Wallis was one of the most original mathematicians of the seventeenth century and he left his mark on mathematics in many ways. He introduced arithmetical limits into mathematics (his famous infinite-product expression for $\pi$ is an example). His researches (for example, the means whereby he obtained the aforementioned product) led directly to Newton's work on the binomial theorem and quadratures. He was the first to see the significance of fractional and negative exponents, and he is responsible for the introduction of such symbols as $\infty$ and such terms as hyper geometric series. He was very influential politically, very quarrelsome, and at the center of the scientific life of his time (for instance, it was owing to his advice that the Gregorian calendar was not introduced earlier into England, as he did not like the Pope). This second edition includes Foreword by E. N. da C. Andrade, a Bibliography and an Index.
Early life and training The beginnings of the Royal Society. Wallis's part in its early history. Appointment as Savilian Professor of Geometry The treatise on the conic sections The Arithmetica Infinitorum The Mathesis Universalis. The Commercium Epistolicum (1657/8). Controversy with Fermat and other members of the French Mathematical School Appointment as Custos Archivorum. The quarrel with Doctor Holder The Mechanica, sive Tractatus De Motu The Hooke-Hevelius dispute. Publication of ancient manuscripts The Treatise of Algebra The dispute with Hobbes summarised Conclusion. Importance of Wallis's work to succeeding generations Appendix I. Brief biographies of Wallis's contemporaries and immediate predecessors, who are mentioned in this work II. Some observations on the development of notation during the seventeenth century, with specimens of notation then current III. List of Wallis's mathematical works, including his contributions to the Transactions Bibliography Index.