Background
It's not always very clear when the first real database management system was formally conceived and implemented. Ever since Babbage invented the first complete Turing computing system (the Analytical Engine, which Babbage never really managed to get built), we have known that computers would always need to have some kind of memory. This will be responsible for dealing with the data upon which operations and calculations will be executed. But when did this memory evolve into a proper database? What do we mean by a database anyway?
Let's tackle the latter question first. A database can be described as any kind of organized collection of data. Not all databases require a management system—think of the many spreadsheets and other file-based storage approaches that really don't have any kind of real material oversight imposed on it, let alone a true management system. A database management system, then, can technically be referred to as a set of computer programs...