Mathematician:John Wallis

Mathematician

English mathematician who made considerable contributions towards the invention of the calculus.

Credited with introducing the symbol $\infty$ for infinity.

One of the first English mathematicians to use the techniques of analytic geometry as defined by Descartes.

Rediscovered a neat proof of Pythagoras' Theorem originally published by Bhaskara II in the $12$th century.

Introduced negative and fractional exponents.

Provided a much-cited but incorrect solution to the problem of Prince Rupert's Cube.

Nationality

English

History

• Born: November 23, 1616, Ashford, Kent, England
• 1649: Savilian Professor of Geometry at Oxford
• Died: October 28, 1703, Oxford, Oxfordshire, England

Theorems and Definitions

• Wallis's Product
• Wallis's Number

Results named for John Wallis can be found here.

Definitions of concepts named for John Wallis can be found here.

Publications

• 1655: Tract on Conic Sections
• 1656: Arithmetica Infinitorum (in which Wallis's Product appears)
• 1659: De Cycloide et de Corporibus inde Genitis (which incorporated William Neile's work on the rectification of the semicubical parabola)
• 1685: A Treatise on Algebra

Treatise of Angular Sections (unpublished for forty years after it was written)

Restored some ancient Greek texts, for example:

• Claudius Ptolemy's Harmonics
• Aristarchus's On the magnitudes and distances of the sun and moon
• Archimedes' The Sand-Reckoner

Dispute with Hobbes

From $1655$ onwards he was involved in an intellectual dispute with Thomas Hobbes, whence various publications with titles like:

• Due Correction for Mr Hobbes, or School Discipline for not saying his Lessons Aright

Non-mathematical

• 1653: Grammatica linguae Anglicanae
• 1687: Institutio logicae

Notable Quotes

These Imaginary Quantities (as they are commonly called) arising from the Supposed Root of a Negative Square (when they happen) are reputed to imply that the Case proposed is Impossible.

Sources

• John J. O'Connor and Edmund F. Robertson: "John Wallis": MacTutor History of Mathematics archive

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.12$: Wallis's Product: Footnote $1$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Wallis, John (1616-1703)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Wallis, John (1616-1703)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Wallis, John (1616-1703)