William Oughtred

Lore & Background

Wallis was born in Ashford, Kent, the third of five children of Revd. John Wallis and Joanna Chapman. He was first exposed to mathematics in 1631 at Felsted School (then known as Martin Holbeach's school in Felsted); he enjoyed maths, but his study was erratic, since 'mathematics, at that time with us, were scarce looked on as academical studies, but rather mechanical' (Scriba 1970). At the school in Felsted, Wallis learned how to speak and write Latin, and was also proficient in French, Greek, and Hebrew. He was sent in 1632 to Emmanuel College, Cambridge, where he kept an act on the doctrine of the circulation of the blood; that was said to have been the first occasion in Europe on which this theory was publicly maintained in a disputation. He received his Bachelor of Arts degree in 1637 and a Master's in 1640, afterwards entering the priesthood. From 1643 to 1649, he served as a nonvoting scribe at the Westminster Assembly. He was elected to a fellowship at Queens' College, Cambridge in 1644, from which he had to resign following his marriage on 14 March 1645 to Susanna Glynde (c. 1600 – 16 March 1687). They had three children: Anne, Lady Blencowe (4 June 1656 – 5 April 1718), John Wallis (26 December 1650 – 14 March 1717), and Elizabeth Wallis (1658–1703).

Reader's Guide

Wallis rendered the Parliamentarian party great practical assistance in deciphering Royalist dispatches. He realised that ciphers based on a variable key were far more secure – even describing them as 'unbreakable', though he was not confident enough in this assertion to encourage revealing cryptographic algorithms. He refused Gottfried Leibniz's request of 1697 to teach Hanoverian students about cryptography. Returning to London, Wallis joined the group of scientists that was later to evolve into the Royal Society. He mastered William Oughtred's Clavis Mathematicae in a few weeks in 1647 and soon began to write his own treatises. Wallis wrote the first survey about mathematical concepts in England where he discussed the Hindu-Arabic system. In 1649 he was appointed to the Savilian Chair of Geometry at Oxford University, where he lived until his death on 8 November [O.S. 28 October] 1703. In 1655, Wallis published a treatise on conic sections in which they were defined analytically, the earliest book in which these curves are considered and defined as curves of the second degree. In Treatise on the Conic Sections, Wallis popularised the symbol ∞ for infinity, writing: 'I suppose any plane (following the Geometry of Indivisibles of Cavalieri) to be made up of an infinite number of parallel lines, or as I would prefer, of an infinite number of parallelograms of the same altitude; (let the altitude of each one of these be an infinitely small part 1/∞ of the whole altitude, and let the symbol ∞ denote Infinity)'. His Arithmetica Infinitorum, published in 1656, systematised and extended the methods of Descartes and Cavalieri, developing standard notation for powers from positive integers to rational numbers.

Did You Know?

• Wallis served as chief cryptographer for Parliament and later the royal court from 1643 to 1689.
• He introduced the symbol ∞ for infinity and used 1/∞ for an infinitesimal.
• Wallis kept an act on the doctrine of the circulation of the blood at Cambridge, said to be the first time this theory was publicly maintained in a disputation in Europe.
• He refused Gottfried Leibniz's 1697 request to teach Hanoverian students about cryptography.
• Wallis wrote the first survey about mathematical concepts in England that discussed the Hindu-Arabic system.