James Gregory was a seventeenth century mathematician and astronomer who developed infinite series representations for various trigonometric functions, but is better known for providing the first account of a practical reflecting telescope. Born in Drumoak, Scotland, Gregory was the sickly son of a clergyman, and was first educated by his mother. She introduced him to a number of advanced subjects at an early age, including elementary mathematics and geometry. Following his father's death in 1650, Gregory was sent to grammar school and then attended Marischal College in Aberdeen, where he focused his studies on astronomy and mathematical optics.

After graduating in 1657, Gregory wrote The Advance of Optics, which discussed such topics as lenses, mirrors, reflection, refraction, parallax, and transits. The work also introduced the use of photometric methods to estimate the distances of stars, but its most notable inclusion was the description of a reflecting telescope. The instrument, now known as the Gregorian telescope, used a secondary concave mirror to collect the reflection from a primary parabolic mirror and refocus the image back through a tiny hole in the primary mirror to an eyepiece. Gregory argued the advantages of such a design, but his depiction was purely theoretical since he did not have the instrument making skill required to materialize his idea.

Gregory journeyed to London in 1662, where he secured a publisher for The Advance of Optics. The work was released in 1663 and Gregory began seeking someone with the ability to fabricate his reflecting telescope. However, his quest was largely unsuccessful and the completion of a functional Gregorian telescope was left for others to achieve. Gregory then redirected his energies, deciding in 1664 to resume his scientific studies in Padua, Italy.

During his stay in Italy, Gregory completed two insightful mathematical treatises, The True Squaring of the Circle and of the Hyperbola and The Universal Part of Geometry. Based on his new works, Gregory found a certain amount of triumph waiting for him upon his return to London in 1668. He was elected to the Royal Society and was offered a position at the University of St. Andrews. He relocated to Scotland in order to accept the professorship and soon married a young widow. There he remained for several years, teaching, studying, and beginning his own family.

Gregory was hesitant to publish during this time because of controversy surrounding his earlier works. Christiaan Huygens had implied in a review of The True Squaring of the Circle and of the Hyperbola that he had been the first to prove some of the findings it held. Not wanting to precipitate similar problems with other scientists, Gregory withheld many of his mathematical methods from the public, though he shared them among friends in correspondence. Consequently, he received only a fraction of the credit he deserved during his lifetime, the magnitude of his achievements only becoming recognized in the 1930s when his papers were examined and published by H. W. Turnbull.

In 1674, Gregory left the University of St. Andrews amid increasing pressure from the school's governing board and other faculty members. Blaming Gregory for interfering with the students' acceptance of the classical curriculum of St. Andrews, they treated him as an outcast and eventually withheld his pay. Pleased to be offered an alternative, Gregory accepted a chairmanship of mathematics at the University of Edinburgh. Unfortunately, less than a year into his new appointment, Gregory suffered a blinding stroke while observing Jupiter through a telescope. He died only a few days later in October of 1675, only thirty-six years old.

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