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Out of sheer desperation, Lambeau finally calls on Sean Maguire (Robin Williams), an estranged old friend and MIT classmate of his. Five psychologists fail to connect with Will. Will chooses the latter even though he seems to believe that he does not need therapy. Realizing Will might have the potential to be a great mathematician, such as the genius Évariste Galois, Lambeau intervenes on his behalf, offering him a choice: either Will can go to jail, or he can be released into Lambeau's personal supervision, where he must study mathematics and see a psychotherapist to help him with his anger and defensive personality.
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A few days later Will attacks a youth who had bullied him years before in kindergarten, and he now faces imprisonment after hitting a police officer who was responding to the fight - a tough judge refuses to be tricked by Will's sharp knowledge of law precedent, which includes citing a case from the 1700s. A potential fight is eventually defused and Will finds that Skylar is attracted to him, getting her phone number. Will steps to Chuckie's defense, matching Clark step-for-step with historical facts he'd memorized. One of Skylar's fellow co-eds, Clark (Scott William Winters), tries to humiliate Chuckie, challenging his knowledge of American colonial history. At the bar, Chuckie spots a beautiful woman, Skylar (Minnie Driver) and he hits on her, claiming to be a Harvard student himself. One night after work, Will and his best friend Chuckie and a couple of their other friends go to a bar near Harvard University. When Will turns out to have solved it correctly, Lambeau tries to track Will down.
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Will is discovered in the act of solving it, and Lambeau initially believes that Will is vandalizing the board and chases him away as Will insults him. Everyone wonders who solved it, and Lambeau puts another problem on the board - one that took him and his colleagues two years to prove. The first week of classes, Will solves a difficult graduate-level math problem that Professor Gerald Lambeau (Stellan Skarsgård), a Fields Medalist and combinatorialist, left on a chalkboard as a challenge to his students, hoping someone might solve it by the semester's end. Hence, he is unable to maintain either a steady job or a steady romantic relationship.
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An abused foster child, he subconsciously blames himself for his unhappy upbringing and turns this self-loathing into a form of self-sabotage in both his professional and emotional lives. Though Will Hunting (Matt Damon) has genius-level intelligence (such as a talent for memorizing facts and an intuitive ability to prove sophisticated mathematical theorems), he works as a janitor at MIT and lives alone in a sparsely furnished apartment in an impoverished South Boston neighborhood.The synopsis below may give away important plot points.