Proof

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* Description: Catherine is a brilliant yet self-doubting young woman who spent years as the primary caregiver for her father, Robert. She is quick-witted, stubborn, and often prickly or cynical as a defense mechanism.

* Conflict: Having inherited her father’s mathematical genius, she deeply fears she has also inherited his debilitating mental illness. Her struggle to prove the authorship of a groundbreaking proof serves as the central "proof" of her own sanity and identity.

Robert (Supporting, 50s)

* Description: A world-renowned mathematician and professor at the University of Chicago whose career was cut short by schizophrenia. He is portrayed as loving and playful yet occasionally manipulative and insufferable.

* Role: Although deceased when the play begins, Robert appears in flashbacks and as a figment of Catherine’s imagination. His presence represents both the heights of intellectual achievement and the tragedy of mental decline.

Claire (Supporting, late 20s to early 30s)

* Description: Catherine’s older sister, a practical, stylish, and successful woman living in New York City. Unlike Catherine, she has little of her father's genius but also seems to have escaped his mental instability.

* Conflict: Claire is often viewed as the "villain" because of her pushy and controlling nature; she wants Catherine to move to New York to be properly supervised, which Catherine perceives as an attempt to institutionalize her.

(Hal) Dobbs (Supporting, 28)

* Description: One of Robert’s former Ph.D. students who is searching through Robert’s 103 notebooks for any remaining fragments of genius. He is portrayed as a bit of a "hipster" who is hyper-aware that he may have already passed his mathematical prime.

* Role: Hal serves as a romantic interest for Catherine and a catalyst for the plot when he discovers a paradigm-shifting proof in the house. His initial disbelief in Catherine's authorship creates the play's primary emotional and intellectual climax.