Intuitions and Schemata in Mathematical Reasoning

The present paper is an attampt to analyze the relationship between intuitions and structural schemata. Intuitions are defined as cognitions which appear subjectively to be self-evident, immediate, certain, global, coercive. Structural schemata are behavioral-mental devices which make possible the assimilation and interpretation of information and the adequate reactions to various stimuli. Structural schemata are characterized by their general relevance for the adaptive behavior. The main thesis of the paper is that intuitions are generally based on structural schemata. The transition from schemata to intuitions is achieved by a particular process of compression described in the paper.This revised version was published online in September 2005 with corrections to the Cover Date.