Math enters the story in four different ways:

• Jeanne is the teaching assistant for a "pure math" class at a Quebecois university (and so I assume she is a graduate student in mathematics). In the film, the professor is shown introducing the class by warning students that they will not be working on questions with definite answers, but instead on insoluble problems leading to other insoluble problems. He also tells them that their friends will think their work is futile, and they will not be able to defend themselves since the work is so abstract as to be impossible to explain. And then, he introduces them to Jeanne who gets up to talk about the Collatz conjecture before the scene cuts to her and the professor in his office talking about her situation with the envelopes.

  [A few comments: The course sounds more like a class on math research than on "pure math". There certainly is a difference between math research and the sort of math that students generally encounter in a math course. One big difference is that at the start nobody knows quite how to answer the questions that are the subject of math research, but of course if the research is successful then they do figure it out eventually. So, the problems are not literally "insoluble". Another difference is the time scale. Making progress on math research can take months or years, not the hours or days that one has to devote in a course. That's why I don't really know of any courses like the one that seems to appear in the film. Moreover, although it is true that it is challenging to explain the relevance of math research to non-mathematicians, the professor's implication that none of your friends will understand it and that you'll necessarily be isolated and lonely seems to ignore the fact that many mathematicians have friends who are other mathematicians with whom they can talk about research and even collaborate. ]

• The seemingly impossible task of finding their lost relatives is intended to resonate with the sorts of "insoluble" math problems that Jeanne works on. This is sometimes made quite explicit, such as when the professor prompts her to figure out where to start working on the problem, and when she suggests starting with her father he points out that you never start with the "unknown" that you are trying to solve for. Furthermore, I suppose one could make an analogy between the professor's remarks about the way that friends will react to math research and the way that Simon initially refuses to be involved in the search for the missing relatives.

• By chance, the professor has a friend in the math department at the Middle Eastern university where Jeanne's mother briefly studied French. He suggests that she should start by talking to his friend and assures her that he can be trusted. Unfortunately, after telling her that he was in Paris during the years that Jeanne's mother was a student, the friend just starts rambling about Euler, the Bridges of Königsberg, Euler's equation and God. All of this is so unhelpful and irrelevant that the professor seems a bit crazy.

  [I do like the implication that mathematicians have international social networks. Indeed, it is one of the things that I like about my job as a math professor that I do know colleagues in math departments around the world.]

Spoiler Alert: The brother that Simon has to deliver the envelope to was born out of wedlock many years before their mother moved to Canada. The father of that baby was killed and their mother was forced to give up the baby for adoption. But, before she did, a tattoo was placed on its foot so that she could recognize him in the future. After that, the mother had many different lives and adventures. She was a student and worked on a newspaper. She saw the horrors of war and became a radical. Then she spent many more years as an inmate in a horrific prison. Before her release, a young radical from the other side tortures and rapes her to get information. The rape leads to the pregnancy that results in the birth of Jeanne and Simon. So, the father to whom Jeanne has to deliver her envelope is the torturer from the prison. The horrific truth that they soon learn is that the two intended envelope recipients are actually one and the same person. This explains what happened at the pool. Their mother saw the tattoo on the foot of a man at the pool in Quebec and realizes it is her son, but when he turns so that she can see his face, she realizes it is also the man who raped her and fathered the twins.

• And now, the fourth way that math comes into it: Simon learns of their Oedipal origins before his sister. She finds him sitting on the bed staring into space (not unlike his mother at the pool). He is mumbling that one plus one always equals two, but then asks her whether it can ever equal one. This is how Jeanne learns that her older brother is her father.