Vorstellung

Vorstellung is a German noun with several related meanings stemming from the verb vorstellen (to present, to introduce, to imagine). In everyday language it denotes the act of introducing someone to another person or presenting something to an audience, as in someone being introduced at a meeting or a product being presented to customers. It also refers to a performance or show, for example a theater Vorstellung that begins in the evening. In a cognitive sense, a Vorstellung can mean a mental image, concept, or notion of something, such as having a Vorstellung of the future or of how a device works.

Etymology and usage notes: Vorstellung combines vor- (before, in front) with stellen (to place, to set). The term is versatile and appears in formal, informal, and professional contexts. In compound forms, it often relates to processes of introducing or presenting, such as Vorstellungsgespräch (job interview) or eine Vorstellung abgeben (to give a presentation).

Mathematical and formal usage: In mathematics and related fields, Vorstellung is used to denote the formal description of a structure by generators and relations, known in English as a presentation. For example, a group G can be described by a presentation G = ⟨S | R⟩, and German texts may say that G wird durch Generators und Relationen vorgestellt. This usage extends to other algebraic structures such as monoids or algebras, where the structure is specified by a chosen set of generators and defining relations.

Nuance and related terms: Vorstellung is often contrasted with Darstellung in German. While both can mean presentation or depiction, Vorstellung emphasizes the act of presenting or imagining, whereas Darstellung focuses more on the depiction or portrayal itself.