James Gregory | Biography

James Gregory's work laid the foundation for the development of calculus, and his work in astronomy and optics for astronomical observations influenced the works of Isaac Newton. He was born in Drumoak, Scotland, the son of John Gregory, a minister, and Janet Anderson Gregory. Gregory was a sickly child, and his mother guided his early education at home; she must have been an unusual woman for the 17th century, because she included geometry among the subjects she taught her son.

In 1651, Gregory left home for grammar school in Aberdeen, Scotland. He completed his preparatory work, then graduated from Aberdeen's Marischal College, where he focused his studies in mathematical optics and astronomy. Frustrated by the lack of scholarly opportunities in Aberdeen, Gregory traveled to London in 1662, where he met Robert Moray, an influential member of the Royal Society. In 1663, Gregory published Optica promota, a work that anticipated Newton's efforts in optics by suggesting the use concave mirrors in telescopes. He searched unsuccessfully to find a technician skillful enough to construct the prototype of such an instrument. Moray attempted to introduce Gregory to the Dutch mathematician Christiaan Huygens to help further the young man's studies, but was unsuccessful. Gregory then decided to pursue scientific studies in Italy with Stefano degli Angeli, and left London for Padua in 1664.

At the University of Padua, Gregory studied geometry, mechanics, and astronomy. In 1667 he published Vera circuli et hyperbola quadratura, in which he explored the nature of the area of circles and hyperbolas. Geometriae pars universalis, inserviens quantitatum curvarum transmutationi & mensurae followed in 1668, where Gregory introduced the concepts of convergent and divergent series. He also discussed the differences between algebraic and transcendental functions, and offered a series of expressions for trigonometric functions and a proof for the fundamental theorem of calculus.

Gregory returned to London in 1668. His work in Italy and his contacts with the Italian scientific community initially earned him considerable notice, and he was quickly elected to the Royal Society. Gregory was named as the new chairman of mathematics at St. Andrew's College, Scotland, in 1668. Gregory's time was consumed by his duties for the next several years. "I am now much taken up and hath been . . . this winter bypast, both with my publik lectures, which I have twice a week, and resolving doubts . . . gentlemen and scholars proposeth to me," he wrote in 1671.

Despite the time devoted to teaching and academic administration, Gregory managed to maintain a voluminous correspondence with John Collins, who forwarded to Gregory copies and transcripts of material from such noted scholars as Isaac Barrow, René-Francois de Sluse, and Newton.

Gregory waged war on the antiquated curriculum at St. Andrew's, but his efforts to incorporate contemporary science into the college's course of studies was resisted by the faculty and the college's governing board of regents. Gregory hoped to establish the first public observatory in Great Britain at St. Andrew's; in 1673, he journey to London to seek advice and obtain instruments for such a facility. Unsuccessful in his efforts to secure financial backing for the project, Gregory returned to St. Andrew's to find himself an academic outcast. A student rebellion against the established curriculum pushed the board of regents to action. Gregory and his radical ideas were the obvious scapegoat; servants were forbidden to wait on him and his salary was withheld. Colleagues and students were instructed to treat him as a pariah. "Scholars of most eminent rank were violently kept from me . . . the masters persuading them that . . . they were not able to endure mathematics," he wrote.

When Edinburgh University offered Gregory its newly endowed chairmanship of mathematics, he fled St. Andrew's. Sadly, within a year of the appointment, Gregory suffered a debilitating, blinding stroke while observing Jupiter through a telescope. He died a few days later, in October 1675.

Before his death, Gregory ceased publishing papers in pure mathematics. His private papers, however, are rich in theories, proofs, and questions that might have earned him wide acclaim during his lifetime, had the materials been issued. Gregory delved into the theory of equations and the location of their roots, and attempted to solve the general quintic. His letters to Collins include his work on quadrature and rectification of the logarithmic spiral, his independent discovery of the general binomial expansion, several trigonometrical series (including those for the natural and logarithmic tangent and secant), and a series solution to Johannes Kepler's problem in which he outlined how the series could be applied to the roots of equations.

Much of the work Gregory pursued during the last years of his life is lost. In a short paper published in 1672, he proved that atmospheric height is logarithmically related to barometric pressure. Other surviving papers demonstrate that he deduced the elliptical integral expressing the time of vibration in a circular pendulum and pursued his work in theoretical astronomy.

Gregory's reluctance to publish limited his success during his lifetime. His work served as the springboard for the published works of others, including Newton and Gregory's nephew, David, who did not acknowledge their debt to Gregory. The scope of Gregory's work and the extent of its influence on the 17th century scientific community were little recognized until 1939, when some of his notes--scribbled in 1671 on the back of a letter from a bookseller--were published and scholarly curiosity in Gregory's work was awakened.