As a graduate student in the field of theoretical computer science, I feel that I understand P vs NP as well as the makers of this film could hope for any viewer to understand them. I felt the treatment was more technically accurate than almost any movie I have seen about a mathematical topic, but it still fell short on a few key moments.
Warning, the following contains spoilers.
First, I was confused when they mentioned PSPACE in a few parts of the film. It made it sound like not only had they proved P = NP, but the main character had proved P = PSPACE, and was using this as his back door algorithm. I don't think this was the intent of the movie, but in any case it was a bit confusing.
A second scene puts the main character in his office with a student and his colleague, and he mentions that he has an algorithm that goes on proving theorems and proving more theorems. It is a well known consequence of P = NP that finding mathematical proofs become trivial, for there is an obvious algorithm to check a purported proof in polynomial time. The world's most renowned mathematicians would have known this as well, and it doesn't make sense that it would occur as some kind of "revelation" to the main character and remain a secret he could use as leverage.
Finally, I felt that some of the phrases used to describe general things (like the field of research, which is theoretical computer science or TCS) made the dialog a bit awkward.
That being said, the movie had absolutely palpable dramatic tension. The lines were witty and sharp, the acting was very believable (and the characters actually had distinct personalities). Their power struggles were very exciting to watch. The color was also very well balanced. None of the Hollywood teal and orange crap that has become so standard and ugly.
In all, I enjoyed the movie and the fact that it gave serious consideration to the most important problem in my field (and treated it fairly). My main criticism is that the plot should have more direct clarity. It's nice to leave a lot up to implication. But mathematicians are rarely indirect, and the best lines of the movie were the pointed, thought provoking comment.
Warning, the following contains spoilers.
First, I was confused when they mentioned PSPACE in a few parts of the film. It made it sound like not only had they proved P = NP, but the main character had proved P = PSPACE, and was using this as his back door algorithm. I don't think this was the intent of the movie, but in any case it was a bit confusing.
A second scene puts the main character in his office with a student and his colleague, and he mentions that he has an algorithm that goes on proving theorems and proving more theorems. It is a well known consequence of P = NP that finding mathematical proofs become trivial, for there is an obvious algorithm to check a purported proof in polynomial time. The world's most renowned mathematicians would have known this as well, and it doesn't make sense that it would occur as some kind of "revelation" to the main character and remain a secret he could use as leverage.
Finally, I felt that some of the phrases used to describe general things (like the field of research, which is theoretical computer science or TCS) made the dialog a bit awkward.
That being said, the movie had absolutely palpable dramatic tension. The lines were witty and sharp, the acting was very believable (and the characters actually had distinct personalities). Their power struggles were very exciting to watch. The color was also very well balanced. None of the Hollywood teal and orange crap that has become so standard and ugly.
In all, I enjoyed the movie and the fact that it gave serious consideration to the most important problem in my field (and treated it fairly). My main criticism is that the plot should have more direct clarity. It's nice to leave a lot up to implication. But mathematicians are rarely indirect, and the best lines of the movie were the pointed, thought provoking comment.