Full Idea
Multiplication in itself isn't is intractable. In 1929 Skolem showed a complete theory for a first-order language with multiplication but lacking addition (or successor). Multiplication together with addition and successor produces incompleteness.
Gist of Idea
Multiplication only generates incompleteness if combined with addition and successor
Source
Peter Smith (Intro to Gödel's Theorems [2007], 10.7 n8)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.79