James Gregory (1638-1675)   Historical Sketch

One seldom (maybe too seldom) hears of mathematicians who got their start in the subject from their mothers, but that is exactly the case with James Gregory, who was born in 1638 into a religious family---his father was a pastor---in a parish near Aberdeen, Scotland. But it was likely through his mother's influence that James Gregory became a mathematician. Or possibly more accurately through the influence of his mother's brother, but James was taught geometry by his mother and one of his two older brothers. James had no difficulty with Euclid's Elements.

After studying at Marischal College in Aberdeen, Scotland, James became very involved with telescopes, even to the point of writing a mathematically-oriented book (definitions, postulates, etc.) about reflecting telescopes, even though one had yet to be constructed. The book was later published

Visiting the University of Padua in 1664, he used infinite series to find areas or regions bounded by circles and hyperbolas. It was here that he was introduced to differentiation and integration, and he produced two publications on such, one in 1667 and one in 1668. This latter has been described as the first textbook on calculus.

In the middle of 1668, Gregory was elected a fellow of the Royal Society, and he presented papers to the Society on various topics such as astronomy, mechanics, etc. The Regius Chair of Mathematics was created for James Gregory at St. Andrews University, a position he occupied for six years. In 1674, he left for the University of Edinburgh, England, where he was the first to hold their Chair of Mathematics. But one year later, while showing his students the moons of Jupiter, he had a stroke and became blind, then died a few days later.

Much in calculus is actually owed to Gregory, though many things he discovered are not attributed to him. Here are just three of many examples: He discovered Taylor series some 40 years before Taylor did. He discovered Cauchy's test before Cauchy did. He defined the Riemann integral before Riemann did.