- Studied under Martin Holbeach (1597-1670), a noted Puritan educator, who also taught Isaac Barrow
- Was the protégé of Herbert Palmer
- Was a Minister of the Gospel
- Served as amenuensis to the scribes of the Westminster Assembly
- Was influential in the preparation and design of the Westminster Shorter Catechism
- Was the author of the first exposition of the Westminster Shorter Catechism (1648)
- Was an Ardent defender of the doctrines of the Trinity, Infant Baptism and the Christian Sabbath
- Was a leading mathematician who is partially responsible for the development of modern calculus, credited with proposing Wallis' Product, introduced the term "continued fraction", coined the phrase "interpolation"
- Was perhaps the first to maintain the theory of circulation of blood in a public disputation
- Was involved in a plan to teach deaf-mutes how to speak
- Authored an English grammar for native speakers and foreigners
- Served as chief cryptographer for Parliament and the royal court between 1643-1689
- Was one of the first members of the Royal Society
- Was appointed Savilian Professor of Geometry at Oxford
- Is credited with introducing the ∞ symbol for infinity
- Was the last surviving member of the Westminster Assembly of Divines (d. October 28, 1703) at the age of 87. [Thomas Case was the last nonconforming Westminster Divine, having died on May 30, 1684, at the age of 84.]
- His autobiography provides the last first-hand account of the proceedings of the Westminster Assembly
- Asteroid 31982 Johnwallis is named for him
One aspect of Wallis's mathematical skills has not yet been mentioned, namely his great ability to do mental calculations. He slept badly and often did mental calculations as he lay awake in his bed. One night he calculated the square root of a number with 53 digits in his head. In the morning he dictated the 27 digit square root of the number, still entirely from memory. It was a feat which was rightly considered remarkable, and Henry Oldenburg, the Secretary of the Royal Society, sent a colleague to investigate how Wallis did it. It was considered important enough to merit discussion in the Philosophical Transactions of the Royal Society of 1685.
Wallis gives his own account of the matter in a letter to Thomas Smith of Madalene College, which is found in the Spectator, Vol. LII (1879), p. 11 and reproduced by E.W. Scripture, "Arithmetical Prodigies," in The American Journal of Psychology, Vol. IV (April 1891), p. 38:
December 22d, 1669. -- In a dark night, in bed, without pen, ink or paper or anything equivalent, I did by memory extract the square root of 30000,00000,00000,00000,00000,
00000,00000,00000, which I found to be 1,77205,08075,68077,29353, fere, and did the next day commit it to writing.
February 18th, 1670. -- Johannes Georgius Pelshower (Regimontannus Borussus) giving me a visit, and desiring an example of the like, I did that night propose to myself in the dark without help to my memory a number in 53 places: 246813579101111214111315161820
7192122242628302325272931 of which I extracted the square root in 27 places: 157103016871482805817152171 proxime; which numbers I did not commit to paper till he gave me another visit, March following, which I did from memory dictate them to him.Yours, etc.,
The discussion by church historians of his role and influence on the productions of the Westminster Assembly may be of particular interest.
William M. Hetherington, History of the Westminster Assembly of Divines, pp. 259-260:
It has been also conjectured, that the first outline of the Catechism may have been drawn by Dr. Wallis, one of the scribes of the Assembly at that period, and afterwards so justly celebrated as Savilian Professor of Geometry at Oxford, and one of the first mathematicians of the age. This conjecture may have arisen from the fact that he wrote a short treatise, entitled, "A Brief and Easy Explanation of the Shorter Catechism;" which was so much approved of by the Assembly that they caused it to be presented to both Houses of Parliament. But in truth, as has been already suggested, the framing of the Catechism appears to have been the work of the committee, and not of any one individual; and it was brought to its present admirable degree of nearness to perfection by the united deliberations of the whole Assembly.
Chad Van Dixhoorn, The Making of the Westminster Larger Catechism:
Having outlined the historical purpose of the Larger Catechism, it still seems appropriate to ask why the Catechism had to be written. After all, respected teachers in Britain had composed good catechisms; Calvin’s catechism was in the bookstores and so was the Heidelberg Catechism. Why could the Assemblymen not agree to use one of these catechisms for purposes of unity and instruction?
One answer has to do with the structure or format of earlier catechisms that the majority of Westminster divines did not like. In the eighth edition of A Brief and Easie Explanation of the Shorter Catechism, a young divine named John Wallis, explains the Assembly’s unique method in setting up the catechism: “The Assembly was careful that all the Answers might be entire sentences by themselves, without depending for their sense upon the foregoing Question, being indeed so many distinct Aphorisms, containing briefly the grounds of Christian Religion.” One benefit of this structure, in Wallis’s view,
is that the learner is not necessitated to charge his memory with the Questions, that he may understand the Answer [sic]; nor is the like danger, as in many other Catechisms, of confounding the understanding by misapplying the Answer to a wrong Question. Their Questions also are so framed, that any one of them may be asked singly and distinctly, without dependance on the Question foregoing.14
14. John Wallis, A Brief and Easie Explanation of the Shorter Catechism Presented by the Assembly of Divines in Westminster, to both Houses of Parliament, and By them Approved. Wherein the Meanest Capacities may in a Speedy and Easie way be Brought to Understand the Principles of Religion, in Imitation of a Catechism, formerly published by Master Herbert Palmer, B. D. and late Master of Queens College (eighth ed., London: for Jane Underhill, 1662), preface. I am grateful to Jason M. Rampelt for bringing this preface to my attention in conversation.
A.F. Mitchell, The Westminster Assembly: Its History and Standards, pp. 430-431:
From first to last, it appears to me in its [the Westminster Shorter Catechism's] clear, condensed, and at times almost frigidly logical definitions, to give unmistakeable evidence of its having passed through the alembic of Dr. Wallis, the great mathematician, the friend of Palmer, the opponent of Hobbes and the Socinians, and probably the last survivor of those connected with the great Assembly who was not ashamed to speak of the benefit he had derived from its discussions during the preparation of its Confession and Catechisms, long after he had conformed to the Church of the Restoration.
James Reid, speaking of his published sermons, Memoirs of the Westminster Divines, Vol. 2, p. 214, sums up his most important qualities:
In these sermons [of Dr. John Wallis], the reader may see both the author's learning and piety; with the Calvinistic doctrines of the Reformation, and of the Holy Scriptures. They may indeed be accounted too Puritannical by some persons; but they will not be the less acceptable on that account to others. The style is plain, and the matter excellent.