What would cause a mathematician to streak naked in public? According to a twenty-five-hundred-year-old legend, it takes nothing more than a great idea.

As the story goes, Archimedes had a problem: how to compute the volume of an irregular object, namely, the king's crown. The king wanted to know whether his royal helmet was made of pure gold or was of the fool's variety, a mixture of silver and gold. His question was whether the maker of the crown had cheated him. Archimedes was stumped. Not until he stepped into his bath, thereby causing the water to overflow, did he realize that he could use water displacement to compute volume. At this point he famously shouted Eureka! ("I have found it") and subsequently ran through the streets of Syracuse naked with excitement (or so the story goes). The question is, Where did the idea come from? (And why didn't he get dressed first?) Even more puzzling, why did the idea appear to Archimedes at a time when he was likely not focused on attempting to solve the problem (or was he?). Could it be that we are more creatively insightful when we are less deliberately thoughtful about the very problem we are attempting to solve? Do we create more by thinking less? The anecdotal evidence does make one wonder. It appears that great ideas are like in-laws: they show up unexpectedly. But are big ideas really that random? Archimedes, like many other innovators, actually knew much more than one would be led to believe. For example, ...

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