Archimedes of Syracuse was a mathematician, inventor, engineer, and stronomer.  He gave the world of antiquity and ultimately the world the principles of hydrostatics (which come down to us today in the Archimedes screw), the method of 'exhaustion' to calculate areas encompassed by curves and the value of pi (reflected in modern calculus), and a mathematical understanding of buoyancy - which resulted in his running through the streets of Athens naked shouting "Eureka" (Greek for "I have found it").

In 212 BCE, during the Second Punic War, the city of Syracuse was captured by the invading Romans following a two year siege.  At the time, Archimedes was engrossed in a mathematical problem, contemplating its geometry.  Approached by one of the invading Roman soldiers, and asked to accompany him to General Marcellus, Archimedes responded "Do not disturb my circles", and continued in his mathematical cogitation - whereupon he was slain.

The first geek to die for a math problem.