Willis was another of those amazingly versatile clerics, like Buckland and Peacock, who taught at the English universities in Victorian times. He was ordained in 1827, elected a Fellow of the Royal Society in 1830, and in 1837 he was appointed Jacksonian Professor of Applied Mathematics at the University of Cambridge, a post which he held for the rest of his life. However, his abiding interest was architecture. Charles Robert Cockerell, the architect of the new University Library and the leading exponent of classical architecture, was a close friend, but it was old Gothic buildings which particularly interested Willis. Here he was able to apply his knowledge as a structural engineer to understand the constructional techniques of medieval times. His studies of vaulting published in 1842 as a paper, On the Construction of the Vaults of the Middle Ages, according to Pevsner ‘established a standard of insight and meticulous accuracy which has never since – in England or anywhere else – been surpassed’, and between 1845 and 1861, he published a series of painstaking studies of the fabric of English medieval cathedrals.