Fixed Point Theory and Applications 
Volume 2004 (2004), Issue 3, Pages 243-250
doi:10.1155/S1687182004310053

The aftermath of the intermediate value theorem

Raul Fierro,1 Carlos Martinez,1 and Claudio H. Morales2

 1Departmento de Matemáticas, Pontificia Universidad Católica de Valparaiso, Casilla, Valparaiso 4059, Chile
2Department of Mathematics, University of Alabama in Huntsville, Huntsville 35899, AL, USA
Received 28 October 2003; Revised 27 January 2004

Abstract

The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000–300 B.C.E.). However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (1781–1848). Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.