1. Please indicate which equations of theoretical aerodynamics (more precisely, fluid dynamics) have been refuted over time? The physical and mathematical basis is mostly just being extended. Yes, the empirical approach is still very common - not everything can be simulated, wind tunnel experiments are extremely important. But very often a calculation is sufficient for an accurate estimation of the parameters of a phenomenon.The equations are not a constant they are based on what is known about what is available, but material science is evolving too.
2. Materials science is poorly related to aerodynamics; in this thread we only consider the contribution of the latter.
How long would it take to develop the F-35 using a purely empirical approach for aerodynamic optimization nowadays?If you gave all the plans for an F35 to Wilbur and Orville Wright in 1903 they would be impressed but they couldnt build one, and probably couldnt get one built in their lifetimes.