A Few Remarks about Mathematical Intuition

• Authors: Jerzy Pogonowski

Title variants

PL

Kilka uwag o intuicji matematycznej

EN

A Few Remarks about Mathematical Intuition

• Languages of publication: PL

Abstracts

PL

This short note is a summary of the talk given at the Adam Mickiewicz University in Poznań during the conference on Philosophy of Mathematics, III, on October 17, 2011. We suggest to understand mathematical intuition as a collection of (verbalized) judgments constituting the core of the context of discovery in mathematics. Mathematical intuition is present not only in the axioms: it can be observed in mathematical research practice as well. A few examples of mathematical intuition in action are given. We discuss the dynamic character of mathematical intuition, trying to reveal the sources of the corresponding changes of intuitive views in mathematics. There are several such sources, e.g.: paradoxes, new research programs (for instance, the program of arithmetization of analysis), explicit definitons of concepts understood so far in an intuitive way, and - of course - the development of the mathematical knowledge itself. We devote special attention to the distinction between standard, exception, and pathology. Finally, we say a few words about conflicts of intuitions in mathematics.

• Publisher: University of Warsaw, Institute of Philosophy
• Journal: Filozofia Nauki
• Year: 2012
• Volume: 20
• Issue: 2
• Pages: 107-113

Dates

published

2012-06-01

Contributors

author

Jerzy Pogonowski