Born: November 23, 1616
Died: October 28, 1703
in Ashford, Kent,
in Oxford, England
Savilian Professor of
of Wallis' Contributions
Wallis vs. Hobbes
Wallis' arch rival, Thomas Hobbes, was vociferiously devoted to
deductive reasoning based on Euclidean structures; thus, Hobbes refuted
all proof based on induction.
more pragmatic. He won respect by showing Hobbes' attempts to
"square the circle" were not possible.
Today mathematicians accept Hobbes' assertion that a rule that holds
for a certain number of cases says nothing about whether it will hold
for other cases not tested. Yet Wallis' premise of induction
opened the door for experimental scientists in the Royal Society to
move forward with different methods of investigation.
In his Treatise on Algebra
(1685), Wallis writes "not so much to shew a Method of Demonstrating
things already known . . . . as to shew a way of Investigation of finding out things
- Algebraic Notation
Wallis' rather unorthodox use of infinitesimal mathematics involved
ideas from Cavalieri, Torricelli, Fermat, Bacon and others. Thus
we find symbols for communication of powerful ideas in his
NCB thanks the Huntington Library, San Marino, California, for the image of Wallis.