But what about below the surface? What about the inheritance you can’t see?

In John Madden’s Proof (2005), Catherine (Gwyneth Paltrow), the daughter of a recently deceased and delusional mathematician, wonders whether her apparent talent for math means that she has also inherited her father’s insanity.

Madden’s adaptation of David Auburn’s Pulitzer Prize-winning play blurs the line between past and present and reality and imagination to create a mathematical thriller of sorts.

Paltrow convincingly balances Catherine’s frigid insecurity with an understated confidence as she comes to terms with her father’s death and the years she lost caring for him, while simultaneously questioning her own sanity.

Catherine’s father, Robert (Anthony Hopkins), apparently revolutionized mathematics in his early twenties before he fell ill, prompting Catherine to abandon her own mathematical studies at Northwestern University to care for him.

After the father’s death, his former student Hal (Jake Gyllenhaal) arrives to sift through the hundreds of notebooks that he left, hoping to find another mathematical discovery inside Robert’s tortured mind.

Catherine then has to struggle with her attraction to Hal and her overriding fear that he just wants to exploit her father’s work.

To complicate the mix, Catherine’s estranged sister Claire (Hope Davis) tries to care for her, but her motherly ways alienate Catherine, who resents her sister for not helping to care for their father.

When Catherine shows Hal a notebook that contains a proof that would revolutionize the field, the question arises: Did Robert write it or did Catherine? And thus a mathematical whodunit ensues.

Gyllenhaal does OK by his subtle portrayal of Hal, but it is Davis’ and Paltrow’s performances that make the film believable.

Davis easily could have made Claire a one-dimensional, detestable character, but she reveals that beneath Claire’s Martha Stewart-like facade, she does care about her sister and is perhaps jealous of her closeness toward their father.

Paltrow gives Catherine a sort of raw anguish in her no-frills performance, full of not-so-flattering close-ups.

Proof applies to Catherine’s three different struggles.

First, there’s the explicit proof and the quest to discover who wrote it, then there is Catherine’s need for proof that Hal’s love for her is real, and finally whether or not Catherine’s mathematical genius is proof that she shares her father’s insanity.

But don’t expect a Pythagorean theorem to solve this triangle. The film suggests that in life, and sometimes in math, there are no easy answers.

this essay first published at The Daily Tar Heel