Archimedes discovered how to calculate the volume of a sphere, and even wanted this diagram on his tombstone. He made so much progress in this area that nothing could be added for 18 centuries. main objective of this lecture is to present on Archimedes: Blast From the Past in Mathematics. Archimedes designed many tools for defending Syracuse from invasion. This is a model of how one of Archimedes war gadgets may have worked. He used mirrors to reflect and intensify the sun, causing the ships to catch on fire.