Archimedes

The story about him leaping from the bath was written down some three hundred years later by the Roman architect Vitruvius. There is no contemporary record of it. So we cannot say whether it happened.

What is certain is this. When Syracuse was besieged by Rome, he designed machines for the walls, and those machines delayed the fall of the city by years — hooks that lifted ships and capsized them, engines that threw stones. Roman accounts name him.

And yet he did not count those machines as his achievement. Plutarch wrote that he regarded such devices as a sideline forced on him by circumstance. What he was proud of lay elsewhere.

So he asked for a sphere and a cylinder on his tomb, and they were carved there. A hundred and thirty-seven years later, Cicero — posted to Sicily as a Roman official — recorded finding the grave under weeds. The locals, he wrote, did not know it existed.

That he was killed by a Roman soldier while drawing figures on the day the city fell, and that he said "do not disturb my circles" — these too are later tradition. But every version hands down the same picture: a man drawing on the ground while the city comes apart around him.

The question that remainsIf he wanted a sphere and a cylinder rather than the machines that saved a city — what did 'useful' mean to him?