I'll let the article (which we are discussing here) speak for itself (my highlighting though):
> accounts of lift exist on two separate levels of abstraction: the technical and the nontechnical. [... The former] exists as a strictly mathematical theory, a realm in which the analysis medium consists of equations, symbols, computer simulations and numbers. There is little, if any, serious disagreement as to what the appropriate equations or their solutions are.
You are misunderstanding what a full solution means and what the article is saying.
There are a systems of equations that allow us to model flight. But they are NOT a full model of flight characteristics, as a consequence of, like mentioned, lack of a full solution to the Navier Stokes equations
> The solutions of those equations and the output of the CFD simulations yield pressure-distribution predictions, airflow patterns and quantitative results that are the basis for today’s highly advanced aircraft designs. Still, they do not by themselves give a physical, qualitative explanation of lift.
> accounts of lift exist on two separate levels of abstraction: the technical and the nontechnical. [... The former] exists as a strictly mathematical theory, a realm in which the analysis medium consists of equations, symbols, computer simulations and numbers. There is little, if any, serious disagreement as to what the appropriate equations or their solutions are.