John Nash was a thinking child, discovering his love of mathematics early. He was a thinking student, abandoning his early plans to become a chemical engineer because "it [engineering] was a matter of doing work neatly rather than thinking." He was a thinking adult, developing a win-win approach to game theory that still has wide-reaching effects.
At Carnegie Tech (known today as Carnegie Mellon), John’s professor thought the young mathematician was brilliant:
His graduate professor, R.J. Duffin, recalls Mr. Nash as a tall, slightly awkward student who came to him one day and described a problem he thought he had solved. Professor Duffin realized with some astonishment that Mr. Nash, without knowing it, had independently proved Brouwer’s famed theorem.
Impressed with the student from West Virginia, Solomon Lefschetz offered him Princeton University’s most prestigious fellowship. Nash accepted, at the urging of his professor at Carnegie, John Synge.
At Princeton, the young scholar was surrounded by other geniuses. There was Albert Einstein, later designated "Person of the 20th Century," although he had been a grade-school failure. There was John Louis
von Neumann, whose game theories Nash later took to a different level of analysis and whose "supercomputer ideas" greatly
contributed to the "Manhattan Project" work at Los Alamos. And there was Lefschetz, a "towering genius" who, according to his students, never came up with an incorrect result or a correct proof!
It was, to put it mildly, a rarefied world.