For many years, large buildings with impressive spans between the building columns were erected without precisely calculating what loads the columns, walls, and buttresses would have to support. Load on a building is a complex calculation taking in account the weight of the roof and potential snow, the size and spacing of columns, how building members are braced, and in modern times wind loads and seismic forces.
I have read that the architects of Gothic cathedrals were not able to calculate with any accuracy the size and number of columns and flying buttresses they needed to support a given design. They worked from geometry, rules of thumb, and prior experience.
At what point in history did mathematics begin to make building design more predictable and foolproof? I suspect that at some point algebraic equations replaced geometry and that after the advent of calculus, the section modulus of various shapes began to be understood, but I cannot seem to find information as to where and when these things happened. A good answer would point out which mathematical concepts were first used rigorously in structural design and also what notable buildings were the result of this more formalized process.