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John Nash, the subject of Sylvia Nasar’s biography A Beautiful Mind, stands out as a mathematician because of his profoundly “independent” nature. Whereas other mathematicians seek to collaborate with others, building on the work of established scholars, Nash prefers to return to problems that established mathematicians haven’t been able to solve—discovering insights that they might have missed by looking back over their work and coming up with new methods for solving these complex problems. While Nash’s independence makes him a daring and highly original thinker, it is also a fatal flaw. For much of his life and career, Nash…