to do some research in set theory. This lead to work in, among many areas, the topology of the real line and plane, measure theory and integration, Fourier series, and the foundations of differential calculus. Bruckner and Thomson write that "The whole field of what was then called 'the theory of functions of a real variable' was reworked and rewritten in those first decades [of the 20th century]. The Youngs played a major role in that effort." Between them they wrote 214 mathematical articles and several books, including one on geometry and one on set theory. (They also had 6 children within the span of 9 years.) It is not clear how much of the mathematical collaboration was really Grace's work and how much was her husband's, but it is now generally agreed that William Young would probably have accomplished much less without the help of his wife, a fact he often acknowledged. Of the 214 publications listed in the bibliography by Grattan-Guinness, 13 were jointly authored and 18 have Grace as the sole author. In his review of a paper by Andrew Bruckner and Brian Thomson, however, Professor Frank Smithies writes that "the authors discuss some of the contributions of W. H. and G. C. Young to real variable theory. They point out that most of the papers attributed to W. H. Young alone were in fact joint work with Grace." In addition, Grace sometimes wrote up her husband's papers for publication, often filling in proofs and correcting mistakes. But she also produced a substantial amount of excellent work herself despite the fact that her husband was often away from the family for large parts of the year, leaving Grace to take care of the children and their home in Switzerland. She won the 1915 Gamble Prize at Cambridge (given by Girton College to distinguished alumnae) for an essay on the foundations of calculus [Summary]. The most famous result with which Grace Young is identified is the Denjoy-Young-Saks theorem [Summary].

In addition to her extensive work in mathematics, Young completed all the requirements for a medical degree except the internship, learned six languages, and taught each of her six children a musical instrument. She wrote one of the first books for children on reproduction. Called "Bimbo and the Frogs," the book was a very tasteful yet scientific explanation that did not talk down to children.

With the start of World War II, Grace Young left Switzerland by train for Paris. In 1940, with two of her grandchildren, she got the last plane out of Paris to England before the Germans captured the city. Her husband, however, could not get out. He died in 1942, and two years later Grace suffered a heart attack and died at the age of 76. The Fellows of Girton College had just recommended that she be awarded an honorary degree, but she died before it could be given to her.

Of her six children,

- the first son, Frank, an RAF pilot, was killed in World War I. He had received an engineering degree at age 18 before his death a year later;
- the oldest daughter, Cecily, took a doctorate in mathematics at Girton but was still not able to receive a formal degree from Cambridge (1929) since such degrees were not yet being granted to women. Despite this, she went on to become a tenured member of the University of London; Cecily Tanner also won the Gamble Prize in 1939.
- the second daughter, Janet, became a physician and the first female member of the Royal College of Surgeons;
- the third daughter, Helen Marion, completed her undergraduate studies in mathematics at the University of Lausanne. She did additional graduate work in other subjects at Bryn Mawr. She married a Frenchman, Jean Canu, an Associate Professor of French at Bryn Mawr from 1927 to 1935, and weathered the second World War in occupied France;
- the second son, Laurence, was also a mathematician, teaching at the University of Cape Town, South Africa, and later at the University of Wisconsin-Madison. He was also a chess grandmaster;
- the youngest son, Patrick, did his academic training in science and earned his D.Phil in chemistry at Oxford University, but pursued a career in public finance and diplomacy.

One of Grace Young's fifteen grandchildren, Sylvia Wiegand, the daughter of Laurence Young, is a mathematician at the University of Nebraska and a past president of the Association for Women in Mathematics.

- Wiegand, Sylvia. "Grace Chisholm Young," in
*Women of Mathematics: A Biobibliographic Sourcebook*, Grinstein and Campbell (Eds.), Greenwood Press, 1987. - Wiegand, Sylvia. "My Grandmother, Grace Chisholm Young," in
*Complexities: Women in Mathematics*, Bettye Anne Case and Anne Leggett, Editors, Princeton University Press (2005), 39-45. - Wiegand, Sylvia. "Grace Chisholm Young," Newsletter of the Association for Women in Mathematics, Vol 7, No. 3 (May-June 1977), 5-10.
- Wiegand, Sylvia. "Grace Chisholm Young and William Henry Young: A
Partnership of Itinerant British Mathematicians," in
*Creative Couples in the Sciences,*Helena M. Pycior, Nancy Slack, and Pnina Abir-Am, Editors, Rutgers University Press, 1996, 126-140. - Koch, Laura Coffin. "Grace Chisholm Young," in
*Notable Women in Mathematics: A Biographical Dictionary*, Charlene Morrow and Teri Perl, Editors, Greenwood Press (1998), 277-282. - Rothman, Patricia. "Grace Chisholm Young and the Division of Laurels," Notes and Records of the Royal Society of London, Vol. 50, No. 1 (Jan., 1996), 89-100.
- Bruckner, Andrew M. and Brian S. Thomson. "Real variable contributions of G. C. Young and W. H. Young," Expositiones Mathematicae, Vol. 19, no. 4 (2001), 337-358.
- Perl, Teri.
*Math Equals*, Addison-Wesley, 1978. - Cartwright, M.L. "Grace Chisholm Young," Journal of the London Mathematical Society 19(1944), 185-191. [Online version from LMS (requires subscription)]
- Grattan-Guinness, I. "A Mathematical Union: William Henry and Grace Chisholm Young," Annals of Science, Vol. 20, No. 2 (August 1972), 105-186.
- Email correspondence from Pierre Canu, April 2000.
- Email correspondence from Beatrice Nearey, April 2003.
- Archive information, Bryn Mawr College Library.
- MathSciNet [subscription required]
- Author Profile at zbMath
- Mathematics Genealogy Project
- Biography at the MacTutor History of Mathematics Archive

Photo Credit: The photos of Grace Chisholm Young are used with permission of Sylvia Wiegand