John Wallis (1616-1703) was appointed Savilian professor of geometry at Oxford in 1649 and over the course of half a century in this post he would build a reputation as one of the leading mathematicians of his generation. On arrival in Oxford he was incorporated MA from Exeter College and became part of John Wilkins’s circle at Wadham. During the 1650s he would publish a series of influential mathematical works, including his ‘Tract on Conic Sections’ which introduced the sign for infinity, ∞, using 1/∞ to represent an infinitesimal height, and ‘The Arithmetic of Infinitesimals’ in which he extended methods devised by Descartes and Cavalieri to deal with sums using indivisible or infinitesimal quantities: this last work would have a significant influence on Newton in his development of calculus. In 1668 he would present a solution to the problem of colliding bodies to the Royal Society, considering both elastic and imperfectly elastic bodies, and in 1670 would produce a comprehensive guide to what was known about statics, impact laws, and centres of gravity. He was a key figure in many of the great mathematical disputes of the age, clashing with Fermat, Pascal and Hobbes, and a dedicated champion of English achievements: something reflected in his last great work, ‘A Treatise of Algebra’ (1685), a blend of mathematics and Anglocentric history. As well as a mathematician Wallis was a renowned cryptographer, deciphering intercepted messages for the British Government for many years – in 1653 he donated some of these deciphered letters to the Bodleian Library. Elected keeper of the university archives in 1658, he revolutionised the organisation and recording of the collections. He was a founding and highly active member of the Royal Society, contributing more than 60 papers to the journal Philosophical Transactions, as well as reviewing and editing publications on all areas of maths.