Brook Taylor was a distinguished English mathematician born on August 18, 1685, in Edmonton, Middlesex, England, to an aristocratic family with deep connections to the English legal and political establishment. Educated initially at home in classics and mathematics, he entered St. John's College, Cambridge as a fellow-commoner in 1701 at the age of sixteen, where he pursued both legal studies and mathematical research simultaneously. While formally studying law under John Machin and John Keill, Taylor earned a Bachelor of Laws in 1709 and a Doctor of Laws in 1714, though historical evidence suggests he never practiced law professionally despite his advanced legal qualifications. His dual dedication to scholarly pursuits characterized his early academic career, establishing him as a prominent figure within the intellectual circles of early 18th century England.
Taylor's most significant mathematical contribution was the development of what is now known as Taylor's theorem and the Taylor series, first presented in his seminal 1715 work 'Methodus Incrementorum Directa et Inversa.' This groundbreaking treatise introduced the 'calculus of finite differences' as a new branch of mathematics and established the method for expanding functions into infinite series, which has become fundamental to mathematical analysis. Additionally, Taylor made important contributions to the field of perspective with his work 'Linear Perspective,' containing the most accurate principles of art available at the time, and he investigated the center of oscillation, projectile motion, and capillary attraction. His mathematical innovations, particularly the Taylor series, provide essential tools for approximating complex functions and solving differential equations across numerous scientific disciplines.
Though Taylor's theorem was not immediately recognized for its full significance, Joseph-Louis Lagrange famously declared it 'the main foundation of differential calculus' in 1772, cementing its importance in mathematical theory. His work laid crucial groundwork for subsequent developments in mathematical analysis and continues to serve as an indispensable tool in physics, engineering, and computational mathematics for approximating functions and solving complex problems. Beyond his mathematical legacy, Taylor held prominent positions including election to the Royal Society in 1712 at the remarkably young age of twenty-seven and service as a Secretary of the Royal Society from January 1714 to October 1718, demonstrating his standing among the leading scientific minds of his era. Today, more than three centuries after his death on December 29, 1731, Taylor's mathematical insights remain fundamental to scientific education and research worldwide, with his series expansion techniques taught in calculus courses across the globe.
