The role of Catherine was originated by Mary-Louise Parker in 2000 at the Walter Kerr Theatre in New York. Her performance won her a 2001 Tony Award for Best Actress in a Play and a 2001 Drama Desk Award for Outstanding Actress in a Play.
According to the clues given in the movie mainly by Hal (Gyllenhaal) the proof can be the proof of Riemann hypothesis. He says "a very important proof, of a mathematical theorem about prime numbers, which mathematicians are trying to prove, it's historic, you can publish it, give press conferences, all newspapers in the world will talk to the person who have found it". Actually it's one of the Millennium Problems.
David Auburn's play "Proof" premiered at the Manhattan Theater Club, New York City, New York, USA in May 2000, and then transferred to the Walter Kerr Theater on 24 October 2000 where it ran for 917 performances. "Proof" won the 2001 Tony Award for the Best Play, and the Pulitzer Prize in Drama the same year.