"Travelling Salesman" won several awards at the Silicon Valley Film Festival and has been compared in reviews to such classics as "12 Angry Men" for its tense scenes of white men (yes, all of the mathematicians seem to be male in this film) sitting around a table debating a serious moral question. Interspersed among those scenes we see the protagonist discussing math with a colleague in England where he works and delivering a speech on the future of mathematics to a large audience at a university.

However, this film has also been criticized from two different directions. Some reviewers who are familiar with the math complain that not enough technical details were provided to entertain or interest them. (In particular, the vague "melt the sand into glass" metaphor used to describe the method applied in the film is not satisfying, and most of the moral implications that are intended to maintain the suspense are things that anyone involved in the field would have spent a lot of time thinking already.) On the other hand, many reviewers not previously familiar with the mathematical background apparently fail to grasp most of what is going on (they just see people talking seriously and saying "blah blah blah") and therefore also fail to care about the characters.

For those who may not know, "P vs. NP" is a real, famous open problem on the border between mathematics and computer science. Loosely put, it has to do with how long it would take to solve certain problems. More specifically, it involves the difference between checking whether some object has a certain property and (on the other hand) finding something with that certain property. In general, it is easier to check a potential answer than to find a real answer. If we want to get even more specific, we have to introduce a number n which shows up in the statement of the question (it generally measures a size or complexity, like the number of digits in the "answer" or the size of the set being considered). We say a problem is in "NP" if the amount of time it would take to check a possible answer for validity is less than some polynomial in n. (Checking to see if a jigsaw puzzle with n pieces was put together properly is probably in P since looking to see that it is done right probably only grows like n².) Similarly, we say that a question is in "NP" if we actually can always find an answer to the question in an amount of time bounded by a polynomial in n. Theoretically, it seems possible for a question to be in NP but not in P, because solving it is so much harder than checking an answer. (Putting together a puzzle with n pieces is very hard if n is large, and it seems that the difficulty may grow so quickly that no polynomial can stay bigger than it for all n.) But is it true? That is the question of P vs. NP and it is an important one because, for instance, the reliability of the codes that protect your credit card number in internet purchases depends upon the the ease of checking an answer and the difficulty of finding one. If there is some easier way to do it, then these codes would no longer be a secure way to transmit information.

I am writing this in the wake of the news that the US government has been reading many encrypted messages for years. This has two implications for the film. On the one hand, it makes the actions of the government representatives in the film (attempting to maintain the secret, if not the violent threats used to achieve this goal) seem realistic. And, on the other, it makes the questions addressed in the film less relevant since the NSA has apparently been doing this by weakening encryption standards, which means that they did not need to do anything with P vs NP at all.