Proof is a 2005 American drama film directed by John Madden and starring Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal, and Hope Davis.
Robert, a brilliant mathematician who used to work at the University of Chicago startles his daughter Catherine while she watches TV.
All of this turns out to be a dream; Robert died the previous week, after a long period of crippling mental illness, and his funeral is tomorrow.
In flashbacks, Robert is shown invigorated, believing that he has seen the beginnings of a new mathematical proof that will prove his triumph over mental illness.
In the present, Catherine gives Hal a key to Robert's desk and tells him to check the locked drawer for a notebook which contains an important proof.
He eventually returns as Claire and Catherine are leaving, with news that the math department believes the proof to be valid.
Hal does not think that Robert wrote the proof because it employs newer mathematics and wants Catherine to explain it.
In another flashback, it is revealed that, while living together, Robert challenged Catherine to work on math, which she does, ultimately completing a proof, which she describes in one of the house's notebooks.
The film opens with a pan of Gwyneth Paltrow's character bicycling across the Midway Plaisance and shows scenes in the quadrangle before Harper Library.
The consensus reads, "Gwyneth Paltrow and Anthony Hopkins give exceptional performances in a film that intelligently tackles the territory between madness and genius.
"[2] Gwyneth Paltrow received a Golden Globe Award nomination for Best Actress – Motion Picture Drama for Proof, but lost to Felicity Huffman for Transamerica.
Since 1993 (when Andrew Wiles first claimed to have proven Fermat's Last Theorem), there have been several feature films about mathematicians, notably Good Will Hunting (1997), A Beautiful Mind (2001), Proof (2005), Travelling Salesman (2012), The Imitation Game (2014), and Gifted (2017).
"[3] He also called Proof: "richer and deeper, simultaneously both funnier and more serious, than either A Beautiful Mind or Good Will Hunting.
Some cited mathematical concepts are Sophie Germain primes, taxicab numbers, abstract algebra, differential equations.