The Romans were already inside the walls of Syracuse, moving house to house, and an old man sat on the ground in the middle of it, bent over figures he had drawn in the dust. He was past seventy. He did not look up. Plutarch says he had fastened his mind and his eyes on the diagram, and never noticed the soldiers had entered, never noticed the city had fallen.

A soldier stood over him and ordered him to come. Archimedes asked to finish the problem first. And the soldier, ignoring his plea to finish the problem, killed him on the spot.

For two years, Archimedes helped hold Rome off with devices of his own design. Levers, cranes, and hooks that could lift a ship and drop it. Rome, master of the world, stalled outside Syracuse in part because a single-minded geometer solved one hard problem after another. He gave one problem everything he had, then the next, then the next.