Algorithms: From Al-Khwarizmi to turing and beyond

Abstract

The foundational work of Alan Turing and contemporaries on computability marked a turning point in the development of mathematical sciences: It clarified in a rather absolute sense what is computable in the setting of symbolic computation, and it also opened the way to computer science where the use of algorithms and the discussion on their nature was enriched by many new facets. The present essay is an attempt to address both aspects: We review the historical development of the concept of algorithm up to Turing, emphasizing the essential role that logic played in this context, and we discuss the subsequent widening of understanding of “algorithm” and related “machines”, much in the spirit of Turing whose visions we see realized today.