“lesser mortals” and thinking he is above going to classes sets him up for the herculean fall we see in the second part of the movie. An important quote to understand John Nash’s mindset at this point in the film is,

Find a truly original idea. It is the only way I will ever distinguish myself. It is the only way I will ever matter.

While Nash is arrogant, it is tempered in part by his yearning for greatness. He has yet to do anything of significance, and the quest to be great is part of what haunts him for most of the movie. Nash might have thought himself above his classmates, but by the end of the film, he has dealt with many difficulties. His fall from grace and mental breakdown do a lot to make him humble.

By the end of the movie, Nash has many accolades and accomplishments, but he also has hit rock bottom. In his speech at the Nobel prize acceptance, Nash shows that his trials with a mental breakdown, marital strife, and the failure to gain employment have worked to make him more appreciative of the things he has in his life. He says,

What truly is logic? Who decides reason? My quest has taken me to the physical, the metaphysical, the delusional, and back. I have made the most important discovery of my career—the most important discovery of my life. It is only in the mysterious equations of love that any logic or reasons can be found. I am only here tonight because of you. You are the only reason I am. You are all my reasons. Thank you.

Nash finds, through his struggles, that love and companionship are far more valuable than accolades and genius. His struggles have forced him to abandon his earlier pride, and the loneliness he felt in his disease has shown him the value of love and family. By the end of the movie, he can look beyond himself and see value in the small and seemingly insignificant things he took for granted at the start of the film.

The move from being self-absorbed to seeing the value in a social system comes at a high cost for Nash. However, he seems genuinely happy at the end of the movie, and he sees the benefit of education for his students. Spending time with real people and having love in his life has transformed him.

Nash changes in the film by being able to allow others into his world.  It starts with Alicia, in terms of telling her about his struggles with schizophrenia.  In allowing her to be a part of his struggle, Nash shows that "a beautiful mind" is one that brings others in and does not seek to keep them out.  At the start of the film, Nash used his intelligence and brilliance to keep others away from him.  His teaching was something that he saw as secondary to his work, confirmed with statements to his students such as "Your comfort is secondary to my ability to hear my own voice."  Yet, once he is able to let Alicia enter his world, he is able to do the same to others.  In bringing others in such as students and colleagues, Nash is able to share his genius with others.  In doing so, Nash demonstrates how the true beauty of a mind is when it seeks to maintain the social order of the world.  Nash's work and his ability to include others resides in the basic idea that human beings are better when they bring others into their world.  Nash does this with Alicia on a personal level.  He then does this with his students, recognizing that his work is the ability to teach and learn from others.  In this, Nash changes, enabling him to make a personal struggle something that apparently is able to be overcome with the help and support of others.

At the open of A Beautiful Mind, John Nash is presented as a promising young student who has returned from World War 2. Although he has trouble with other students, specifically Hansen, he shows himself to be a brilliant and put-together student in college. He is constantly hounded by the possibility that he is not as good as other students; this is amplified in the beginning by scenes like the game of Go that he plays against Hansen. He thinks differently and is shown to the audience as a person that thinks outside the box—“Classes will dull your mind, destroy the potential for authentic creativity”—this quote is meant to show the fact that he is a genius, and sets up his eventual success in finding unknown equations and ideas. In the first third of the movie, he is able to write a high-level critique of Adam Smith’s The Wealth of Nations which highlights how promising his future is at the start of the movie.

In the second third of the movie, we see the peak of his initial brilliance. Nash is offered a spot at MIT based on his new theory developed in the bar. He makes friends with the other mathematicians, finds love with his wife, and is eventually offered a position at the Pentagon cracking enemy codes during the cold war. However, the success we see in the middle of the movie begins to erode as Nash’s schizophrenia begins to show itself in his life.

