Full Idea
Denoting phrases are central to mathematics, especially in Russell's 'logicist' theory, in which they are crucial to identifying classes ('the class of all mortal beings', 'the class of natural numbers').
Clarification
'Denoting' is the same as reference. 'Logicism' reduces arithmetic to logic.
Gist of Idea
Denoting is crucial in Russell's account of mathematics, for identifying classes
Source
report of Bertrand Russell (On Denoting [1905]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.6
Book Reference
Monk,Ray: 'Bertrand Russell: Spirit of Solitude' [Vintage 1997], p.175
A Reaction
This explains the motivation for Russell's theory of definite descriptions, since he thinks reference is achieved by description. Russell nearly achieved an extremely complete philosophical system.