The three illusions represent his three kinds of desires. The first one is his roomate. He filled his loneliness, shared his confusion and showed up whenever Nash needed him. It represent a unbetrayed friendship. The second one was his friend's niece, a beautiful little girl who lost his father and never growed up. She represent a feeling of dependency. The last one was a military person who requested Nash to decipher Russian code. This represent a self-actualization. He was eagar to be successful so he imagined some tough work to do. And he resisted to these works subconciously.
I think his best achievement is not win Nobel Prize but married this woman who didn't abandon him even he suffer heavy schizophrenia. What a great woman. Withour her 30-year industrious care, Nash may won't get over his illness.
In American academic world, giving a pen to others to show your great respect to him. At last, i was touched to see so many professors to give pen to Nash. His life was difficult but successful.