Anne was born December 14, 1630, a week after her father, Sir Heneage Finch, who was speaker of the House of Commons, died. Having learned Latin, Greek, and Hebrew at home, she began a correspondence with Henry More (1614–1687), who had been her brother’s tutor at Christ College. More held her in very high intellectual esteem, and their correspondence continued after she married Edward Conway, at the age of 20. More wrote of her that he had “scarce ever met with any Person, Man or Woman, of better Natural parts than Lady Conway.”

One of her motivations for studying philosophy and possibly converting to Quakerism was her need to reconcile the existence of a good, all-powerful God with pain and suffering in the world. Anne herself was afflicted with extraordinarily severe headaches all her life. At one point, she had her jugular arteries “bled” in search of relief.