# 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

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*Treatise of Angular Sections* (unpublished for forty years after it was written)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

- 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): Entry:**Wallis, John**(1616-1703) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Wallis, John**(1616-1703) - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Wallis, John**(1616-1703)