The fifth of seven children, three of Mary's siblings died young. Another sister was born when Mary was 7 and a brother when she was ten.
Although her brothers received an education, Mary's parents saw no need to educate their daughters. Her mother taught her to read, but no one felt she needed to learn to write. About the age of ten, she was sent to Miss Primrose's boarding school for girls in Musselburg to learn the niceties of being a lady, but spent only one year there, neither happy nor learning. On her return she said she felt "like a wild animal escaped out of a cage."
After returning home, she began reading everything she could lay her hands on, but was continually criticized for this. Only one member of her family provided any encouragement at all. When her uncle in Jedburgh learned that Mary had been teaching herself Latin, he encouraged her and the two would read Latin before breakfast while Mary stayed in the Jedburgh home.
About the age of thirteen, Mary and her family began spending winters in Edinburgh. There, Mary continued to learn the skills of a lady, even as she continued her own self-study. She learned needlework and piano while studying painting with the artist Alexander Nasmyth. This proved to be a boon to her education when she overheard Nasmyth telling another student that not only did Euclid's Elements form the basis for understanding perspective in painting, but that it was also the basis for understanding astronomy and other sciences. This caused Mary to develop an interest in Euclid's Elements. With the help of her younger brother's tutor, she began her study of higher mathematics.
In 1804, at the age of 24, Mary was wed to Samuel Greig, who, like her father, was a naval officer. He was also distantly related, being the son of a nephew of her maternal grandmother. She moved to London and bore him three children, but was unhappy that he discouraged her continued education. Three years into the marriage, Samuel Greig died and Mary Geig returned to Scotland with her children.
By this time, Mary had developed a group of friends who all encouraged her studies in Mathematics and science. Included among these friends were John Playfair, then professor of natural philosophy at Edinburgh and William Wallace, professor of mathematics at the Royal Military College at Great Marlow. Mary's studies began to pay off as she received a silver medal for her solution to a mathematical problem set in the Mathematical Repository.
In 1812 she wed William Somerville who was the son of her aunt Martha and her husband Thomas Somerville in whose home she had been born. William was interested in science and supported of his wife's desire to study. They maintained a close circle of friends who were also interested in education and the sciences, including Playfair, Leslie, Sir William Scott, and the physicist David Brewster.
1814 was a bad year for the family as Mary's oldest daughter from her marriage to Greig died at the age of nine and the only son of her marriage to Somerville died as a baby.
