Thomas Simpson
Thomas Simpson, born in Leicestershire, England, in 1710, had almost no formal instruction---teaching himself mathematics---and is assessed as "a self-taught genius" by Carl B. Boyer in his book A History of Mathematics. Indeed, he moved from Leicestershire at the age of 15 to Nuneaton, Warwickshire, to became a schoolmaster, teaching mathematics there for eight years or so. Later, he taught in London coffeehouses, becoming well known in these venues of casual education, as did some other mathematicians such as de Moivre.
In 1737, Simpson took to writing textbooks on mathematics, his first one being on the infinitesimal calculus of Isaac Newton. In 1740, he published another book, The Nature and Laws of Chance, about probability theory. He also wrote textbooks on algebra, geometry (both plane and spherical), and trigonometry. Many of them were very popular, enjoying numerous editions and printings.
In 1743, Simpson was appointed to the Royal Military Academy, teaching mathematics of course, in Woolrich. The curricular characteristics of that Academy impelled him to research activities in engineering that related to fortifications.
In 1745, he was elected a fellow of the Royal Society.
But he did not invent what is called Simpson's rule, which was in fact invented by Newton, to whom he gave credit in his calculus textbook.
Thomas Simpson died in May of 1761.