Isaac Barrow (1630-1677) was an English mathematician and theologian who discovered and proved the fundamental theorem of the calculus. Though he wrote many lectures on mathematics, he felt his true calling was theology, and he wrote many works about the Church of England.
A Life of Study
Isaac Barrow was born in London and attended Trinity College, Cambridge. He received his bachelor’s degree in 1648 and his master’s in 1652. He was an excellent student of the classics, but distinguished himself in mathematics as well. A renowned Greek scholar, during the 1650s he worked on Latin translations of texts from Greek mathematicians, including "Euclid’s Elements" and "Data," which he published in 1656 and 1657 respectively. He later translated those texts into English.
Teaching and Publishing
Barrow was given a Greek professorship at Cambridge; he was also made a professor of geometry. In 1663, he was the first person to occupy the Lucasian Chair at Cambridge, a position of mathematics that is the most famous academic chair in the world. (Isaac Newton, who attended Barrow's lectures and met with him many times, was the second holder of the chair.) During this time, Barrow delivered a series of lectures on mathematics, helping to institutionalize the study of mathematics at Cambridge. His math lectures were more popular with students than his lectures as a professor of Greek.
Breakthroughs In Calculus
Barrow's lectures were published under the Latin titles "Lectiones Mathematicae" and "Lectiones Opticae et Geometricae." In these books, he began by exploring the basics of numbers, magnitude, proportion and the concept of space. He was the first mathematician to discover that differentiation and integration are inverse operations, which pertain to the fundamental theorem of calculus. The differential triangle that he utilized is still in use in textbooks today. He explored new ways of determining the areas and tangents of curves, brought geometrical focus to the problems of reflection and refraction of light, and simplified the Cartesian explanation of a rainbow. He advanced the study of astigmatism and developed theories about light and colors.
A Theologian at Heart
For all his contributions to mathematics, Barrow considered himself a theologian first and foremost. When he resigned the Lucasian Chair, he was made a chaplain to Charles II, and later Master of Trinity College, a position he held for the remainder of his life. His sermons were extremely popular and were reprinted for centuries after his death.