She was educated at Girton College, Cambridge, England and continued her studies at Göttingen University in Germany, where in 1895 she received a doctorate.

[1] Her early writings were published under the name of her husband, William Henry Young, and they collaborated on mathematical work throughout their lives.

Her father was a senior civil servant, with the title Warden of the Standards in charge of the Weights and Measures Department.

At this time the college was only associated with the University of Cambridge with men and women graded on separate but related lists.

[3] Chisholm remained at Cambridge for an additional year to complete Part II of the Mathematical Tripos, in the hope of being able to follow an academic career.

Again government approval had to be obtained to allow her to take the examination, which consisted of probing questions by several professors on sections such as geometry, differential equations, physics, astronomy, and the area of her dissertation, all in German.

They visited Turin in Italy to study modern geometry and under Klein's guidance they began to work in the new area of set theory.

In 1908 they moved to Geneva in Switzerland where she continued to be based while her husband held a series of academic posts in India and the UK.

In addition to her career as a pioneering woman in what was then a discipline with significant barriers to entry, she completed all the requirements for a medical degree except the internship.

[1] Of their six children, three continued on to study mathematics (including Laurence Chisholm Young and Cecilia Rosalind Tanner), one daughter (Janet) became a physician, and one son (Patrick) became a chemist and pursued a career in finance and business.

Their eldest son (Frank) was killed in World War I, when his plane was shot down in 1917,[7] and his death had a profound effect on his parents, reducing their mathematical creativity.

[3] One of Grace's fourteen grandchildren, Sylvia Wiegand (daughter of Laurence), is a mathematician at the University of Nebraska and is a past president of the Association for Women in Mathematics.