MATHEMATICAL METHODS AS COGNITIVE PROBLEM‐SOLVERS

The applications of mathematics to the solving of factual problems should run in a certain prescribed form called a mathematical method. Whereas a mathematical method is an only scheme that is a set of mathematical means, rules, hints, procedures, etc. how to solve a factual problem on some body of data, it becomes a Cognitive Problem‐Solver after its implementation on an appropriate computer which is able to solve, if need be, by the help of man, a class of special cognitive problems corresponding to the method arising out of their background and initial knowledge. Computer and man can act here in a symbiotic manner as intelligent agents, realizing each alternately the sequence of conceptual operations prescribed by the given method. The incidental difference between the routine and creative actions of the single agents is discussed, as well as the advantages of natural and artificial intelligence in automatic problem‐solving and automatic cognition.