This is the first success at a Gothic cathedral, correct?
If so, how did they apply their knowledge to physics, etc to determine the needed material for this wonderful architecture?
Well Gothic architecture didn’t just pop out of no-where! Over the centuries, knowledge of church construction (and what materials were needed) was passed down, technical skills of architects increased, more design was included, and it gradually developed into the Gothic style.
Before they began work on Gothic cathedrals, they would have small-scale models, just to see if the design was stable. And the construction was largely trial-and-error. Don’t think that nothing ever went wrong!
The materials used in Gothic architecture depends on the country (although they are largely made from stone). France (where the style developed) had fine limestone, which they found through experience, was good for buildings with detail. In England they used a lot of marble and sandstone. Italy used stone and marble. Whereas in Northern Europe, they used a lot of brickwork.