Engineering the Impossible

Gothic cathedrals relied on engineering that wasn't fully understood mathematically until the nineteenth century. Flying buttresses carried the weight of stone vaults outward and down, freeing walls from their load-bearing job so they could be replaced almost entirely with glass.

Master builders had no formal engineering training. They worked from practical geometry and workshop knowledge passed from master to apprentice. When experiments failed — and they did, spectacularly — collapsed vaults taught lessons that surviving buildings absorbed.