English mathematician and cleric who made important contributions to the development of algebra and analytical geometry. He was one of the founders of the Royal Society.
Wallis was born in Ashford, Kent, and studied at Cambridge. In 1640 he was ordained in the Church of England. He moved to London in 1645 and assisted the Parliamentary side by deciphering captured coded letters during the Civil War. From 1649 he was professor of geometry at Oxford, and in 1658 he was appointed keeper of the university archives. In 1660 Charles II chose him as his royal chaplain. After the revolution of 1688–89, which drove James II from the throne, Wallis was employed by William III as a decipherer.
Wallis also conducted experiments in speech and attempted to teach, with some success, congenitally deaf people to speak. His method was described in his Grammatica linguae anglicanae (1652).
Wallis's Arithmetica infinitorum (1655) was the most substantial single work on mathematics yet to appear in England. It introduced the symbol ∞ to represent infinity, the germ of the differential calculus, and, by an impressive use of interpolation (the word was Wallis's invention), the value for π. His Mechanica (1669–71) was the fullest treatment of the subject then existing, and his Algebra (1685) introduced the principles of analogy and continuity into mathematics.