CALCULUS Understanding Its Concepts and Methods

Giuseppe Peano (1858--1932) --- Historical Sketch

Giuseppe Peano was born in 1858 on a farm in Italy. When his uncle, who was a priest, recognized that the boy was talented, the uncle took him to Turin for his secondary school years. When he graduated in 1876, he entered the University of Turin. He took analytic geometry and algebra in the first year. In his second year, he took calculus and descriptive geometry. He was the only student to continue with pure mathematics in the third year, taking analysis and geometry. In his fourth year, he took another geometry course and a course in mechanics. At the end of this, in 1880, he was awarded his doctorate and became a member of the mathematics staff at the University of Turin. Within the first two years as an assistant to a professor, he published four research papers in mathematics.

He then assisted in editing, and contributed in writing, a textbook entitled Course in Infinitesimal Calculus. He became a professor in late 1884 at age 26. Two years later, still teaching at the University of Turin, he began also to teach at the Military Academy in Turin. In 1888, he published a book entitled Geometrical Calculus. The first chapter of that book is on logic and the book also contains the first definition of a vector space. The next year, he published his famous axioms, more familiarly known today as Peano's postulates, for defining the natural numbers. A year later, he constructed his famous "space-filling curve," a continuous curve that passes through every point in a square.

The space-filling curve flew in the face of the standard idea of dimension wherein it takes two numbers to locate a point in a plane region. Since a continuous curve can fill a square, you can locate a point in a square using only one number. You can imagine what a furor this caused in the mathematics community.

Peano published more than two hundred mathematics books and papers. He died of a heart attack in the spring of 1932.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.