James Gregory published papers on a number of mathematical and scientific subjects, and a look at his unpublished papers suggests an even more wide-ranging talent. Among his most notable contributions were his laying of the groundwork for the development of calculus, as well as his experiments in optics, which greatly influenced the later work of Isaac Newton (1642-1727). Yet Gregory had the misfortune to be caught up in political struggles that pitted his new ideas against a stodgy and powerful academic establishment, and this greatly limited the influence and perhaps even the length of his career.
Gregory was born in Drumoak, Scotland, the son of John, a minister, and Janet Anderson Gregory. Because her son was sickly, Janet Gregory proceeded to teach him at home, including in the curriculum subjects—most notably, geometry—barely known to most men at the time, let alone most women. From 1651 to 1662, Gregory studied in Aberdeen, first at grammar school, then at the city's Marischal College. He then traveled to London, where he published his Optica promota (1663). The latter suggested that telescopes should use concave mirrors, an idea upon which Newton later drew without giving Gregory credit.
Frustrated in his efforts to secure a position in London, Gregory in 1664 travelled to Italy, where he spent four years in study and research. His Vera circuli et hyperbolae quadratura (1667) discussed the means of finding the area for a circle or a hyperbola, and Geometriae pars universalis the following year examined convergent and divergent series. The latter work also contained Gregory's foundational ideas for what became calculus.
By 1668, Gregory was back in London, where he won election to the Royal Society and an appointment as chairman of mathematics at St. Andrew's College in Scotland. It seemed that at 30, he had found lasting career success, but this was not to be: at St. Andrew's, Gregory was confronted with an extremely conservative college governing board, who greeted all his efforts to update the curriculum with hostility.
He was not the only one dissatisfied with the current state of academic affairs: in an incident more like something from the twentieth than the seventeenth century, a group of students revolted against the university establishment, demanding change. Gregory was away in London at the time, hoping to secure support for his plan to establish the first public observatory in Britain at St. Andrew's; nonetheless, the administration found him a convenient scapegoat for the uprising, and punished him by withholding his salary.
When Edinburgh University offered him a position as chairman of its mathematics department, it seemed that once again Gregory's fortunes had taken a turn for the better. But within a year he was dead at age 37, having suffered a massive stroke. His papers lay dormant for many years, and only began receiving attention after some of them were published in 1939. Based on the many subjects covered in his unpublished writings, it seems clear that if Gregory had been allowed greater intellectual freedom, he might well have emerged as one of the preeminent mathematical thinkers of his time. Ironically, St. Andrew's—now St. Andrew's University—today operates one of the World Wide Web's best sites on the history of mathematics (http://wwwgroups.dcs.st-andrews.ac.uk/%7Ehistory).