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Abstract: In 1735, at the age of 28, the Swiss mathematician Leonhard Euler, one of the greatest mathematicians of all time, solved a problem that had thwarted the best efforts of the best mathematicians for nearly a century. In this talk, I'll explain how Euler solved this problem, and how a hundred years later another great mathematician, Bernhard Riemann, picked up his ideas and posed a question that has stumped the best efforts of the best mathematicians to this day. Most of this talk should be accessible to students at all mathematical levels.