John Wallis Was Born On November 23, 1616 In Ashford, Kent,
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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
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.
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John Wallis, Mathematics education in the United Kingdom, Thomas Hobbes, Ren Descartes, Calculus, Cavalieris principle, Integral, Pi, Savilian Professor of Geometry, Wallis, Geometry, HobbesWallis controversy
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