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Correspondence of John Wallis (1616–1703). Vol. 1: 1641–1659. Edited by Philip Beeley and Christoph J. Scriba. With the assistance of Uwe Mayer and Siegmund Probst. (English) Zbl 1029.01022

The Correspondence of John Wallis 1616-1703. Oxford: Oxford University Press (ISBN 0-19-851066-7/hbk). xlvii, 651 p. (2003).
This is the first of a six volume collection of the complete correspondence of John Wallis. The first two of them cover the following years: Vol. 1, 1641-1659, Vol. 2, 1659-1668. The present Vol. 1 starts with Introduction, where a biography of John Wallis is given together with a short characterization of his correspondence. References to and excerpts from the Wallis autobiography, published by Scriba in 1970 are often used. Wallis was a Savilian professor of geometry at Oxford since 1649 until his death and was a founding member of the Royal Society. In addition to serving as a decipherer on the Parlamentary side during the Civil Wars, he prepared the ground for the discovery of infinitesimal calculus by Newton and Leibniz. Little of Wallis’s correspondence in the early 1640s has survived. The present volume mainly contains the correspondence on university affairs, family matters, theological topics, cryptanalysis. The most important part is the scientific correspondence: with Hevelius, Schooten, Oughtred, Gassendi, Huygens, Brouncker, a.o. In 1657-58 Fermat posed the challenges on number theory, which led to an extensive exchange of correspondence. This motivated Wallis to publish the collection of corresponding letters under the title of Commercium epistolicum (1658). Many of these letters are reproduced in this Vol. 1. The following year saw the appearence of Wallis’s Tractatus duo, which contained not only Wallis’s account of, but also his contribution to, the challenge on the cycloid set by Pascal. Two anonymous circular letters by Pascal are included in this volume, together with Wallis’s letters about them to de Carcavi.
The volume is supplemented by biographies of correspondents, lists of manuscripts and letters, and bibliography. All this will be of interest to historians of science and mathematics at all levels, from undergraduates to researchers.

MSC:

01A75 Collected or selected works; reprintings or translations of classics
01A45 History of mathematics in the 17th century
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