Mathematical Intuition (Poincaré, Polya, Dewey)

Abstract

Practical calculation of the limit of a sequence often violates the definition of convergence to a limit as taught in calculus. Together with examples from Euler, Polya and Poincare, this fact shows that in mathematics, as in science and in everyday life, we are often obligated to use knowledge that is derived, not rigorously or deductively, but simply by making the best use of available information- plausible reasoning. The "philosophy of mathematical practice" fits into the general framework of "warranted assertibility," the pragmatist view of the logic of inquiry developed by John Dewey. [ABSTRACT FROM AUTHOR] Copyright of Montana Mathematics Enthusiast is the property of Information Age Publishing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)