一个麻省理工学院的数学教授，在他系上的公布栏写下一道他觉得十分困难的题目，希望他那些杰出的学生能解开答案，可是却无人能解。结果一个年轻的清洁工(麦特戴蒙饰)却在下课打扫时，发现了这道数学题并轻易的解开这个难题。数学教授在找不到真正的解题之后，又下了另一道 更难的题目，要找出这个数学天才。 原来这个可能是下一世纪的爱因斯坦的年轻人叫威尔杭特，他聪明绝顶却叛逆不羁，甚至到处打架滋事，并被少年法庭宣判送进少年观护所。 最后经过数学教授的保释并向法官求情，才让他免受牢狱之灾。虽然教授希望威尔能够重拾自己的人生目标，而用尽方法希望他打开心结，但是许 多被教授请来为威尔做心理转导的心理学家，却都被这个毛头小伙子洞悉心理反被威尔羞辱，纷纷宣告威尔已“无药可救”。 数学教授在无计可施的情况下，只好求助他的大学同学及好友(罗宾威廉斯饰)，希望他来开导这个前途汲汲可危的年轻人。到底最后他能不能 打开心胸拥抱生命？会不会把他之前所遭遇的困境抛诸脑后？
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