Among many great deeds we attribute to Archimedes of Syracuse, there are some which probably never happened. One of them, frequently appearing in many famous history books, is a myth that during the Roman siege of the city of Syracuse, Archimedes allegedly burned roman warships by sunlight, reflected by complex system of mirrors.
Modern engineers have proven during attempts to recreate this feat, that it’s impossible to burn ships with reflected sunlight, even when using present-time technologies. Even when the Mythbusters tested this myth in three full episodes of their show, they never achieved the desired effect of ships catching fire.
Greek historian Plutarchos, who depicted many other great inventions of Archimedes in his books, including catapults and special cranes, designed to drag roman ships to craggy coastal rocks, never mentioned the Death Ray in any way. It was mentioned for the first time in scriptures by Anthemius of Tralles, one of the architects of Hagia Sophia, and then another 600 years later in the Chronicles of the World by monk Johannes Zonaras.
Nevertheless, fire-starting mirrors were well-known by Archimedes’s time. Romans themselves often used them to start ceremonial fires in temples, and we can’t rule out the possibility that Archimedes really thought about aiming them on enemy ships. But even if he had thought about that before, he would most likely dismiss the idea, because it was impossible to achieve with the technologies in ancient Greece.