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Grace Chisholm was educated by a governess at home, then at the age of 17 she passed the Cambridge Senior Examination. Following her family's wishes Grace become involved in social work among poor people in London. She was stopped by her family from studying medicine, the topic of her choice, then decided to enter Girton College, Cambridge in 1889. At Girton her tutor was William Young. She obtained a first class degree in mathematics in 1892.
The place to go to study mathematics at that time was Göttingen and that is where Grace Chisholm decided to continue her studies. In  a letter she wrote from Göttingen is quoted. In this letter she described Klein's attitude towards women:-
Professor Klein's attitude is this, he will not countenance the admission of any woman who has not already done good work, and can bring proof of the same in the form of degrees or their equivalent ... and further he will not take any further steps till he has assured himself by a personal interview of the solidity of her claims. Professor Klein's view is moderate. There are members of the Faculty here who are more eagerly in favour of the admission of women and others who disapprove altogether.Under Klein's supervision she completed a doctorate in 1895. Her thesis was on The algebraic groups of spherical trigonometry and Klein discusses the results in one of his books.
In the following year she married William Young. They settled in Switzerland where they created a true mathematical partnership in which both contributed. This is described in detail in . To quote from one letter of William Young to his wife (see  for more details):-
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. ... At present you can't undertake a public career. You have your children. I can and do.Together William Young and Grace wrote 220 mathematical articles and several books. One of the books The Theory of Sets of Points (1906) was published under their joint names and when Grace Young sent the book to Cantor he replied:-
It is a pleasure for me to see with what diligence, skill and success you have worked and I wish you, in your further researches in this field as well, the finest results, which, with such depth and acuteness of mind on both your parts, you cannot fail to attain.It is almost impossible to tell exactly how much of the work in these papers was due to Grace Young. As William Young wrote himself, in the same letter part of which has already been quoted above:-
I am very happy that you are getting on with the ideas. I feel partly as if I were teaching you and setting you problems which I could not quite do myself...Between 1914 and 1916 she published work on the foundations of calculus under her own name that won the Gamble Prize from Girton College.
When World War II began to affect their lives in Switzerland, Grace Young brought two of her grandchildren to England in early in 1940. Although she had intended to return at once, it became impossible on the fall of France and she had to remain in England. Depressed at being separated, William died in 1942, Grace Young outliving him by two years.
References (5 books/articles)
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