Algebra is an abstraction over arithmetic, which is an abstraction layer over counting. Or at least that is the abstraction I am using today after reading the article.

As a nitpick, I am not convinced that arithmetic is prior to geometry - e.g. Stonehenge and celestial navigation require geometric abstractions but not arithmetic. "Fabricate bricks until I tell you I have enough" is a more reliable logistical model for the construction of Rome's aqueducts than "provide x bricks for each of the y miles."