In 1640, he was ordained in the Church of England and served as a chaplain. He became the chief cryptographer for Parliament as the English Civil War broke out in 1642, decoding secret messages. As the Westminster Assembly gathered in London in 1643 to reform and clarify the government, worship, and doctrine of church, it asked Parliament to appoint Wallis, "a godly & industrious young man," as an assistant to the scribes of the assembly. He was appointed and he eventually became one of the non-voting scribes himself. In 1648 he wrote the earliest commentary on the Westminster Shorter Catechism.
At the same time Wallis joined a group of scientists that would become the Royal Society, of which he remained a member when it was formally organized. While he opposed the execution of King Charles I, he was appointed by Cromwell as a professor of geometry at Oxford in 1649, a post he would fill for 50 years.
He received the degree of Doctor of Divinity in 1654. Upon the restoration of the monarchy, he was appointed a royal chaplain and was one of the presbyterian members of the Savoy Conference. While he was presbyterian in his doctrine, he remained in the Church of England.
He was a leading English mathematician of his day and an influence on his younger contemporary, Isaac Newton. He made significant contributions to trigonometry, geometry, and the origins of calculus. He is credited with introducing ∞ as the symbol of infinity.
He was skilled in doing mental calculations. “On one occasion he extracted the square root of a number expressed by fifty-three figures, and dictated the result to twenty-seven places next morning to a stranger. It proved exact.” (DNB). He did this at night to test the strength of the mind at night. This feat was described in the journal of the Philosophical Society of Oxford.
He continued to serve as a cryptographer throughout his life, deciphering codes for parliament and later for King William. He wrote books on mathematics, music theory, logic, grammar, and theology, defending infant baptism, the sabbath, and the Trinity.
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