What’s that I hear you say, "Maths is rubbish, it'll never come in useful...". The geometry, mental arithmetic, calculation, multiplication tables, all of that... Well, you would be wrong, unfortunately! Unless you've lived in a cave for 5 years, you could not have missed the enormous success of Games Of Thrones, or "GOT" for avid fans. Adapted from the novels of George R. Martin, the television series is currently a worldwide hit and attracts more than 8 million viewers each week on HBO in the United States. Acclaimed for its realism and intrigues, sharply criticised for its scenes of violence and sex, the Iron Throne is responsible for a lot of ink and blood... In just a few years, GOT has acquired a fan base (the "GOT fans") across the globe, engaging in, sometimes fiery, debates. One of the most contested: who is the show's main character? It is true that the saga contains a lot of characters and, judging by each seasons, we really do not know who is the true hero! The directors also take sly pleasure in making you fall in love with certain characters before they violently die a few episodes later... This is where maths comes into play. Yes, you read correctly, mathematics! In this article, we will not discuss mathematical formulas and puzzles. There will be no:

• Theorems (Pythagoras 'theorem, Thales' theorem)
• Trigonometry,
• Arithmetic,
• Not even physics or chemistry!

No, let's focus on a new science that is based on the mathematical formula of graphs. Maths teachers, A. Beveridge and J. Shan, wondered how it would be possible to figure out the main character of GOT using a mathematical formula? They finally solved the problem with a conclusion that might surprise you, because as you know, the battle for the iron throne is seemingly never-ending and the answer to this mathematical problem could reveal a lot about the rest of the show... SPOILER ALERT: the answer is below...

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## The Phenomenon that is Game of Thrones

Before getting to the heart of the matter, it might be interesting to take a quick look at the series. Games Of Thrones is a drama set in a fantasy-medieval universe, first released in the United States in 2011. To understand why mathematicians are interested in this Television programme, we must look at the story itself. The story takes place on the imaginary continent of Westeros, governed by the Seven Kingdoms and under the rule of King Robert Baratheon. The plot, over the course of the series, reveals the different "houses" to which many protagonists belong. Despite the pacts and alliances between the different houses, families have only one objective: to dethrone the king and rule the kingdom themselves. While this little world is trying to conquer the Iron Throne, the kingdom must also defend itself against the threat from the north "beyond the ice wall": the White Walkers, made of ice and possessing terrifying magical powers. Yes, in GOT there's magic and dragons too! Are you still with me? To understand the mathematical reasoning that will be revealed shortly, and not get lost in all the information, here is a quick list of the main characters of GOT, classified according to their house:

• House Lannister: (you will love to hate them ...) with Cersei, Jaime, Tyrion, Joffrey Lannister.
• House Stark : The Starks are the first characters we meet in the series with Ned Stark, Robb Stark, Sansa Stark, Arya Stark, Bran Stark and, of course, the famous Jon Snow.
• House Bolton: with Roose and Ramsey Bolton.
• House Greyjoy: with Theon Greyjoy.
• House Targaryen: with Daenerys Targaryen, "the mother of the dragons".

Many other characters appear throughout the episodes and are also important, but those listed above are the most recurring ones throughout the 6 seasons. Just for reference, statistically speaking, a main character in the series has 28% chance of dying at some in a season. To grasp the success of the series, GOT is also:

• Broadcasted in 173 different countries, but also the most pirated series in history.
• Has won hundreds of awards.
• Has a budget of \$ 100 million to shoot the 10 episodes of season 6.
• Is filmed in 30 locations around the world.
• Has 3,000 different costumes.
• Invented a language called dothraki.

It's an extremely complex world created entirely by George R.R Martin. Just as complicated as learning advanced mathematics at Undergraduate, Master's, or even a Doctorate. Do you think the two scientists used Pi in their formula?

## Using "the Science of Networks" to Discover the Main Character in GOT

Now that the context is set, let's go back to the mathematics and the following problem: How to figure out the lead character in GOT using maths? This was the question asked by maths teachers, Beveridge and Shan of Macalaster College.

