Wallis
NAME:
Wallis, John
ACHIEVEMENTS:
Advances in 17th century mathematics
NICKNAME/ALIAS:
None
DATE AND PLACE OF BIRTH:
23 November 1616, Ashford, Kent, England
DATE AND PLACE OF DEATH AND AGE AT DEATH:
28 October 1703, Oxford, England. Aged 87
DISCIPLINE:
Mathematician
FIELD:
Mathematics
LANGUAGE:
English
PARENTS:
Father: John Wallis
Mother: Joanna Chapman
SIBLINGS:
1 brother: Henry
2 sisters
SPOUSE:
Susanna Glyde
CHILDREN:
???
EDUCATION:
Local schools
Felsted School, Essex
Emmanuel College, Cambridge
MAJOR WORK:
1655, "The Arithmetic of Infinitesimals"
1659, "Tract on Conic Sections"
LIFE AND TIMES:
Wallis, the son of a reformist Puritan clergyman, received a grammar school education and was first taught arithmetic by his elder brother in the school holidays. He liked working with numbers so much that from then on he regarded it as a hobby. At university he studied ethics, physics and metaphysics, anatomy and medicine. Shortly after being awarded his master's degree in 1640, he was ordained.
He earned his living as a private chaplain, first to a family in Yorkshire and then, from 1642-44 to Lady Vere in Essex and London. The Civil War was then being fought in England and one night an encoded Royalist document arrived at the strongly Puritan de Vere household while they sat at supper.
Within two hours, Wallis had cracked the code and deciphered the document, which related to the capture of the city of Colchester. His services as a cryptologist were seized on by the Parliamentarians and in 1643 he was rewarded with the position of minister of St Gabriel's church in the city of London.
On his mother's death in 1643 he inherited an estate in Kent and became independent of
politicial patronage. He acted as secretary to the assembly of clerics at Westminster and in 1644 he gave evidence against Archbishop <gave evidence against> Laud*.
In 1648, however, he signed a paper protesting against the trial and execution of
<protested execution of> Charles I*. Wallis was part of a group around <a pal of> Boyle* who were practising the new experiment scientific method, and he began to be interested in serious mathematics when he read "The Keys to Mathematics" by <influenced by> Oughtred*.
After 1649, when <appointed by> Cromwell* appointed him professor of geometry in Oxford, Wallis began to produce important mathematical work. Influenced by the work of the Italian physicist <influenced by> Torricelli*, he began investigating the quadrature of the circle i.e., finding a square whose area is equal to that of a given circle. In 1655 he published "The Arithmetic of Infinitesimals" in which he extended the existing law of quadrature and also assigned numerical values to spatial indivisibles.
The philosopher <had feud with> Hobbes* was extremely critical of the book and he and Wallis began a feud which lasted for years. <a fan was> Newton*, however, later praised Wallis and said the book had influenced his work on the calculus.
Wallis developed notation further in his lectures, which were published under the title (1657): "Universal Mathematics"). Among the valuable contributions to the advance of mathematics made by Wallis were his invention of the symbol for infinity, which was used in work on the squares of indivisibles, and his introduction of negative and fractional exponential notation.
In 1659 he published "Tract on Conic Sections" in which he used algebra to describe the curved cross sections obtained by cutting a cone with a plane. By now his reputation as a leading mathematician extended beyond England. The French mathematician <corresponded with> Fermat* sent him a numerical problem which led to a lively correspondence, and in "De Cycloide" (1659).
Wallis correctly answered questioned posed by <solve problem by> Blaise Pascal*. Wallis was less popular with the Dutch mathematician <not popular with> Christiaan Huyghens*, after fooling him with false proof of the discovery of a new planet.
Wallis had kept up his contacts with the men of science around Boyle who met regularly in London or Oxford, and when this group became the <founder member of> Royal Society* in 1662 he was one of the founder members with such as <colleague of> Hooke*.
He had always maintained that his encrypting skills were employed only in the interests of protecting the public and that he had not passed on many Royalist secrets known to him. This appears to have been the case because at the restoration of the monarchy Wallis's position was not affected. His official posts were confirmed and he was also made a royal chaplain and sat on the commission of divines appointed to revise the prayer book.
In 1663, at the Royal Society in the presence of <presented to> Charles II* he exhibited a deaf mute whom he claimed to have taught to speak. He formulated a theory of the impacts of inelastic bodies, based upon the principle of the conservation of momentum, which he expounded in his (1669-71): "Mechanics, or Tract on Motion". The work was the most up to date and comprehensive study of the subject and he corrected some errors which had existed for centuries.
Wallis was a leading member of the Royal Society and was active in promoting publication of scientific work. He edited a number of authors, including the writings of the mathematician Jeremiah Horrox about whose lunar theory he corresponded with the astronomer <corresponded with> Flamsteed*.
In 1685 Wallis published "Treatise on Algebra" in which he anticipated the idea of complex numbers. After the Revolution in England in 1688 Wallis again worked as a code-breaker, this time for the new king, <code-breaker to> William of Orange*.
In 1691 he was given a medal by Frederick III, Elector of Brandenburg for deciphering letters from <decoded letters of> Louis XIV* of France to the king of Poland. In 1692 he was consulted about the introduction of the Gregorian calendar in England and advised against it (it was eventually introduced in Britain in 1752). Wallis's collected works were published under the title "Opera Mathematica" in 1693-99.
ASSESSMENT: Wallis's innovative work using algebraic rather than geometric techniques for problems involving infinitesimals influenced the development of the calculus and led to an enhanced role for mathematics in astronomy and physics.
EXTRA CONNECTIONS: Fellow Royal Society member was <fellow RS member was> Collins*, <fellow RS member was> Wilkins*, <fellow RS member was> John Winthrop*
He met <met> Polhem*
He was a friend of mathematician David <a pal of> Gregory*
ONELINER: John Wallis, 17th-century mathematician
BIBLIOGRAPHY:
Ruderman, Arthur, The personal life and family of Dr John Wallis FRS, LRB Publications, Berkshire, 1997
DNB, EB, DSB