Full Idea
Frege's logicism is the theory that mathematics has no special axioms of its own, but follows just from the principles of logic themselves, when augmented with suitable definitions.
Gist of Idea
Mathematics has no special axioms of its own, but follows from principles of logic (with definitions)
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by David Bostock - Intermediate Logic 5.1
Book Reference
Bostock,David: 'Intermediate Logic' [OUP 1997], p.191
A Reaction
Thus logicism is opposed to the Dedekind-Peano axioms, which are not logic, but are specific to mathematics. Hence modern logicists try to derive the Peano Axioms from logical axioms. Logicism rests on logical truths, not inference rules.