Allthough modern CAD software seems to do magic, the geometry formulae behind are quite simple and can typically be solved geometrically. One of the first lessons engineers took in the past was how to dertime the intersection of two cylinders just be use of a ruler, pen and sheet of paper. It really is not black magic.
the numbers come out of equations although
Or out of diagrams or Nomograms some clever scientist were coming up with.
In old style manufacturing you anyway required simple 2D drawings, for example to do a sheet metal cutout. You needed some simple basic geometry data to build your rigs, jigs and templates. So were used to already design that way, you defined your geometry in a way that you can determine the intersections and shapes you needed.
Today you design however you like (and however Nastran gives you some nice results) and then you hae to mill the part from a huge block of metal or (in the very near future) 3D print it. Old school engineers always designed with production and strength calculation in mind. They designed shapes for which reliable stress/strain/stiffness/buckling formula were existing and which were easy (and precise) to manufacturer. Many Details on the drawings were actually just "artists impression", as they did not define actual dimensions. Especially rounded sahpes (e.g. of a fuselage nose) were somehow accidental and high tolerance between frames / stringers, as the exact shape simply does not matter. Today in CAD you have to define all shapes exactly, as the computer can not deal with "some arc between these two points", it needs to know everything exactly. Much more exactly than it can finally be manufactured...
There are great benefits of modern technology CAD/CAM/FEM tools, but when it comes to initial design, to get quick estimates, to decide whether something can be realistically done or is practically impossible, old style scratch and simple formula technique work still great. If you want to optimize the last kg of dead weight out of an aircraft, modern tools are perfect. If you want to have a quick estimate, they fail.