"Proof" (2005) is a poignant drama that delves into the complexities of genius, mental illness, and the bonds of family. The story revolves around Catherine, played by Gwyneth Paltrow, the daughter of a brilliant but mentally unstable mathematician, Robert, portrayed by Anthony Hopkins. Following her father's death, Catherine grapples with her own fears of inheriting his mental illness while also trying to prove her worth as a mathematician.

As she navigates her grief, Catherine finds herself in a complicated relationship with Hal, a former student of her father, who is eager to uncover Robert's lost work. Tensions rise when Catherine reveals a groundbreaking proof she claims to have authored, leading to questions about authorship, trust, and the fine line between genius and madness. The film explores themes of love, loss, and the quest for validation, ultimately asking whether the pursuit of knowledge can coexist with the fragility of the human mind.