Mathematician:John Wallis

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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.




  • 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.


Treatise of Angular Sections (unpublished for forty years after it was written)

Restored some ancient Greek texts, for example:

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


  • 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.