Math is definitely needed to craft an airplane. There are a lot of calculations that need to be used to make sure the plane flies correctly and can support all the people on board. We need to make sure flying is as safe as possible and to do that we need to do a lot of calculations.
Not being either a scientist or an engineer, I can not say for sure but it seems to me that good engineering requires good mathematical computation. If we do not have good engineering that is precisely calculated, then I for one would not want to fly anywhere in that airplane that was created.
Engineers can't craft an airplane without mathematical computation because this isn't some sort of guessing game. By guessing at the dimensions of the plane, engineers would craft death machines that plummet into the ground soon after takeoff. For obvious reasons, engineers need to avoid such a consequence to keep people safe.
I believe it is impossible to craft a real, flying, and functional airplane without mathematical computations. Airplanes require some strict features that rely on trajectory and wind resistance, among other things. These things are most accurately judged through mathematical computations and without them, I feel as though an airplane would be less likely to function properly.
Mathematical computation would be needed to craft an airplane, let alone anything. That is a huge part of where geometry and algebra come in. You need to find the right dimensions to make everything balance together perfectly. Sometimes you can't find one angle so you use algebra to find out what is missing.