Navier-Stokes equations
Now that is a very unfair thing to do bringing them into play.
We used to do a exercise in the lab in the wind tunnel.
Various cross sections and angles etc.
And yes you could get a plank of wood to fly but you got lots of votex shedding and it was pretty crap. And virtually impossible to get any trailing edge controls to work in the turbulent flow. But you needed relatively little mass flow to get a reasonable up force.
Now a pure areofoil with zero angle didn't produce much lift but had very good drag characteristics the flow was laminar and trailing edge controls worked a treat.
As with most things looking at nature has given the optimised shape for the most energy effective design.
Personally I think newton does the bulk of the job. The fancy shape lets you control and lower the drag into a cost effective machine.
MJ