Abstract: William, Viscount Brouncker (c.1620-1684) was once described by Sir Kenelm Digby as one of ‘the greatest mathematicians of the age’. He was chosen by Charles II as the inaugural President of the Royal Society, and held the post unopposed for fifteen years from 1662 to 1677. Brouncker's finest mathematical work was done in the 1650s, before the period of his Presidency, all of it in association with John Wallis. A study of their joint work provides fascinating insights into different forms of mathematical creativity and contrasting mathematical styles, and quickly puts paid to any notion that mathematics is a purely logical and impersonal subject.

Keywords: mathematics, William Brouncker, John Wallis, hyperbola, circle, Fermat,