https://www.scientificamerican.com/article/no-one-can-explain-why-planes-stay-in-the-air/

No One Can Explain Why Planes Stay in the Air

In December 2003, to commemorate the 100th anniversary of the first flight of
the Wright brothers, the New York Times ran a story entitled “Staying Aloft;
What Does Keep Them Up There?” The point of the piece was a simple question:
What keeps planes in the air? To answer it, the Times turned to
John D. Anderson, Jr., curator of aerodynamics at the National Air and Space Museum and
author of several textbooks in the field.

What Anderson said, however, is that there is actually no agreement on what
generates the aerodynamic force known as lift. “There is no simple one-liner
answer to this,” he told the Times. People give different answers to the
question, some with “religious fervor.” More than 15 years after that
pronouncement, there are still different accounts of what generates lift, each
with its own substantial rank of zealous defenders. At this point in the history
of flight, this situation is slightly puzzling. After all, the natural processes
of evolution, working mindlessly, at random and without any understanding of
physics, solved the mechanical problem of aerodynamic lift for soaring birds
eons ago. Why should it be so hard for scientists to explain what keeps birds,
and airliners, up in the air?

Adding to the confusion is the fact that accounts of lift exist on two separate
levels of abstraction: the technical and the nontechnical. They are
complementary rather than contradictory, but they differ in their aims. One
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. The objective of technical mathematical theory is to make
accurate predictions and to project results that are useful to aeronautical
engineers engaged in the complex business of designing aircraft.

But by themselves, equations are not explanations, and neither are their
solutions. There is a second, nontechnical level of analysis that is intended to
provide us with a physical, commonsense explanation of lift. The objective of
the nontechnical approach is to give us an intuitive understanding of the actual
forces and factors that are at work in holding an airplane aloft. This approach
exists not on the level of numbers and equations but rather on the level of
concepts and principles that are familiar and intelligible to nonspecialists.

When I studied aerodynamics on my own I also found that there were
no actual explanations of flight. Not only that, the theories of flight, the
equations, were not actually theoretically based, but rather required empirical
measurements in order to determine the coefficients of lift and drag. In other
words there was no definition of what a wing was.