John West was educated at St Andrews and was assistant to Nicholas Vilant from 1775 to 1784, during which time he taught John Leslie and James Ivory. For financial reasons, he went to Jamaica in 1784, despite having just published his Elements of Mathematics and A new system of shorthand.
Apart from a few visits to England, he spent the remainder of his life in Jamaica becoming an Anglican priest and was for 28 years rector of St Thomas in the East, Morant Bay.
Two manuscript treatises were sent, after his death, to John Leslie, but these were not published until 1838. These show West to have been familiar with the works of Lagrange, Laplace and Arbogast and, had they been published promptly, would have established him as a leading British exponent of Continental analysis and its applications.