Wallis, John: British mathematician; born November 23, 1616 in Ashford; died November 8, 1703 in Oxford. Invented the theory of infinite number series and introduced the ►lemniscate ∞ as a symbol for the potentially infinite.
The son of an English village priest, Wallis first attended school in Ashford but later, following an epidemic of plague in the region, transferred to James Movat's grammar school in Kent. Although he pronounced himself ready for university studies at the age of 13 (as reported in his autobiography), he was to remain in school until 1632 to perfect his knowledge of Latin, Greek, and Hebrew.
At that time, mathematics was not taught in schools. Rather, it was regarded as a mere occupational skill practiced by traders, carpenters, land surveyors, and the like, and hence not worthy to be part of a gentleman's education. Nonetheless, John was immediately fascinated when he came upon a book on arithmetic in 1631. At that point mathematics became his principal leisure activity. In 1632, just after his 16th birthday, he entered Emmanuel College in Cambridge.
To his disappointment, mathematics was not taught there either, so he decided to study ethics, metaphysics, geography, astronomy, medicine, and anatomy instead. He was the first to publicly defend his anatomy professor Francis Glisson's revolutionary new concept of blood circulation. He received his first college degree in 1637 and a doctoral title in 1640. After completing his degrees he was ordained as a priest by the Bishop von Winchester and became a chaplain — not an unusual career for a 17th-century English academic.
However, in 1642 something occurred that would fundamentally change his life. At the time England was shaken by a civil war between king and parliament. Wallis, who sided with the parliament, was presented with an intercepted royalist message that was in code. He cracked the code in a mere two hours (the message was about the planned seizure of Chichester). This event determined his future career path. Wallis became the first professional cryptographer, using his mathematical skills to decode encrypted royalist messages for the parliamentarians.
He did not have to wait long for his reward, which came in the shape of a highly remunerative church position and a fellowship at Queen's College in Cambridge. Wallis was now financially independent. Starting in 1645 he arranged weekly meetings with like-minded academics in his London apartment. This scholarly group eventually evolved into the Royal Society, the first national scientific association. The meetings were subject to strict rules. Discussions of religion, politics, or daily news were prohibited. Members were obliged to discuss only scientific topics and experiments, in which areas each participant had to make a weekly contribution.
These meetings gave birth to the conception of empirical science as we know it today (see ►Laws of Nature). Wallis himself, of course, specialized in mathematics. He made presentations on trigonometry and developed a method to solve 4th degree equations. Oliver Cromwell, the leader of the parliamentary faction, arranged for him to be awarded a chair of geometry in Oxford, the so-called Savilian Chair. (Wallis's predecessor on this post had the misfortune of being a royalist.)
Although he obtained the Savilian Chair for political reasons, Wallis would prove himself more than worthy of the prestigious position throughout the remaining half-century up to his death in 1703. In 1656 he published Arithmetica Infinitorum, which made him famous among scholars throughout Europe and eventually became a standard textbook in mathematics. In this book, which deals with infinite number series, he first introduced the symbol of infinity (∞). The book also introduced the Wallis product for approximate calculation of the number ►Pi.
Cromwell was defeated in 1660, and Charles II was restored to the throne of England. Fortunately for Wallace, the new king acknowledged his having signed a petition twelve years earlier against the execution of Charles I. As a result, Wallis not only was allowed to keep his professorship, but was even appointed Royal Chaplain!
Thus unperturbed by the political turmoil, Wallis was able to continue his studies in mathematics. He studied negative roots and ►complex numbers, developed methods for conical sections, and derived the laws of inelastic impacts with which physics students are still confronted today. A true universal scholar, he also went on to publish works on religion, etymology, grammar, and logic. He drew upon his knowledge of Greek to reconstruct texts by Ptolemy, Aristarch, and Archimedes. He even developed a method for teaching deaf children. Unlike most mathematicians, he had highly developed skills in mental arithmetic: the protocols of the Royal Society meetings document contemporary discussions of Wallis's ability to calculate in his head the square root of a number with 53 digits.