He was admitted at Emmanuel College in Cambridge; 'where he was a pupil, then a fellow of King's College at the same place' (Mr Oughtred's preface to his Key to Mathematics). He was a good student, but fell not to the study of mathematics until he was above twenty.
A remarkable passage of his life was, that he was a witness of W. Laud's (archbishop of Canterbury) trial, for his introducing popish innovations into the University of Cambridge. The first remarkable passage of his life was his deciphering the letters of King Charles I taken at Naseby, which book is called the King's Cabinet Opened. He was scholar to Mr W. Oughtred.
In 1649 after the visitation by the parliament, [commissioners were sent to remove royalist or high church sympathisers from the Universities] he came to Oxford, and was made Savillian Professor of Geometry. He was a Fellow of the Royal Society. Great contests between him and Mr Thomas Hobbes, of Malmesbury: sure their Mercuries are in square or opposition. In 1657, he got himself to be chosen by unjust means to be keeper of the archives of the University of Oxford, at which time Dr Zouch had the majority of voices, but because Dr Zouch was a malignant (as Dr Wallis openly protested, and that he had talked against Oliver), he was put aside. Now for the Savillian Professor to hold another place besides, is so downright against Sir Henry Savile's statutes, that nothing can be imagined more; and if he does, he is downright perjured. Yet the Dr is allowed to keep the other place still.
In (1654) he took his degree of Doctor, at the Act, at Oxford, and went out grand compounder [candidates for degrees with estates of over £300 p.a. paid this extra fee, and took precedence over ordinary degree-holders] (which costs £200), only that he might take precedence over Dr Seth Ward, who was about a year his senior. In 1661 Dr Ward was made dean of Exeter, and the next year bishop of the same place; and so Dr Wallis's £200 was merely cast away. The bishop protested he was troubled for the loss of his brother Wallis's two hundred pounds.
He has written several treatises, and well; and to give him his due praise, has exceedingly well deserved of the commonwealth of learning, perhaps no mathematical writer so much.
'Tis certain that he is a person of real worth, and may stand with much glory upon his own basis, needing not (to) be beholding to any man for fame, of which he is so extremely greedy, that he steals flowers from others to adorn his own cap, -- e.g. he lies at watch, at Sir Christopher Wren's discourse, Mr Robert Hooke's, Dr William Holder, etc; puts down their notions in his note book, and then prints it, without owning the authors. This frequently, of which they complain.
But though he does an injury to the inventors, he does good to learning, in publishing such curious notions, which the author (especially Sir Christopher Wren) might never have the leisure to publish himself.
When Mr Oughtred's Key to Mathematics was printed at Oxford (third edition, with additions) Mr W.O. in his preface, gives worthy characters of several young mathematicians that he informed, and, amongst others, of John Wallis, who would be so kind to Mr Oughtred, as to take the pains to correct the press (proofs), which the old gentleman does with respect there acknowledge, after he has enumerated his titles and preferments: 'an ingenious, pious, industrious man, deeply versed in all recondite literature, most perspicacious in things mathematical, and in the unravelling and explanation of ciphered writings most intricately concealed (which is an argument of very subtle ingenuity) miraculously successful.' This last, on the cyphers, was added by Dr Wallis himself; which when, the book being printed, the old gentleman saw, he was much vexed at it; and said, he had thought he had given him sufficient praise, with which he might have rested content
He has a good temporal estate in Kent. He has only two daughters, handsome young gentlewomen; one married to Mr Blencowe of Middleton Cheyney.
He lives at a well-built house, near New College in Oxford; is a justice of the Peace there, and has been 167-, 1679, 1680.