Welcome to our roundup of all things Cambridge Mathematics

A message from our Director

Dear reader

Marhaba,

Situated learning, learning by doing, real-world learning, or context-based learning are all interconnected terms and / or theories that highlight how important it is to include relevant context in the learning process. While one could cite several possible challenges, it is something that brings a lot of joy and benefits when done right.

Mathematics is no exception. When students understand why they are learning certain topics and how they could use certain results in their daily life, it adds a layer of excitement and boosts interest which makes them appreciate the topic and its relevance even more. I remember seeing a clip for a comedian asking his audience, 'What is the square root of 25?' Everyone answered '5' to which he responded, 'So what? When did knowing this get you out of trouble?' Everyone laughed. Knowing why we are learning something and how it could be useful to us is important. I tried to embed this approach in a talk I delivered recently at the Judge Business School to an audience of executives from various fields, and I can say it was well received as I had comments like 'I wish we were taught mathematics this way'. The same approach is something we talk about a lot at Cambridge Mathematics; we consider it in our research and approach; and it is the topic of one of our Espressos. It is also highlighted in many of our Intersections interviews, as Lynn explains in one of her blogs. Moreover, many organisations and projects in the UK and internationally consider the importance of context while teaching and learning mathematics, as you can see, for example, in these resources from MEI, NCETM, NCTM, and NRICH.

So, speaking of context, what better context to consider nowadays than the FIFA World Cup! Forty-eight countries (we can debate later if having more teams in this edition is good or bad 😊), several rounds, and one winner. This year, we saw the event bring together tens of thousands of spectators per game and millions of people behind their screens; why not capitalise on this passion for the game of football (you can use the 's' word if you prefer!)? This competition offers a wealth of ideas that could be implemented in a teaching / learning context, from early years to higher education, and digital technologies including AI can support with that as and when needed! We can start with counting, be it the number of players or number of teams in a group; we can do arithmetic with the total points of a given team; geometry is also everywhere in a football game, from a rectangular pitch to a spherical ball and more; combinatorics, probability, and statistics are in the winning and losing odds and the number of games that could be played; algebra can be used for multiple equations from linear to quadratic, like when talking about the trajectory of a ball during a free kick. We can also have simulation and modelling problems at higher levels. It would be a fun exercise for both students and teachers alike to explore situations that bring together mathematics and the game they enjoy (of course, this can be done with other games or activities).

To give an example, here is a problem that mathematics and World Cup enthusiasts can attempt; for transparency, it was created with some help from AI. It mainly requires school-level mathematics to tackle, and the four parts are (in principle) in ascending order of difficulty. The answers are provided at the end of the newsletter (but not the full solutions)!

The FIFA World Cup in 2026 has 48 teams drawn into 12 groups of 4. In the first round, every pair of teams in each group plays once. Then, the top two teams from each group and the best eight third-place teams qualify to the second round. Assume standard tiebreakers strictly resolve any ranking ties so that exactly 32 teams advance and 16 are eliminated. As usual, a win in any match gives 3 points, a draw gives 1 point to each team, and a loss gives 0 points.

1. What are the possible point totals that a team can score in the first round?
2. How many different sets of 16 teams could be eliminated after the first round?
3. What is the largest possible total number of points that can be earned by the 16 eliminated teams after the first round?
4. What is the smallest possible total number of points that can be earned by the 32 teams that qualify for the second round?

That being said, this newsletter offers many exciting resources and announcements, mainly welcoming John, our new full-stack developer, based in Manila; we couldn’t be happier to have him so we can continue growing and improving our content. We also have a new page for our research on our website, talking about our approach as well as our outputs: do check it out. Moreover, Nadia, in her first blog for us, tries to convince you that LaTeX is the way to go, and Xinyue takes a playful look at whether or not AI can really ‘do maths’. Last but not least, two new guests join us for our seven questions: Steven Walker and Rebecca Atherfold.

I am sure you will enjoy exploring all that this newsletter has to offer, and I hope you share your feedback and suggestions with us and keep following us on our social media channels for the latest updates!

Best wishes,

In this update you can find out more about our research areas and publications, how we translate our research into practice and design, and the vision, mission and strategy which guide our research efforts.

The FIFA World Cup in 2026 has 48 teams drawn into 12 groups of 4. In the first round, every pair of teams in each group plays once. Then, the top two teams from each group and the best eight third-place teams qualify to the second round. Assume standard tiebreakers strictly resolve any ranking ties so that exactly 32 teams advance and 16 are eliminated. As usual, a win in any match gives 3 points, a draw gives 1 point to each team, and a loss gives 0 points.

1. What are the possible point totals that a team can score in the first round?
   {0, 1, 2, 3, 4, 5, 6, 7, 9}
2. How many different sets of 16 teams could be eliminated after the first round?
   C(12,4).6⁴.4⁸=42,042,654,720
3. What is the largest possible total number of points that can be earned by the 16 eliminated teams after the first round?
   64
4. What is the smallest possible total number of points that can be earned by the 32 teams that qualify for the second round?
   96

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