Mechanics-based mathematical studies proving spontaneity of post-impact WTC towers collapse

The cause of collapse of the World Trade Center (WTC) in New York on 9/11/2001, clarified mathematically by mechanical analysis, has been questioned by some lay critics without any meaningful calculations. They blame the collapse on controlled demolition, implying some sort of conspiracy. The present article summarizes the reasons why the collapse must have been spontaneous and an inevitable result of the aircraft impact damage and the subsequent fire, and how the collapse is explained by mathematical analysis based on mechanics and confirmed by all the available observations.