為何在a beautiful mind 中,他們會贈筆呢??

Many of the specific incidents and life events depicted in the movie do not correspond to anything mentioned in Nasar's biography. "There are many discrepancies between the book and the film," says a Nash FAQ on the Princeton website. For example, the pen ceremony was completely fabricated in Hollywood. No such custom exists."

是虛構的.

It's not real, the scene is to show how people in princeton respect John Nash.

Reason why people giving out their pen to John is that they want to pay their respect to him, as John Nash is quite famous, they must have heard about his schizophrenic problem, mainly referring to his hallucination. (Remember the scene that the noble prize office talked to him outside his classroom and he asked one of his girl students to see if she can see the noble prize officer?) So by giving pens to John, it is the evidence for proofing that they are actually paying respect to him, it'sREAL, not imaginery.