James Gregory (mathematician)

James Gregory FRS (November 1638 – October 1675) was a Scottish mathematician and astronomer. His surname is sometimes spelt as Gregorie, the original Scottish spelling. He described an early practical design for the reflecting telescope – the Gregorian telescope – and made advances in trigonometry, discovering infinite series representations for several trigonometric functions.

In his book Geometriae Pars Universalis (1668) Gregory gave both the first published statement and proof of the fundamental theorem of the calculus (stated from a geometric point of view, and only for a special class of the curves considered by later versions of the theorem), for which he was acknowledged by Isaac Barrow.^{[excessive citations]}

Gregory was born in 1638. His mother Janet was the daughter of Jean and David Anderson and his father was John Gregory, an Episcopalian Church of Scotland minister, James was youngest of their three children and he was born in the manse at Drumoak, Aberdeenshire, and was initially educated at home by his mother, Janet Anderson (~1600–1668). It was his mother who endowed Gregory with his appetite for geometry, her uncle – Alexander Anderson (1582–1619) – having been a pupil and editor of French mathematician Viète. After his father's death in 1651 his elder brother David took over responsibility for his education. He attended Aberdeen Grammar School, and then Marischal College from 1653–1657, graduating AM in 1657.

In 1663 he went to London, meeting John Collins and fellow Scot Robert Moray, one of the founders of the Royal Society. In 1664 he departed for the University of Padua, in the Venetian Republic, passing through Flanders, Paris and Rome on his way. At Padua he lived in the house of his countryman James Caddenhead, the professor of philosophy, and he was taught by Stefano Angeli. The geometrical treatises he published in Padua, Vera circuli et hyperbolæ quadratura (1667) and Geometriæ pars universalis (1668), testify to the deep influence the works of Angeli and other leading Italian mathematicians, such as Gabriele Manfredi, exerted on him.

Upon his return to London in 1668 he was elected a Fellow of the Royal Society, before travelling to St Andrews in late 1668 to take up his post as the first Regius Professor of Mathematics at the University of St Andrews, a position created for him by Charles II, probably upon the request of Robert Moray. There at the University of St Andrews, he laid the first meridian line across the floor of his lab in 1673, which was 200 years prior to the Greenwich Meridian being established, and thus "arguably making St Andrews the place where time began".

He was successively professor at the University of St Andrews and the University of Edinburgh.

He had married Mary, daughter of George Jameson, painter, and widow of John Burnet of Elrick, Aberdeen; their son James was Professor of Physics at King's College, Aberdeen. He was the grandfather of John Gregory (FRS 1756); uncle of David Gregorie (FRS 1692) and brother of David Gregory (1627–1720), a physician and inventor.

About a year after assuming the Chair of Mathematics at Edinburgh, James Gregory suffered a stroke while viewing the moons of Jupiter with his students. He died a few days later at the age of 36.