At the beginning of the movie and through his success Nash has promising potential, while quirky his theories make sense and he seems put together as a person. As his paranoia and schizophrenia begin to take their toll he loses it. He stops dressing up and is seen at work without his normal suit and tie. That outward change is accompanied by, and really represents, the internal struggle he feels because of his increasing confusion and worries about secret Soviet agents chasing him. His life falls apart as a result of his hallucinations and paranoia and eventually comes to a climax when he punches Dr. Rosen at his guest lecture at Harvard.

His rise and fall in the first two-thirds of the movie are what make his eventual struggle more meaningful in the last third of the movie. We as the audience feel more connected to him because we have followed his progress and empathize with his struggle.

The opening scene in A Beautiful Mindshows how different John Nash is from everyone else around him.

The first words of the film attest to the importance of mathematicians.  The aspiring math students listen to a Princeton graduate school professor speak to how mathematicians "won the war" and how they are the key to stopping Soviet "world domination." While all the students look similar in their absorption of the professor's ideas, Nash sits in the back of the room, alone. He is processing a different reality.  While Nash pays attention to the professor's words, the way the scene is shot makes him appear to be different than his colleagues. 

Nash's distinct nature is further underscored at the luncheon.  While the other students are networking with one another, trying to ascertain who "among them will be the next Morse, the next Einstein," Nash stands apart. Nash walks to a table where two other students are talking about job placement and fellowships.   Nash takes a glass from the table to position the sunlight's reflection off of it.  As it converges upon one of their ties, Nash says that he is able to provide a "mathematical explanation as to how bad" the colleague's tie is.  The two colleagues stop talking and are visibly taken back, as Nash has demonstrated his "beautiful" gift of seeing patterns and functions in the natural world.

Nash's talent differentiates him from the other students. While his peers are very good at regurgitating currently accepted mathematical ideas, Nash is working on another level.  He strives to find mathematic ideals that have not yet been articulated.  He sees what is as what can be. This film's opening scene communicates how Nash's gift makes him different than his colleagues.

One of the ways people say the intelligence works is through the ability to see patterns out of chaos. So, when John Nash is able to see patterns,  this show that he is somehow different. In short, he is a genius. The patterns, he sees are in numbers, people, animals, etc. However, there is a fine line between genius and insanity. And there may even be a blurring of the two. The movie, in my opinion, does a superb job exploring this tension. In the end, John Nash is both - an insane genius whose genius controls the former.

John Nash freely admits to his roommate at Princeton, Charles, that he is far more adept at dealing with numbers than he is at interacting with people, and it is immediately obvious that his social skills leave much to be desired. In fact, it is trying to think of a new strategy for picking up girls at a local bar which inspires his work in governing dynamics.

Since we are discussing only the first third of the movie here, we are dealing with the period when he is working towards his Ph.D. at Princeton University as a graduate student and winner of the Carnegie Prize for Mathematics. Later in this first segment of the film, he starts working at MIT and for the United States Department of Defense. This section of the movie covers a time in Nash’s life before he falls in love or gets to know people who are on the same level as him intellectually and can challenge his ideas. It is also the period before paranoid schizophrenia takes hold of his mind.

In the first third of the movie, he’s not a man who lots of people would want to be friends with. His extreme intelligence has led him to arrogance and a tendency to belittle others. While he is aware of his own brilliance, he also suffers immense self-doubt, and his few social interactions are characterized by awkwardness.

John Nash at the beginning of the film A Beautiful Mind is incredibly brilliant, successful, and arrogant. He is a prestigious graduate student at Princeton with a very promising career ahead of him. His intellect is unparalleled, and he quickly creates some profound new mathematical theories, particularly the "Nash Equilibrium," which is a novel approach to Game Theory. He is very socially inept, however, and has difficulty connecting with others, in part because of his awkwardness and in part due to his ego.

Because of his intellect, he insists on publishing an original theory instead of rehashing something that has already been examined, which leads him to publish his theory of the "Nash Equilibrium." He begins, purportedly, to work for the American government, deciphering codes left by Soviet spies. As he does this, he grows more reclusive and paranoid, although he does meet and marry Alicia Larde. Soon after their marriage, it is revealed that Nash has paranoid schizophrenia and that he has hallucinated large amounts of his activities, including his involvement with the US government.

