WALLIS , JOHN

Wallis , John: translation

Born at Ashford in Kent, Wallis was educated at Cambridge University (1632–40), obtaining his MA in 1640. His early training was in theology and it was as a theologian that he first made his name. He took holy orders and eventually became bishop of Winchester. He moved to London in 1645 where he became seriously interested in mathematics and in 1649 he was appointed to the Savilian Chair in Geometry at Oxford University.

Wallis's most celebrated mathematical work is contained in his treatise theArithmetica infinitorum(1655; The Arithmetic of Infinitesimals). In this work he gave an infinite series expression for π. Generally the treatise took the development of 17th-century mathematics a significant step nearer Newton's creation of the infinitesimal calculus. Wallis was one of the first mathematicians to introduce the functional mode of thinking, which was to be of such importance in Newton's work. He also did notable work on conic sections and published a treatise on them,Tractatus de sectionibus conicis(1659; Tract on Conic Sections), which developed the subject in an ingeniously novel fashion. His writings were certainly read by Newton and are known to have made a considerable impact on him. Before Newton, Wallis was probably one of the most influential of English mathematicians.

Wallis wrote a substantial history of mathematics. His other interests included music and the study of language. He was active in the weekly scientific meetings that eventually led to the foundation of the Royal Society in 1662. During the English Civil War he was a Parliamentarian and put his mathematical talents to use in decoding enciphered letters.