Got it. I volunteer to move out of this discussion because you could have as well said that primary purpose of stairs had something to do with going up or down?
Most architecture around the world from Eiffel tower to Pyramids to Angkorvat has something to do with proving a point. Usually the point is that 'we have achieved this engineering marvel, we have the capability to build this'.
By your logic people possibly got to Eiffel tower or Golden gate by simple pattern and repetition, even experimentation, devoid of any math. That's just plain stupid.