In mathematics, the concept of essence can be replaced by the concept of a characterizing property — a property unique to a given entity or structure within a family of such entities
characterizing property(Introduced by Steiner to replace the notion of essence or essential property in mathematical contexts, where all truths are necessary)
A property unique to a given entity or structure within a family or domain of such entities or structures
entity(as used in metaphysics)
Any individual thing or being that exists—could be a person, object, or anything else that is one distinct thing.
essence(Medieval realist metaphysics)
The defining nature of a species, held by some to be distinct from and capable of surviving the destruction of all individual members of that species
Steiner proposed his model of mathematical explanation in 1978a. In developing his own account of explanatory proof in mathematics he discusses—and rejects—a number of initially plausible criteria for explanation, e.g. the (greater degree of) abstractness or generality of a proof, its visualizability, and its genetic aspect that would give rise to the discovery of the result. In contrast, Steiner takes up the idea “that to explain the behaviour of an entity, one deduces the behavior from the ess