Archimedes of Syracuse is one of the WorldGeniuses by anyone's definition. His work on the area and volumes of surfaces and solids is a hair's breadth away from being TheCalculus?, which makes him, oh, about 2000 years ahead of his time. Definitely a strong contender for the smartest human that ever lived.
Actually, to give credit where it is due: the method of exhaustion originated with EudoxusOfCnidus?, not Archimedes. In fact, Eudoxus is also responsible for the theory of proportions and EuclidOfAlexandria drew heavily off of him. But he is rarely mentioned since none of his writings survived. - Addendum: some sources I've read say Eudoxus wasn't the originator either.
In short - great people are usually on the ShouldersOfGiants. Others tend to stand on each others' toes. (or in each others' footprints.)