John Wallis was born on November 23, 1616 in Ashford, Kent,

England.When Wallis moved from his school in Ashford to Tenterden, he

showed his potential for the first time as a scholar. In 1630 he went to Felted

where he became proficient in Latin, Greek, and Hebrew. He later went to

Emanual College Cambridge and became first interested in mathematics.

Because nobody at Cambridge at this time could direct his mathematical

studies, his main topic of study became divinity and was ordained in 1640.


During the Civil War, Wallis was so skilled in cryptograghy that he

decoded a Royalist message for the Parliamentarians. Because of this, it was

suggested that he was appointed to the Savilian Chair of geometry at Oxford

in 1649. The then holder of the chair, Peter Turner, was dismissed and

Wallis held the chair for over 50 years until his death.


In London there was a group that was interested in natural and

experimental sceince that Wallis was a part of. The group became the Royal

Society and Wallis is a founder member and one of its first Fellows.


Wallis greatley contributed to the beginning of calculus and the most

influentail English mathematician before Newton. He studied the works of

Kepler, Cavalieri, Roberval, Torricelli, and Descartes. He then went to

introduce ideas of the calculus going beyond that of these other authors.


In Arithmetica infinitorum, around 1656, Wallis evaluated the integral

of (1-x2)n from 0 to 1 for integral values of n, building off of Cavalieri's

method of indivisibles. In an attempt to compute the integral of (1-x) from 0

to 1, he devised a method of interpolation. While using Kepler's concept of

continuity he discovered methods to evaluate integrals that were later used by

Newton in his work on the binomial theorem.


Wallis also established the formula
3.14/2=(2.2.4.4.6.6.8.8.10...)/(1.3.3.5.5.7.7.9.9...)


During 1656 Wallis described the curves that are obtained as cross

sections by cutting a cone with a plane as properites of algebraic coordinated

without the embranglings of the cone in his Tract on Conic Sections. He

followed methods in the style of Descartes' analytical treatment.


Wallis was an important early historian of mathematics and in his

Treatise on Algebra he has a wealth of historical material. The most

important feature of this work, appeared in 1685, is that it brought to

mathematicians the work of Harriot in a clear exposition. Wallis accepts

negative roots and complex roots in Treatise on Algebra. He shows that

a-7a=6 has exactly three roots and that they are all real. He criticises

Descartes' Rule of Signs stating correctly, that the rule which determines the

number of positive and the number of negative roots by inspection is only

valid if all the roots of the equation are real.


Wallis introduced our symbol for infinity.


Wallis also restored some ancient Greek texts such as Ptolemy's

Harmonics, Aristarchus's On the magnitudes and distances of the sun and

moon and Archimedes' Sand-reckoner.


His non-mathematical works include many religious works, such as a

book on etymology and grammar Grammatica linguae Anglicanae along with

a logic book Institutio logicae.


Wallis had a bitter dispute with Hobbes, who was a fine scholar and

far from Wallis's class as a mathematician. In 1655 Hobbes claimed to have

discovered a method to calculate the area of a circle by integration. Wallis's

book with his methods was in press at the time and he refuted Hobbes's

claims. Hobbes replied with a pamphlet Six lessons to the Professors of

Mathematics at the Institute of Sir Henry Savile. Wallis then replied with

the pamphlet Due Correction for Mr Hobbes, or School Discipline for not

saying his Lessons Aright. Hobbes wrote the pamphlet The Mards of the

Absurd Geometry, Rural Language etc. of Doctor Wallis to Wallis. The

dispute continued for over 20 years, becoming extended to include Boyle,

and ending only with Hobbe's death. John Wallis later died in Oxford,

England on October 28, 1703.