CALCULUS Understanding Its Concepts and Methods

James Gregory (1638--1675)--- Historical Sketch

One seldom hears of mathematicians who got their start in the subject from their mothers, but that is exactly the case with James Gregory who was born in 1638. His father was a pastor in a parish near Aberdeen, Scotland. It was likely because of his mother's influence that James became a mathematician. He was taught geometry by his mother and one of his two older brothers. He had no difficulty mastering Euclid's Elements.

After studying at Marischal College in Aberdeen, James became very involved with telescopes, even to the point of writing a mathematically-oriented book (definitions, postulates, etc.) about reflecting telescopes, even though one had yet to be constructed. The book was later published.

Visiting the University of Padua in 1664, he used infinite series to find areas or regions bounded by circles and hyperbolas. It was here that he was introduced to differentiation and integration, and he produced two publications on these subjects, one in 1667 and one in 1668. The latter has been described as the first textbook on calculus.

In 1668, Gregory was elected a fellow of the Royal Society, and he presented papers to the Society on topics such as astronomy and mechanics. The Regius Chair of Mathematics was created for him at St. Andrews University and he occupied this position for six years. In 1674, he left for the University of Edinburgh where he was the first to hold the Chair of Mathematics. One year later, while showing his students the moons of Jupiter, he had a stroke, became blind, and died after a few days.

Much in calculus is actually owed to Gregory, though many of the things he discovered are not attributed to him. Here are three examples: He discovered Taylor series some 40 years before Taylor did. He discovered Cauchy's test before Cauchy did. He defined the Riemann integral before Riemann did.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.