The a-priori/a-posteriori distinction is essentially: is its truth subject to observation of the world. Most mathematicians will argue that even complex ideas like imaginary numbers are the result of the system of mathematics, and can be arrived at and proved without observing the world. Physics is a-posteriori because the math involved is used to describe the world, and the correct formulas and the truth of the formulas cannot be arrive at without observation. Even if someones work is just performing certain calculations on others work, somewhere, working backwards, observation is necessary. If you start with imaginary numbers, and work backwards to simpler and simpler math, it is purely self referential. You don't need anything other than the base concepts to prove the truth, and the base concepts are true by definition, not by observation. You don't have to see a triangle to know it has three sides. It has three sides because that is the definition of a triangle.