Philosophical Mathematics of Isaac Barrow (1630-1677). Conserving the Ancient Greek Geometry of the Euclidean School

Author: Gillette, Gregory
Isaac Barrow largely responsible for that preservation and promulgation of the Euclidean tradition which, on the one hand, invigorated the physical science and mathematics of Newton and others, and on the other hand, allowed for an ongoing engagement with classical Greek mathematics, which continues down to the present day. Barrow’s philosophy of mathematics remains relevant to many key issues still at the forefront of modern philosophies of mathematics.


“. . . with painstaking academic rigor, demonstrates the necessary philosophical connections among words, ideas, and things by means of the important study of mathematics, particularly as regards the inescapable relationship between the legacy of mathematical theory and the question of geometrical reality.” – Prof. Eric Grabowsky, University of Mary

“Especially valuable is Gillette’s exposition of how Barrow’s classical geometrical knowledge informed that work. Gillette shows the reader how Barrow was able to geometrically demonstrate the Fundamental Theorem of the calculus, without using the more modern formalism of limits and limit notation, or any of the new mathematical concepts introduced by Leibniz or Barrow’s student Newton (such as fluxions).” – Prof. Gary Jason, California State University, Fullerton

Table of Contents

Preface by Eric Grabowsky
1. Euclid’s Legacy
2. Geometry and the Fundamental Theorem
3. Arithmetic as Geometry
4. The Geometry of Space and Time
5. On the Generation of Magnitude