At the start of the movie, John Nash is full of vanity and ambition. He thinks highly of himself—and he isn’t entirely inaccurate in thinking he is a genius. However, he is altogether arrogant. He doesn't prove himself to be that much smarter than his classmates. Therefore, calling his classmates...
“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.