Algorithmic Difficulties Since the 1950s

Abstract

We review mathematical approaches to complex engineering problems since the 1950s including rule systems of artificial intelligence, pattern recognition, neural networks, model systems, fuzzy systems. As soon as computers become available in the 1950s, solving complex engineering problems was closely tied with understanding working of the mind. In the 1950s many scientists and engineers were sure that soon computer intelligence would far exceed that of the human mind. It did not happen. In this chapter we consider difficulties faced by algorithms and neural networks designed for modeling the mind and for solving complex problems; we analyze these difficulties and relate them to the fundamental inconsistency of logic discovered by Gödel in the 1930s.