Wallis's Opera mathematica

Portrait of John Wallis, from: Opera mathematica. Oxoniæ: E Theatro Sheldoniano, 1695 [Rare Books Collection FOL. QA33.W15]John Wallis (1616-1703), a founder member of the Royal Society, was the foremost English mathematician of his time after Newton. Although Wallis was largely self-taught, having received no formal training in mathematics either at school or at university, he was appointed Savilian Professor of Geometry at Oxford in 1649.

First published in 1655, Arithmetica infinitorum (The arithmetic of infinitesimals), is arguably his most important work and marked an important step towards the development of calculus. Its early reception was mixed; although praised by William Oughtred it was heavily criticised by other mathematicians, such as Christiaan Huygens and Pierre de Fermat.

However, it had a profound impact on the young Isaac Newton. Newton read it during the winter of 1664-65 and by building on Wallis’s techniques made his first major mathematical discovery - the general binomial theorem.

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