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Mathematical Treasure: Peano’s Vector Calculus

Frank J. Swetz (The Pennsylvania State University)

Giuseppe Peano (1858–1932) was an Italian mathematician who taught for many years at the University of Turin. Peano is most famously known for his work in set theory and mathematical logic. He is responsible for the axiomatization of the natural numbers (Peano’s Axioms, 1889), but he also made many contributions to the field of analysis. In 1888, Peano published Calcolo geometrico (Geometric Calculus), which today would be recognized as “vector calculus.” In 1891, this work was translated into German as Die Grundzüge des geometrischen Calculs.

The “Table of Contents” gives the scope of the text:

These images are obtained through the courtesy of the Columbia University Libraries.

In 1889 Peano published his Arithmetices Principia:

Title page of Peano's 1889 Arithmetices Principia.

First page of Peano's 1889 Arithmetices Principia.

Images from a copy sold by the Manhattan Rare Book Company.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Peano’s Vector Calculus," Convergence (June 2017)