Full Idea
The primary aim of our 'Principia Mathematica' was to show that all pure mathematics follows from purely logical premisses and uses only concepts definable in logical terms.
Gist of Idea
We tried to define all of pure maths using logical premisses and concepts
Source
Bertrand Russell (My Philosophical Development [1959], Ch.7)
Book Reference
Russell,Bertrand: 'My Philosophical Development' [Routledge 1993], p.57
A Reaction
This spells out the main programme of logicism, by its great hero, Russell. The big question now is whether Gödel's Incompleteness Theorems have succeeded in disproving logicism.