The latest Special Issue of Notes and Records examines John Wallis at 400 and is guest edited by Adam D. Richter and Stephen D. Snobelen. We asked them some questions about their research.


Who was John Wallis and why did you decide to do the Special Issue?

John Wallis (1616-1703) was a pioneering mathematician, his work with algebra and infinite series in Arithmetica infinitorum (1655) spurred Isaac Newton’s development of calculus. Serving as Savilian Professor of Geometry at Oxford for over fifty years, Wallis also found time to publish his popular Treatise of Algebra, Both Historical and Practical (1685), tracing the development of algebra from antiquity to his own time. Wallis was not only a mathematician but a polymath. A founding member of the Royal Society, he was a skilled codebreaker employed by the English government. He published major works on logic, grammar and theology, the latter a subject that he returned to often as a doctor of divinity.

This Special Issue had two main motivations. First, 2016 marked the 400th anniversary of Wallis’s birth commemorated by an academic workshop at the University of Toronto, which served as this issue’s foundation. Second, this is an exciting time to be a Wallis scholar as his complete correspondence is being published for the first time.


Wallis was a member of the early Royal Society. Can you give us a sense of what types of material he studied, and the intellectual milieu in which he worked? In fact, I read he even wrote a Defense of the Royal Society. What was that work about?

Wallis had a role in founding the Royal Society. Starting in the 1640s, experimentalists met in London and later Oxford to conduct experiments and discuss new developments in natural philosophy. Wallis participated in both of these groups. He moved to Oxford in 1649 to begin his career as Savilian Professor, rubbing shoulders with the likes of Robert Boyle and John Wilkins. When the Royal Society was founded in 1660, Wallis was an active member, publishing in Philosophical Transactions on a huge range of subjects, including the tides, measurements of temperature and atmospheric pressure, astronomy, extreme weather events and the laws of motion.

Wallis’s Defence of the Royal Society (1678) has a misleading title. It has to do more specifically with a dispute between him and William Holder, a cleric and FRS. Each of them claimed credit for teaching language to Alexander Popham, who was born deaf. Wallis had an account of his work with Popham published in Philosophical Transactions but neglected to mention Holder, who had taught Popham years earlier. Holder published a Supplement to the Philosophical Transactions (1678) lashing out at Wallis and the late Henry Oldenburg, Secretary of the Royal Society. Wallis responded with his Defence, which is really meant to defend himself and Oldenburg rather than the Royal Society itself. The dispute came close to tearing the Royal Society apart, almost cutting its 350-year history short.


Adam, you’ve written a good deal about Wallis’s religious views, particularly his anti-Catholicism (and anti-Quakerism). How does Wallis’s anti-Catholic position motivate his acceptance or rejection of certain ideas about nature or mathematics?

It’s sometimes difficult to pin down Wallis’s precise religious views, though Jason Rampelt’s contribution to this issue will help, but one position he adopted throughout his career was a strong antipathy toward Roman Catholics. This anti-Catholic prejudice affected his reception of ideas in natural philosophy and mathematics. It played a role when he opposed England’s adoption of the Gregorian calendar, even though it more accurately matches the length of the astronomical year than the older Julian calendar. The new calendar had been sponsored by Pope Gregory XIII. Wallis worried that adopting it would be like admitting Rome’s authority over England.


Stephen, based on your work with Isaac Newton, a contemporary of Wallis’s, what would you say about similarities and differences in their careers?

There are obvious parallels between the careers of John Wallis and Isaac Newton beyond the mere facts that both were educated at Cambridge colleges, played crucial roles in the history of calculus and held endowed mathematics professorships at Oxford and Cambridge, respectively. Though their lives overlapped by many decades, it’s not clear if Wallis and Newton ever physically met. But they were aware of each other’s work and they did correspond. In the 1660s the young Newton read and annotated two of Wallis’s mathematical works: Arithmetica infinitorum (1656) and Commercium epistolicum (1658). As Adam mentioned, the first of these books gave impetus to Newton’s development of calculus and the binomial theorem. Wallis also published some of Newton’s mathematical works.

Wallis and Newton were supreme polymaths in an age of polymaths. Newton has long been known for his work in mathematics, optics and physics, but the availability of his manuscripts and the expanded horizons of the history of science have led to Newton being studied also as theologian, historian, alchemist and administrator at both the Mint and The Royal Society. The Special Issue also emphasises Wallis’s polymathy in mathematics, geometry, music, phonology, cryptography, history and theology.

Wallis and Newton were also both anti-Catholic, but they differed on the key issue of the Trinity. Against Wallis’s more orthodox Calvinism, the anti-Trinitarian Newton was a heretic. Wallis defended the Trinity in print and created an analogy between the Trinity and the three dimensions of a cube to argue that it was logically coherent. Newton’s “Two notable corruptions” (1690) was likely intended as an anonymous statement about the falsity of the Trinity, although he suppressed it.

Wallis and Newton also had different attitudes towards promoting their work. Wallis sent letters to Newton in the 1690s to rebuke the younger mathematician for failing to publish his calculus, and insisted he printed his Opticks. Near the end of his missive, he explodes: “I should say the same about many things you keep hidden, of which I am not yet aware” (Correspondence of Newton, 4:239). Perhaps Wallis’s impatience was because he was increasingly aware of his mortality and, as it happened, he died the year before the Opticks was published. Even though I am a student of Newton, I sympathise with the exasperated Savilian Professor.


A final thought from Adam

Yes, but Wallis would probably be pleased that we are drawing attention to his work!



Notes and Records is an international journal which publishes original research in the history of science, technology and medicine. Find out more information about submitting to Notes and Records.


Image credits:

1 – A diagram of Wallis’s tidal theory. Phil. Trans. 30 May 1665 vol 1, no 16 263-281.

2 – Wallis’s Grammatica from Cambridge University Library.

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