In the article The 'Useless' Perspective That Transformed Mathematics Kevin Hartnett explains representation theory thus:
Representation theory is a way of taking complicated objects and “representing” them with simpler objects. The complicated objects are often collections of mathematical objects — like numbers or symmetries — that stand in a particular structured relationship with each other. These collections are called groups. The simpler objects are arrays of numbers called matrices, the core element of linear algebra. While groups are abstract and often difficult to get a handle on, matrices and linear algebra are elementary.
A financial report is a complicated object that can be represented using simpler objects. The Logical Theory Describing Financial Report describes those objects and the relations between the objects.
You can represent all of those objects using XBRL, see this PROOF BASELINE. The PROOF BASELINE can be reconciled to high quality financial reporting schemes such as US GAAP, IFRS, UK GAAP, Australian IFRS, etc.
All this yields a more modern approach to accounting, reporting, auditing, and analysis.
Folks, fundamentally all this is math.