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This fourth volume in "The Works of Jakob Bernoulli" centers on "Positiones de Seriebus Infinitis" whose five sections were defended from 1689 to 1704 by Bernoulli's students in dissertations. It represents what was probably the first systematic investigation of the summation of infinite series. In notes supplemental to the dissertations (Epimetra) contemporary questions in mathematics, the natural sciences and philosophy are addressed. In four journal articles, Bernoulli applies his theory of series methods to classic problems in Cartesian geometry as well as to the computation of compound interest. Furthermore, thirty preliminary papers (Meditationes) on Bernoulli's theory of series, taken from his scientific diary, appear here in print for the first time, as does his Vice-chancellor speech of 1701 tracing the study of cycloids. The paper illuminates Bernoulli's "modern" views on scientific methodology. Editor and famed French mathematician André Weil places Bernoulli's work on the theory of series on a broad evolutionary curve that extends from Oresme and Cusanus through Mengoli, Mercator, James Gregory and Wallis to the consolidation of the field by Euler and Abel. ... Read more

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From the reviews:

"…All of Weil’s works except for books and lecture notes are compiled here, in strict chronological order for easy reference.

But the value … goes beyond the convenience of easy reference and accessibility. In the first place, these volumes contain several essays, letters, and addresses which were either published in obscure places (…) or not published at all.

Even more valuable are the lengthy commentaries on many of the articles, written by Weil himself. These remarks serve as a guide, helping the reader place the papers in their proper context. Moreover, we have the rare opportunity of seeing a great mathematician in his later life reflecting on the development of his ideas and those of his contemporaries at various stages of his career.

The sheer number of mathematical papers of fundamental significance would earn Weil’s Collected Papers a place in the library of a mathematician with an interest in number theory, algebraic geometry, representations theory, or related areas. The additional import of the mathematical history and culture in these volumes makes them even more essential."

Neal Koblitz in Mathematical Reviews

"…André Weil’s mathematical work has deeply influenced the mathematics of the twentieth century and the monumental (...) "Collected papers" emphasize this influence."

O. Fomenko in Zentralblatt der Mathematik

Also available:

Volume I (1926-1951) ISBN 978-3-540-85888-1

Volume III (1964-1978) ISBN 978-3-540-87737-0

Customer Reviews (1)

Wonderful reading, will make you smile, if not laugh.
This is a monograph (in English, even though the title is in French) of two lectures given by Andre Weil in the early 60's showing the continuity of Number theory from Euler to Riemmann and beyond. Patrick Gallagher recommended it to me, and I am grateful to him for this.

Weil's lectures are full of witticisms, that perhaps only he could pull off. e.g. Weil claims that Analytic Number Theory is not Number Theory, and says that Hadamard was certainly not a Number Theorist (he knew him well). He also shows Euler's version of the functional equation of the Zeta function and guides the reader through a wonderful historical panorama of people and results related to the Zeta Function. ... Read more