Charles is Nash's British roommate. He is majoring in English and refers to himself as the "Prodigal Roommate." Later in life, Charles cares for his niece, Marcy.
It is revealed that Charles is actually a figment of Nash's imagination, but he is much more of a positive influence than Parcher, who plays on Nash's vanity and paranoia. Charles is supportive of Nash in that he's a source of companionship during Nash's early Princeton days, when his arrogance and awkwardness alienate him from peers. Charles is particularly supportive at times when Nash needs courage to deal with social situations. We see this most prominently when Charles encourages Nash to propose to Alicia.
Initially a student in one of Nash's classes, Alicia pursues him romantically, and they eventually marry and have a child. As Nash's wife, she is certainly the most important and strongest source of support for him. Early on, we see how her charm and assertiveness complement Nash's retiring manner when she politely asks groundskeepers to work somewhere else while Nash is teaching.
Alicia is strong enough to recognize Nash needs help and commits him involuntarily to Dr. Rosen's care. She bears with Nash's illness, though we can see it is difficult for her, as Nash is out of work, unhelpful with childcare and household tasks, and unresponsive to her sexually (a consequence of his medication). She only comes close to leaving when she fears for her safety and that of their child, but the threat of losing her is what makes Nash confront his illness. Finally, Alicia supports him when he begins coping with schizophrenia without medication. This is perhaps the most admirable support she gives, as Nash's approach is strongly discouraged by his doctor.
Hansen is initially Nash's greatest rival at Princeton. He is the co-recipient, along with Nash, of a prestigious scholarship. Charming and personable, Hansen enjoys greater success in the academic world and eventually becomes head of the mathematics department. Later in the film, we see that Hansen has come to respect Nash's brilliance as a theoretician. He also shows genuine concern for his mental decline.
Years later, when Nash is attempting to regain control of his life, he asks Hansen if he can work in one of the libraries so as to re-immerse himself in an academic environment. Despite initial misgivings, Hansen agrees, and he later supports Nash's return to teaching. When Nash wins the Nobel Prize, Hansen and the other professors honor his achievement by each giving him a pen. This can be interpreted as a tribute to his brilliance but also to his strength, overcoming mental illness.