The arch is probably on of the most important design discoveries dealing with math. Its shape allows it to withstand a massive amount of weight without crumbling. It must be meticulously built in order to not fracture under stress. A lot of math is involved.
The bridge is another major design involving mathematics. While it shares many attributes of the arch, it also requires bracing and structural support. It must be meticulously designed and tested by computers to assure that it will stand.
The circle is a mathematically inspired shape that is used in architectere to create a different feeling than that inspired by the square.
Skyscrapers require a lot of mathematical testing to withstand wind shear and the rotation of the earth.
The triangle is the foremost geometric shape that everyone can identify. It is easy to see that these buildings are inspired by the triangle.
It is readily apparent that architecture would not exist without mathematics.