During the initial introduction between Martin (Elijah Wood) and Mrs. Eagleton (Anna Massey), they speak about her replica of the German Enigma cipher machine. Mrs. Eagleton states everything was done manually to break the Enigma messages. Mrs. Eagleton states "there were no computers in those days (World War II)" and "calculations were done by hand." Actually, the British, working in Bletchley Park, did build a computer called Colossus by January 1944. Colossus was constructed with up to 2,400 vacuum tubes and programmers used approx. 1" wide paper tape to store programming. By the end of the war, Bletchley Park was using 10 Colossus computers to break various German cipher machines, including Enigma.
The "Bormat's Last Theorem" that is solved in the movie is clearly a reference to Fermat's Last Theorem. Like Bormat's theorem in the movie, Fermat's theorem was widely considered to be (one of) the most difficult problems of the last 300 years. It was solved fairly recently (in 1995 by Andrew Wiles). It was solved using elliptic curves, and the proof was first demonstrated at Cambridge. Like the proof of Bormat's theorem in the movie, the proving of Fermat's was a very big deal in the world of number theory.
(at around 18 mins) The film gives a nod to director Brian De Palma with an apparently seamless 2+ minute tracking shot, traveling through multiple interior and exterior locations to reveal the first murder victim.
(at around 1h 8 mins) John Hurt's character dresses as Guy Fawkes for Guy Fawkes Day. In V for Vendetta (2005), a fake V removes his Guy Fawkes mask, revealing himself to be Adam Sutler, played by John Hurt.