Aya Sofia Dome

One of the highlights of my recent trip to Turkey was the chance to see the spectacular Aya Sofia in Istanbul. My tour book explains that

The present structure [from 537 AD], whose dome has inspired religious architecture ever since, was designed by two Greek mathematicians -- Anthenius of Tralles and his assistant Isidorus of Miletus, who were able to apply to architecture the enormous strides that had recently been made in geometry. Unfortunately, part of the dome collapsed during an earthquake a mere 21 years later, revealing a fault in the original plans -- the dome was too shallow and the buttressing insufficient.

Here we have a potential instance of a pattern common from the use of mathematics in engineering and design: a mathematical theory fails to be adjusted to the materials or circumstances of application. Exactly what went wrong is unclear, but it is important to keep in mind how rare successful applications of mathematical theories really are.