John Nash is a brilliant mathematician who ends up developing a mental disorder that derails his studies later in life. The beginning third of the film outlines his time in school when he is working towards his Ph.D. Because of his undeniable brilliance and the prodigious nature of his work, he turns out to be extremely arrogant.

He is clearly an incredible individual with advanced mental capabilities. Unfortunately, however, this is to his detriment, because he is very self-centered and proud in the beginning of the story, showing disregard for others: he is clearly egotistical. This eventually changes when he falls in love and meets others who can challenge him intellectually, but there is not a definitive turning point until his mental illness starts to derail his life.

The first third of A Beautiful Mind encompasses John Nash's time at Princeton as a PhD student and his early work at the MIT and the Defense Department. Nash at Princeton is portrayed as extraordinarily drive—he is obsessed with coming up with what he refers to as an "original idea" for his dissertation—and very socially awkward. He is also undeniably brilliant, as his "original idea" demonstrates, and he knows it—although he displays a great deal of self-doubt. At MIT, Nash is arrogant and utterly self-confident. He treats the classes he is supposed to teach with contempt and focuses on his classified work for the US military. He has little interaction with other people besides his immediate colleagues, who defer to him on most things. He begins to have what the viewer learns are serious delusions about working as a codebreaker for the Department of Defense. It is here that, despite his obvious awkwardness and arrogance, he meets Alicia, who, in the movie, would become the love of his life. Later in the film, we discover that much about Nash's life in the first third of the movie existed only in his mind, which is of course crucial to understanding his character.

At the beginning of the film, Nash's character is difficult yet still sympathetic. He has a prickly personality. He is well aware of his gift, and at the same time, he is frustrated by the challenges and burdens it poses. He is aware that he is like a magnificent swan running around with common pigeons, in terms of his intellect. This leads to the disagreeable side of his personality coming out. He apparently views himself as above most others, whom he refers to as "ordinary mortals."

He often lives in his own head and thereby shuts out a lot of ordinary human interaction. In fairness, shutting out ordinary human interaction is not his primary intention—his primary intention is using his gifts to think, and he has the gears turning all the time. Because of this, he is perceived as odd and standoffish.

He is quirky and hard to reach, but he eventually finds ways to open up to others.

My suggestion would be to use at least two or three specific scenes from the movie to underscore your points about Nash's character. Good luck!

In director Ron Howard’s adaptation of Sylvia Nasar’s biography of gifted mathematician and Nobel Prize recipient John Nash, A Beautiful Mind, the titular character’s mental illness manifests itself in delusional relationships with nonexistent people and in the belief that he was part of a Cold War–era intelligence struggle in which his skills at decoding were crucial to the American effort. For moviegoers unfamiliar with Nash’s story and Nasar’s biography, the revelation in the film that people close to him, mainly the characters of “Charles” (performed by Paul Bettany), the young girl Marcee, and the government agent Parcher (portrayed by Ed Harris) were figments of Nash’s imagination represented the film’s biggest surprise.

John Nash struggled with serious mental illness throughout his entire adult life—a struggle that did not prevent him from making significant contributions in the field of mathematics but severely compromised his and his wife’s ability to maintain a semblance of stability in their lives. As Nash, under years of treatment, began to gain a better grasp on the distinctions between reality and illusion, the realization that much of what had seemed real to him was actually imagined complicated most of his personal and professional relationships. His situation is summed up well in the film by the character of Dr. Rosen (Christopher Plummer):

Imagine if you suddenly learned that the people, the places, the moments most important to you were not gone, not dead, but worse, had never been. What kind of hell would that be?

Nasar’s biography of John Nash is well worth reading. It is, after all, a nonfiction biography of a fascinating individual. Ron Howard’s adaptation of the book, however, provides a good introduction to Nash’s story.