### The Mathematical Study of the Relations between the Characters

For their research they did not use geometry, algebra, wacky mathematical equations or even exponential functions. They used a thriving research field: the science of networks! What is the Science of Networks? Network Science is a scientific discipline usually linked to mathematics, the study of which deals with relationships, connections and interconnections between things. Established in 2007 in the United States, network science is a brand new field of research that can also be applied by:

• Physics (physical sciences),
• Biology (or Life & Earth Science),
• Information and Cognitive Science,
• Social networks.

Based on the novels of George R. R Martin and between two maths courses, the two mathematicians transformed the universe of GOT into a gigantic network, using as an example the theory of graphs. Not the graphs you know, with abscissa, ordinates, curves, functions... No, they studied how information flows from one character to another in a complex network! Why not get maths help to figure out the main characters, death rate or statistical likelihood of two characters getting together in your favourite series?

### The Process Used by the Two Maths Teachers

To guarantee the result (all of you are guessing!), the mathematicians began by listing all the interactions between the characters in the 3rd novel of the saga and counting the number of times the names of the characters appeared. They then used an algorithm to distribute the results in 7 distinct communities and to appropriate one color to each, here is the result.

Through this modeled graph, the researchers listed 107 different protagonists (called "vertices") connected by 353 connections (these are the "edges"). Mathematical research does not stop there: the researchers then had to take several scales of measurement ... Among them, 6 degrees of centrality and Google's PageRank algorithm. The objective? To classify the characters according to their interactions with the most important characters. The maths teachers have used the centrality to understand the importance of the characters, as Beveridge says:

"A character can play a leading role in several ways. "

In order to model the graph, it was necessary to study several measures of centrality:

• The number of links of the character to the other protagonists,
• The number of interactions,
• The character's connections to the most important protagonists (Google's PageRank algorithm was used to define who were the most important characters in the series),
• The values of average distance, between the characters,
• The frequency of presence of a character.

AND THE WINNER IS ...

Tyrion Lannister would be mathematically speaking the main character of Games Of Thrones!

Although the experiment also highlights the names of Jon Snow and Sansa Stark, who are very present in the series, Tyrion is the first result of the first 4 centralities, it is only dethroned by Jon Snow on the last.

Tyrion, Jon, Sansa? Who will emerge victorious in this war and seize the Iron Throne?

A mathematical exercise that once again proves the power of this subject and puts forward a new field of research in full motion, the science of networks.

## The Science of Networks at the Heart of the World?

Used for a decade now, the science of networks has emerged thanks to the advent of computer systems in the world. When we look closer, the notion of networks is everywhere on our planet:

• Transport networks (road, air, rail, etc.),
• Natural networks (hydraulic, biological ...),
• Infrastructure networks (water, gas, electricity, etc.),
• Social networks,
• Etc.

The study of these networks is a key issue in several field: marketing, security, trade, politics, etc. A new science modeled as classical mathematical graphs with vertices and edges dating back to the study of Euler, the famous eighteenth-century mathematician. So where can I find maths tutors near me who will teach me fun exercises like this one? On Superprof of course! What if the study of networks could reconcile the sciences? This is what historian M. Gribaudi and physicist J.P Nadal want to prove. They wish to invite researchers from all walks of life: mathematicians, physicists, historians, linguists, sociologists, etc. to collaborate and debate in order to advance research. Starting from the observation that each researcher is enclosed in his field of expertise, the study of the science of networks could, according to them, pave the way for great discoveries. With this method, the search process could be much more effective. They use mathematicians and sociologists as an example. Social scientists, on the other hand, would provide qualitative data which would then be made available to mathematicians to develop specific models. Mathematics is still a field full of resources and wealth.

"Mathematics is no less immense than the sea" Victor Hugo"

In the meantime, you know how to impress your friends and colleagues by telling them how, thanks to mathematics, you discovered who is the protagonist in GOT and maybe the future leader of Westeros! Perhaps if the Board of Education proposed in its mathematics curriculum to teach maths by tackling more fun themes like this, students from primary to secondary education (Key Stage 2, Key Stage 3, GCSEs and A-levels etc.) could learn more easily:

• Learn subjects in maths class,
• Calculation exercises (addition, subtraction, division, multiplication),
• Geometric figures (square, right triangle, isosceles triangle, hypotenuse ...),
• Fractions,
• Probability,