Qohen Leth corrects people who call him a number cruncher: he's an entity cruncher. Even though he is very good at his job, processing data in the office at his company's famous cubebased computer terminals, he is obsessed with the meaning of life. He would prefer to stay home where he expects to receive a phone call telling him why he exists. Management recognizes his potential and instead allows him to work from home on an important project: attempting to prove "The Zero Theorem".
As we soon learn, the "Zip T" (as it is called by those who have worked on it unsuccessfully for years) will show that the universe will end with everything being reduced to a zerodimensional point in space after being devoured by a black hole, a corollary of which is the meaningless of life.
This film certainly has that Terry Gilliam feel, somewhere between steampunk and psychedelia with helpings of Kafka and Monty Python thrown in. If you are interested in plot and comprehensibility, however, then this movie may not be for you, as that feeling is really what takes center stage.
Now, some comments on the math:
 The visual portrayal of the way theorems are proved was really cool. It looks like a video game, somewhere between Tetris and Minecraft. The "player" has to twist and steer the cubes so that they fit together into a huge structure in such a way that the mathematical symbols on the surfaces of the cubes form mathematical statements. Occasionally, huge sections of the construction collapse, presumably because the mathematical statements they formed were found to be invalid. (Now, I must say that I do not use a joystick when I am proving new theorems, but that what I do can feel like this looks. I can write pages of formulas that I think are valid and true mathematical statements, and then I find either a logical contradiction or try a computer experiment that does not behave as predicted by the formulas and the whole thing collapses.)
 Leth, unfortunately IMHO, displays many of the stereotype qualities of mathematical characters in fiction. He is neurotic, depressive, obsessive, and antisocial. For example, he always refers to himself in the plural, hates parties, expects to receive a personal phone call telling him the secret of life, avoids food with taste, etc.
 It is similar to Good Will Hunting both in that it features Matt Damon (who plays "Management" in The Zero Theorem) and in that the mathematician character is seeing a therapist. (Qohen's therapist is a virtual one, but still . . . )
 Most of the mathematical notation we see in the film comes in the form of symbols (derivatives of ψ, looking like wave equations from a quantum field theory, perhaps) on the surfaces of cubes on Leth's computer display. However, Management's son, Bob, does write some formulas in chalk on Qohen's wall when explaining the theorem to him. (I'm afraid I couldn't quite see what he wrote.)
 Leth frequently asks why anyone would want to prove that life is meaningless. One could argue that Leth (who lives in an old abandoned church, by the way) represents those who find math and science unappealing because it interferes with their spirituality and faith. Management represents those who profit financially from technology, as he explains he plans to do with the Zero Theorem once it is proved. There does not seem to be anyone in the film who likes math and science for esthetic or ethical reasons. That's a shame, because it is important to be aware that awe and beauty can be found in these discoveries, and that a good case could be made that the discoveries of science and math have made the world a better place.
 Spoiler Alert: Like Pi and Good Will Hunting, the end of the movie seems to suggest that the best thing one can do with math is ignore it. In each of these films, there are people who are pressuring the protagonist to pursue a mathematical goal. In each of them, the protagonist is made miserable and "crazy", finding happiness only when they give up and live a "normal life". I really do fear that this will give viewers a serious misconception about math. Let me assure you that being a career mathematician is actually a nice job. It always ranks highly on "job satisfaction surveys". Contrary to the portrayal in film, it can be a very social activity and be done by people who have ordinary lives and other hobbies.
