'Travelling Salesman'

Written and directed by Timothy Lanzone

It's not often the very first person you meet in a movie is a mathematician. The second, third and fourth people on screen also being mathematicians is even rarer. But the movie Travelling Salesman is a rare movie: not only are almost all of the characters mathematicians, the central plot also hinges on the solution of one of the most important problems in mathematics.

This tense thriller is an independent movie written and directed by Timothy Lanzone. We were lucky enough to host the UK premiere here at the Centre for Mathematical Sciences in Cambridge. It has all the vital ingredients for an edge-of-your-seat film: hidden identities (indeed we learn the name of only one of the characters), surly government agents, threats of violence, moral dilemmas and a potential global catastophe.

Most of the movie is set in a single room, a secret government location, where four men are waiting to be debriefed by a government agent as their highly classified project has been completed. It turns out they are all brilliant mathematicians and one of the outcomes of their project, an outcome which seemed to have been somewhat unexpected, was that they solved one of the greatest problems in mathematics and theoretical computer science: that P=NP.

The NP in this statement refers to the class of mathematical problems whose answers are easy to check, that is a computer can verify the answer is correct in a reasonable amount of time. Some of these problems, those in the class P, can also be solved in a reasonable amount of time. However there are some NP problems, such as the eponymous Travelling Salesman problem, that we do not know how to solve quickly and, in fact, we don't know if that is even possible. Since this problem was posed in 1971 no one has managed to prove definitively if P equals NP. (You can read more about the maths in our article The travelling salesman.)

In the movie the unexpected proof of P=NP has massive consequences, such as being able to break any current cryptographic system rendering all digital security worthless. "We always assumed that brute force search was hard and that it takes a long time... and we just showed it was easy," says one of the mathematicians in the film. Their breakthrough was illustrated by a card trick: Pick a card from a pack, look at it and return it to the pack. The magician could do a brute force search and check every card, asking if it was your chosen card, but this could take ages, particularly if you had a million cards. Instead, the mathematicians have developed a "nondeterministic oracle", a kind of a mathematical black box, that you can just ask 'what is the chosen card?' and it will tell you.

The film is essentially a debate between the four mathematicians and their government handler about the ethical consequences of their work. Will it be used for evil, by governments (or worse) to spy on all communication and data? It could be used for good but will keeping it secret mean that medical advances and scientific discoveries will be hampered? Throughout the film the mathematical result is compared to Oppenheimer's nuclear research that was used for nuclear bombs but also gave us nuclear medicine.

Although the use of their work for good versus evil was the concern for three of the main protagonists, for one character – Dr Tim Horton – the bigger question was one of academic and intellectual morality. Was it right to keep one of the most fundamental mathematical results secret from the world? Was mathematical knowledge bigger than national security or personal gain?

It was wonderful to hear so many mathematicians name-checked – Hardy, Gödel, von Neumann – and very refreshing to see mathematicians portrayed as normal three-dimensional people. The four main characters were just as human, and as flawed, as any of us, although it was a bit of a shame that every character in the film was white and male (bar an underperforming student who appeared for less than a minute). Mathematicians are usually portrayed as crazy (as in the film Pi) and even if they are heroic they also have to be eccentric characters (as in Independence Day). This time they were just normal people. And excitingly in this movie they were both the heroes and the villians of the piece, often both at the same time.

It was also very impressive to see such a sophisticated mathematical concept used with such imagination and integrity on the screen. A real effort had been made to portray the mathematics, and how mathematics is done, accurately. I did wonder if the slew of mathematical jargon would put a nonmathematical person off, but perhaps that is no different from me watching a medical drama and letting the stream of medical terms wash over my brain while I focussed on the drama at the heart of the story. And at the heart of this story was that mathematics now underpins so much of our lives, meaning that mathematical discoveries could have a dramatic impact on the world, leading to new advances or to potential catastrophe and all the moral dilemmas that entails. Perhaps an ethics class, or at least a trip to see this movie, might become an obligatory part of all maths degrees.

To find out where this movie is screening next visit the Travelling Salesman website.