Bolzano in the New Millennium

Dr. Claudio Morales

Department of Mathematical Sciences
University of Alabama in Huntsville

March 9, 2001

Abstract

As we well know, the solvability of nonlinear equations has awakened interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3,000-300 BCE). However, we intend to bring to our attention that some of the problems studied nowadays first arose during the time of Bolzano's era (1781-1848). Indeed, this Czech mathematician has rigorously proven a well-known result, which can be found in every Calculus textbook today. Incidentally, this result is intimately related to various classical theorems studied nowadays. We will give a historical approach to see how the original problem has evolved in time.