the Nash equilibrium
John Nash, about whom the film A Beautiful Mind was released in 2001, arrived at Princeton in 1948 recommended by his Carnegie professor with the words this man is a genius on the basis of a 27-page dissertation completed at the age of 21.
Two years later, this precociously brilliant youngster published a mere two-pager giving the Nash Equilibrium, now a cornerstone of game theory. Initially John von Neumann was dismissive of Nash's reasoning, but its very simplicity led to proof that equilibrium can exist with many players of conflicting and common interests, and in a wide variety of interactions.
Other mathematicians, recognising the originality and value of the Nash Equilibrium, soon devised the Prisoner's Dilemma to illustrate it. Nash himself recovered after years of debilitating mental illness, was awarded the Nobel Prize in Economic Sciences in 1994. An interview with him can be seen at www.nobelprize.org.