# John Wallis

# John Wallis

**1616-1703**

**English Mathematician**

John Wallis coined the mathematical use of the word "interpolation," and was the first to use the infinity symbol (∞). He introduced a number of other terms and varieties of notation, and made the first efforts at writing a comprehensive history of British mathematics. A founding member of the Royal Society, Wallis was also involved in a number of other scientific endeavors: for instance, he was the first hearing person to develop a means of teaching deaf-mutes.

Wallis was born on November 23, 1616, to John, a rector, and Joanna Chapman Wallis in the Kentish town of Ashford. His father died when he was six, and at age nine an outbreak of the plague forced Wallis to leave Ashford. He attended several boarding schools, and while on Christmas break one year during the equivalent of grammar school, he first displayed his prodigious mathematical talents. After asking his brother to teach him arithmetic, he mastered the subject in two weeks, and soon proved himself able to perform extremely difficult computations—for instance, calculating the square root of a 53-digit number—in his head.

During his studies in medicine at Emmanuel College, Cambridge, Wallis wrote one of the first papers on the circulatory system. He graduated in 1637, and earned a fellowship to Queen's College. By 1640 he had been ordained in the Church of England, and five years later married Susanna Glyde, with whom he had three children. The English Civil War (1642-60) had broken out in the meantime, and Wallis was recruited to Oliver Cromwell's cause, using his intellectual skills as a cryptographer. For his help in deciphering Royalist communiqués, he was granted the Savilian professorship in geometry at Oxford, which he would hold for the rest of his life.

*Arithmetica infinitorum,* published in 1655, was Wallis's first important work, and was destined to become a standard information source for mathematicians during the coming decades. He followed this with a treatise on conics in 1658, and produced a number of other writings on a wide variety of mathematical subjects. His *Algebra: History and Practice* (1685) not only discussed the
whole history of the discipline, but marked the first recorded attempt at graphically displaying the complex roots of a real quadratic equation. A second edition contained the first systematic use of algebraic formulae, including numerical ratios.

In addition to his many accomplishments—including a celebrated public disagreement with noted philosopher Thomas Hobbes (1588-1679)—Wallis seems to have been adept at steering the ever-changing political tides of seventeenth century England. Thus despite his serving the Puritan cause, he went to work as chaplain for King Charles II following the restoration of the monarchy. After the Glorious Revolution of 1688, a bloodless change of governments, the newly installed William III put Wallis to work at a familiar task, deciphering enemy communications. Wallis died on October 28, 1703, in Oxford.

**JUDSON KNIGHT**

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