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 alid 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.
