John Wallis

John Wallis was a seminal English mathematician and clergyman who made foundational contributions to the development of infinitesimal calculus and modern mathematical notation. Appointed as the Savilian Professor of Geometry at the University of Oxford in 1649, his work bridged the gap between the geometry of Bonaventura Cavalieri and the later calculus of Isaac Newton and Gottfried Wilhelm Leibniz. Wallis also played a key role in the early Royal Society and served as a leading cryptographer for the Parliament of England during the English Civil War.

Early life and education

Born in Ashford, Kent, Wallis initially studied at Felsted School in Essex where he showed an early aptitude for languages, mastering Latin, Greek, and Hebrew. He entered Emmanuel College, Cambridge in 1632, where he earned a Bachelor of Arts in 1637 and a Master of Arts in 1640, originally intending for a career in the Church of England. His introduction to serious mathematics was somewhat accidental, occurring around 1647 after encountering the works of William Oughtred; this late start did not hinder his rapid ascent in the field. Following the outbreak of the English Civil War, his sympathies lay with the Parliamentarian cause, which later influenced his academic and governmental appointments.

Mathematical contributions

Wallis's most influential work, Arithmetica Infinitorum (1656), pioneered the use of infinite series and products to determine areas and volumes, directly influencing Newton's development of the binomial theorem and calculus. In this treatise, he introduced the now-standard symbol ∞ for infinity and presented the famous Wallis product for π. He also made significant advances in analytic geometry, extending the work of René Descartes, and provided the first published treatment of continued fractions. His 1685 A Treatise of Algebra served as a vital historical survey of the subject, chronicling the work of English mathematicians like Thomas Harriot and engaging in a bitter priority dispute with Pierre de Fermat over methods in number theory.

Work in cryptography

During the 1640s, Wallis's intellectual talents were recruited for the Parliament of England's intelligence efforts. He became a highly skilled cryptanalyst, successfully deciphering coded Royalist messages captured during the English Civil War and later during the Anglo-Dutch Wars. His expertise was so valued that after the Restoration, King Charles II continued to employ his services, despite Wallis's previous Parliamentary allegiance. This work established a notable English tradition in cryptography, and his methods were studied by later figures in the field. He maintained a lifelong interest in the subject, corresponding on ciphers with notable contemporaries like Samuel Pepys.

Role in the Royal Society

Wallis was a founding member and a pivotal early figure in the Royal Society, one of the group of savants who began meeting in the 1640s and 1650s that would formally constitute the society in 1660. He served on its council and was a frequent contributor to its journal, Philosophical Transactions, presenting papers on topics ranging from mechanics and the collision of bodies to linguistics and phonetics. His debates within the society, particularly with Thomas Hobbes on the subject of squaring the circle and the nature of geometric proof, were famous for their vigor and helped define the society's commitment to experimental and mathematical rigor.

Later life and legacy

Wallis retained his position at Oxford until his death, actively publishing and corresponding with the leading European intellectuals of his era, including Christiaan Huygens. His later works included theological writings and efforts to devise a universal language for the deaf. He died in Oxford in 1703 and was buried in the University Church of St Mary the Virgin. Wallis's legacy is profound; his symbolic and conceptual innovations provided essential tools for the Scientific Revolution, directly paving the way for the monumental achievements of Isaac Newton. His papers and extensive correspondence remain valuable sources for historians of seventeenth-century science and mathematics. Category:1616 births Category:1703 deaths Category:English mathematicians Category:English cryptographers Category:Fellows of the Royal Society Category:Alumni of Emmanuel College, Cambridge Category:Savilian Professors of Geometry