Gregory | James | 1638-1675 | professor of mathematics, St Andrews and Edinburgh

Biographical Information

Occupation, Sphere of Activity

James Gregorie (he favoured this Scottish spelling over 'Gregory') was born in Drumoak, near Aberdeen, Scotland, in November 1638. His father having died young, he was sent by his older brother to Aberdeen to attend grammar school and then Marischal College. Their mother had taught her sons to love geometry, and everyone hoped that James in particular would developed his clear talent in mathematics, and also his growing interests in optics and astronomy.

The young graduate established a grown-up reputation in London in 1663, with a digest of what he had learned thus far, the Optica Promota. It was unremarkable except for some very original thoughts on a compact reflecting telescope. Suddenly he had admirers in the scientific establishment. They included John Collins, accountant and science gossip, Robert Hooke, the Oxford physicist who eventually built the telescope, and Sir Robert Moray, Scots polymath and founding member of the Royal Society, who introduced him to as many influential men as he could. The telescope design also attracted the attention of a young man in Cambridge, one Isaac Newton, who was at work on a similar project of his own; Gregorie carried on much friendly correspondence with him later.

He bolstered his reputation in1664 by moving to Padua for a few years, for study under Stefano degli Angeli, pupil of Evangelista Torricelli (1608-1647). There he brought out two works of proto-calculus, the Vera circuli et hyperbolae quadratura and the Geometriae pars universalis. These, breathlessly reviewed by Collins, secured his admission to the Royal Society upon his return. He updated his colleagues, who were eager to hear, on continental science, and he entered the professional lists on his own, with an Exercitationes geometricae. These were meant as a sortie against Christian Huygens and Nicholas Mercator.

By 1669 his prestige was great enough that Sir Robert could help find him a job. He arranged an appointment to the new chair of mathematics at St Andrews. Gregorie went, married a local widow, and settled into teaching basic maths and science. He found the post disappointingly provincial. Through Collins he kept corresponding with the scientific establishment, which continued to hold him in high esteem. Even Huygens, he learned, his erstwhile enemy, tried for a while to persuade Louis XIV to invite him to Paris on a stipend from the Académie des Sciences.

Indeed St Andrews was comparitively inward-looking. Not only could Gregorie not evangelize for higher mathematics, he was hindered in his plans for a formal astronomy programme, complete with an observatory. He had been known to go door-to-door to raise funds for this. However, in 1672, in exchange for contributing a little essay to a colleague's scurrilous book against a Glasgow rival, (the Great and New Art of Weighing Vanity), he was given the University's commission to proceed at last. Its grateful author, regent William Sanders, wrested it from a stoutly resistant faculty. Gregorie left for London in raptures in 1673, meaning to caucus with astronomer John Flamsteed, to buy equipment, and to meet Newton if he could.

He had the misfortune to return to St Andrews after a student uprising. Young scholars had rebelled, sure enough, over the issue of antiquated curriculum. Regents resentful of Gregorie's established modishness now withheld his servants and salary, and debarred professional visits from colleagues. Gregorie was compelled by 1674 to accept a new professorship of mathematics at Edinburgh. There, at last, he had money and encouragement, and he was not denied contact with colleagues. Sadly, he was felled by a stroke in October of the very next year, at the age of 37, and was dead a few days later. It was fitting at least that he was stricken before a telescope, showing the moons of Jupiter to enthusiastic students.

Denied by geography much knowledge of the parallel mathematical work in Britain and abroad, James Gregorie nevertheless discovered for himself the general interpolation and biomial theorems, derived a number of trigonometric series, notably for the natural and logarithmic tangent and secant, and found a series solution to a problem posed by Kepler, employing 20 years before Newton a Taylor development of a function in terms of its nth order derivatives. In applied science, in dynamics in particular, he bridged Galieleo's Discorsi and Newton's Principia, proposing solutions to dozens of astronomical problems, ranging from planetary ellipses to designing the 'catadioptric' telescope of mirrors and lenses. Much of the correspondence from his short career is lost to us, and he was reluctant to publish. But all evidence suggests that James Gregorie was a weightier figure than tradition has allowed. Newton, in particular, almost certainly owes him more than anyone has yet recognized.


John Collins (1625-1683), maths teacher, book seller, and accountant, collected and disseminated scientific news zealously, a friendly register of all the latest developments. He was famously encouraging of young mathematicians like Gregorie. Christian (or Christiaan) Huygens (1629-1695), the formidable Fleming, was famous by James Gregorie's scientific coming-of-age for his work in the early calculus, statics, and practical astronomy, and above all, for inventing the pendulum clock. Sir Robert Moray, or Murray, or Murrey (c1608-1673), was a professional diplomat, friendly with Richelieu, Mazarin, and Charles II. His avocational interest in chemistry made him a formidable lobbyist for scientific enterprises like the Royal Society. Gregorie probably never met Sir Isaac Newton (1642-1727) in person. Stefano degli Angeli (1623-1697) was a Bologna-trained statics expert. He was also a priest, in which capacity he remained even while occupying the chair in mathematics in Padua. Nicholas Mercator (c1620-1687), was England's German-born expert on logarithms, and the designer of the fountains at Versailles. John Flamsteed (1646-1719), not appointed astronomer royal until 1675, was still teaching himself the art, enrolled as a non-resident student in Cambridge. When James Gregorie went to see him, Sir Jonas Moore, Master of the Royal Ordnance, was about to propose that Flamsteed be installed in an observatory at Chelsea College. Nephew David Gregory (1659-1708), who favoured this English spelling of the family name, sat eventually in the maths chair at Edinburgh and then the Savilian chair of astronomy in Oxford, but was still a student in Marischal College when his Uncle James died.

Other Significant Information

Notable publications:

Optica Promota, Seu Abdita Radiorum Reflexorum & Refractorum Mysteria, Geometrica Enucleata; cui Subnectitur Appendix, Subtilissimorum Astronomiae Problemata in Resolutionem Exhibens, ( London,1663)

Vera Circuli et Hyperbolae Quadratura, in Propria Sua Proportionis Specie, Inventa & Demonstrata, ( Padua,1667)

Geometriae pars Universalis, Inserviens Quantitatum Curvarum Transmutatationi & Mensurae, ( Padua,1668)

Exercitationes Geometricae, ( London,1668)

Honours, Qualifications and Appointments

1668: Elected member, the Royal Society of London

1669: Appointed Professor of Mathematics, University of St Andrews

1674: Appointed Professor of Mathematics, University of Edinburgh


List of sources for the biographical information:

Gillespie, CC, ed, Dictionary of Scientific Biography, (New York, Scribner's, 1970-1990), s.v. "Gregory, James" by DT Whiteside

Turnbull, Herbert Westren, James Gregory. Tercentenary Memorial Volume, (London, for the Royal Society of Edinburgh G Bell & Sons Ltd, 1939)