Three members of the eminent academic dynasty who held many chairs in St Andrews, Edinburgh and Oxford, the Gregories were pre-eminently mathematicians.
James Gregory (1638-1675), Scottish mathematician and astronomer, was born in the Manse of Drumoak, Aberdeenshire. His father, John Gregory (d. 1651), had studied at Marischal College, Aberdeen, then gone on to study theology at St Mary's College in the University of St Andrews before spending his life in the parish of Drumoak. His mother was Janet Anderson, whose brother Alexander was a pupil of mathematician Viete, edited his works and taught in Paris. James was the youngest of three sons and learned mathematics first from his mother who taught him geometry. He attended Grammar School and then proceeded to Marischal College, Aberdeen.
Gregory began to study optics and the construction of telescopes. Encouraged by his inventor brother David (1627-1720), he wrote a book entitled Optica Promota in which he describes the first practical reflecting telescope now called the Gregorian telescope. His novel idea was to use both mirrors and lenses in his telescope, a combination which he showed would work more effectively than a telescope which used only mirrors or used only lenses. In 1663 Gregory went to London where he secured the publication of his book and aimed to find someone who could construct a telescope to his design. The first Gregorian telescope - the type of instrument that would be used universally throughout the eighteenth century - was presented to the Royal Society in February 1674.
In 1664 Gregory went to Italy. He visited Flanders, Rome and Paris on his journey but spent most time at the University of Padua where he worked closely with Angeli and focussed on using infinite convergent series to find the areas of the circle and and hyperbola. Gregory published Vera circuli et hyperbolae quadratura (1667) and Geometriae pars universalis (1668) before returning to London from Italy in 1668. He entered into a dispute with Huygens over their research and, as a consequence, Gregory became much less keen to announce the methods by which he made his mathematical discoveries.
He was elected a fellow of the Royal Society in 1668 and presented various papers to the Society on topics including astronomy, gravitation and mechanics. He was first occupant of the Regius Chair of Mathematics in St Andrews where he arrived in late 1668. He was not attached to a College, as were the other professors, but was given the Upper Hall of the university library as his place of work. Gregory found that St Andrews was of classical outlook where the latest mathematical work was totally unknown. In 1669, Gregory married widow Mary Jamesone. They had two daughters and one son. While in St Andrews Gregory gave two public lecture each week which were not well received, but he carried out much important mathematical and astronomical work during his six years in the Regius chair. He kept in touch with current research by corresponding with John Collins. Gregory wrote notes of his own on the backs of the letters which are held in the St Andrews University library and provide a vivid record of how one of the foremost mathematicians of his day made his discoveries.
A pendulum clock, made by Joseph Knibb of London, was purchased by Gregory in 1673, the same year in which the university allowed Gregory to purchase instruments for an observatory, but told him he would have to make applications and organise collections for funds to build the observatory. Gregory left St Andrews to become the first Professor of mathematics in Edinburgh in 1674 but he died after just a year in post. His reluctance to publish his methods has meant that his remarkable contribution has gone largely unrecognised. He anticipated Isaac Newton in discovering both the interpolation formula and the general binomial theorem as early as 1670 and discovered or solved problems later defined by Brook Taylor, Cauchy and Riemann.
David Gregory (1661-1708), astronomer and mathematician, was a nephew of James Gregory, born in 1659 or 1661. He studied at Marischal College, Aberdeen between 1671 and 1675. David travelled prior to studying at Edinburgh University, graduating M.A. on 28 November 1683. A month prior to his graduation he was elected to the Chair of Mathematics at the University of Edinburgh. At Edinburgh David Gregory taught Newtonian theories. He was the first university teacher to teach the 'modern' theories at a time when even Cambridge was still teaching Greek natural philosophy. Gregory's lecture notes at Edinburgh were to form the basis of Maclaurin's Treatise of Practical Geometry which was published in 1745. Gregory himself published Exercitatio geometria de dimensione curvarum in 1684 while at Edinburgh in which, with the assistance of his uncle's work, he extended the method of quadratures by infinite series. Gregory also lectured at Edinburgh on mechanics and hydrostatics.
In 1691 he went to London where he was introduced to Newton and recommended to John Flamsteed (1646-1719), the first astronomer royal. With the combined influence of Newton and Flamsteed, Gregory was awarded the Savilian Chair of Astronomy at Oxford in 1691. In 1692 he took the degrees of M.A. and M.D. at Oxford, and he became a master commoner of Balliol College. Also in 1692, he was elected a fellow of the Royal Society. In 1699 he was appointed as mathematical tutor to William, Duke of Gloucester. The substance of his work delivered in Edinburgh, and published there in 1684, was contained in his Catoptricae et dioptricae sphaericae elementa (1695) and was adapted to undergraduates. In this work, Gregory gave the first hint of the achromatic telescope when he referred to the possibility of counteracting colour aberration in lenses by combining in them media of different densities. The work was reprinted in Edinburgh in 1713 and translated into English (from Latin) in 1715.
His principle work however was Astronomiae physicae et geometricae elementa (1702). This was the first text-book on gravitational principles and it remodelled astronomy in conformity with physical theory. His next work, in Greek and Latin, was Euclides (1703) which was an edition of all the writings attributed to Euclid. In 1704, Gregory was nominated to the committee charged by Prince George with the inspection and printing of the Greenwich observations, and in 1705 he was chosen as honorary fellow of the Royal College of Physicians of Edinburgh. Gregory died on 10 October 1708 at the Greyhound Inn at Maidenhead, Berkshire, while on his return to London from Bath after taking the cure there for consumption.
David Gregory (1712-1765) was grandson of James Gregory's brother David (c. 1625-c. 1720). He succeeded his father Charles (Regius Professor of Mathematics at the University of St Andrews, 1707-1739) as Regius Professor, a post he held until his death in 1765.