Born in Ashford, England, Wallis was the son of minister, who died when Wallis was only six years old. In 1631 he attended the Martin Holbeach school in Essex, where he trained in Latin, Greek, Hebrew, and logic. Although mathematics was not part of the curriculum, Wallis was taught arithmetic by his older brother during a Christmas vacation. While he was avidly interested in mathematics, Wallis chose the medical field as his profession, obtaining a master's degree from Emanuel College, Cambridge in 1640, and becoming an ordained minister as well.

Following the overthrow of King Charles I by the Parliamentarians, Wallis was offered a position as professor of geometry at Oxford in 1649. The appointment came as a surprise to many, as Wallis's accomplishments in mathematics had been insignificant up to that time. He took up a systematic study of all the mathematical literature available to him at Oxford and proved to his critics that his true expertise was indeed in mathematics. Known for his remarkable intellect, Wallis reportedly worked out the square root of a 53 digit number in his head, correct to 17 places. In 1656 he published one of his most important books, Arithmetica infinitorum, which contained several noteworthy mathematical "firsts," among them, the first use of the symbol to represent infinity; the first interpretation of imaginary numbers by geometric means; the first analysis of conic sections as curves of the second degree; the introduction of the term interpolation ; an early form of differential calculus ; and a famous formula using the value of pi ():

4/ =3/2 x 3/4 x 5/4 x 5/6 x 7/6 x 7/8 x 9/8...

In 1663, Wallis, along with his close friend Robert Boyle, founded the Royal Society, an organization devoted to scientific and mathematical research. During his tenure as a member of the Royal Society, Wallis produced and published more than 60 mathematical papers, covering a wide variety of subject areas. A man of exceptional intelligence and mathematical knowledge, Wallis stands as one of the most important mathematicians of the seventeenth century.