# John Wallis

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John Wallis (Ashford, November 23, 1616 – Oxford, October 28, 1703) was an English mathematician who is partly credited with the development of modern calculus. It was a precursor of the infinitesimal calculus (introduced the use of the symbol

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to represent the notion of infinity). Between 1643 and 1689 he was a cryptographer of Parliament and later of the Royal Court. He was also one of the founders of the Royal Society and a professor at the University of Oxford.

## John_Wallis’s Biography

Born in Ashford (Kent), he was the third of the five children of Reverend John Wallis and Joanna Chapman. He started his education at the local Ashford school, but moved to the James Movat school in Tenterden in 1625 due to the outbreak of a plague epidemic. He had his first contact with mathematics in 1631 at the Martin Holbeach school in Felsted; he liked them but his study of them was erratic, “the mathematics that we currently have, are rarely seen as academic studies, but as something mechanical” (Scriba 1970).

With the intention of obtaining a PhD, in 1632 he was sent to Emmanuel College in Cambridge. There, he defended an argument about the doctrine of the circulation of blood; it is considered that it was the first time in Europe that this theory was publicly maintained in a discussion. In any case, his interests remained focused on mathematics. He obtained a degree in Arts in 1637, and a master’s degree in 1640, later he joined the priesthood. He was granted a scholarship to study at Queen’s College (Cambridge) in 1644, which did not stop him from continuing with his plans for his wedding with Susana Glyde, held on March 14, 1645.

During this time, Wallis remained close to the Puritan party, which he helped to decipher the messages of the monarchists. The quality of the cryptography of the time was not uniform; Despite the individual successes of mathematicians such as François Viète, the principles underlying the design and analysis of encryption were vaguely understood. Most of the ciphers were made with ad-hoc methods that relied on secret algorithms, as opposed to systems based on a variable key. Wallis made the latter much more secure and even described them as indecipherable.

He was also concerned about the use that foreign powers might make of encryption; rejected, for example, a request to teach cryptography to students of Hannover conducted in 1697 by Gottfried Leibniz.

Back in London (in 1643 he had been appointed chaplain of San Gabriel on Fenchurch Street), Wallis joins the group of scientists who would later form the Royal Society. At last he was able to satisfy his mathematical interests, and in a few weeks in 1647 he succeeded in dominating the book Clavis Mathematicae by William Oughtred. In a short time, he began writing his own treatises on a wide range of subjects: throughout his life, Wallis made significant contributions to trigonometry, calculus, geometry and the analysis of infinite series.

John Wallis joined the moderate Presbyterians in supporting the proposal against the execution of Charles I, which earned him the permanent hostility of the Independents. Despite his opposition, he was proposed in 1649 to occupy the Savilian Chair of Geometry at the University of Oxford, where he lived until his death on October 28, 1703. Apart from his work in mathematics, he also wrote about theology, logic, English grammar and philosophy; He was also one of the pioneers in the introduction in England of a teaching system for deaf-mutes, inspired by the method of the Spanish Juan de Pablo Bonet.

## More Facts about John Wallis

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