Young Mathematicians Summer School Detailed Outline

This page provides a detailed outline of the online Young Mathematicians Summer School, a two-day course for students aged 12-14 who enjoy puzzles, patterns, strategy, and surprising ideas. Across the course, students become part of MIπ – Mathematics Intelligence Pi – and use mathematics to crack codes, solve mysteries, and complete a series of linked missions.

The course is taught fully live online, with students working together in real time through discussion, problem-solving, games, and collaborative challenges. It is designed to show that mathematics is not just about getting answers, but about spotting hidden patterns, thinking cleverly, and seeing the world in new ways.

Prefer to view and download the PDF version of this outline? You can do so here.

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Day One – Welcome to MIπ – Fractals, Traps and Secret Number Worlds
Day Two – Mission to Topolograd – Shapes, Spies and Secret Messages

Across the two days, students explore mathematical thinking through cryptography, number systems, logical puzzles, probability games, and topology. They are encouraged not just to find answers, but to notice patterns, test strategies, communicate clearly, and reflect on how mathematicians approach unfamiliar problems.

10.00 – 12.30 Fractal Forests and Paradox Puzzles

The course begins with students being recruited into MIπ, a secret mathematical intelligence agency. From the very start, the atmosphere is playful, collaborative, and puzzle-driven. Students tackle training challenges that reward sharp observation and creative thinking, then move into one of the strangest and most beautiful ideas in mathematics: fractals.

Fractals are patterns that repeat at different scales, and they open the door to some wonderfully surprising questions. How long is a coastline, really? How can a simple rule create something that looks endlessly complicated? Why do the same kinds of patterns appear in geometry, in nature, and in snowflake-like designs? Students explore these ideas through visual investigations and mathematical puzzles that are as imaginative as they are challenging.

The morning then turns to paradoxes – problems that seem to twist logic back on itself. These are the kinds of ideas that make students stop, laugh, argue, and then think harder. Instead of mathematics feeling neat and predictable, it suddenly becomes strange and intriguing. Students discover that some of the most interesting mathematical questions are the ones that make us realise our first instinct may not be enough.

12.30 – 1.30 Lunch

1.30 – 3.30 Goats, Guesses and Hidden Number Codes

In the afternoon, students meet one of the most famous problems in probability: the Monty Hall problem. It begins with a simple choice, but leads to an answer that feels completely wrong until you work through it properly. This is a great example of the course as a whole – mathematics here is full of surprises, and part of the fun is learning when to trust logic over instinct.

The second half of the afternoon explores number systems from different cultures and different ways of thinking. Students see that the numbers we use every day are not the only possible system, and that mathematics looks very different when you change the structure underneath it. This part of the course is especially good at showing that maths is not fixed and ordinary – it is inventive, human, and full of alternative possibilities. The day ends with students creating a number system of their own, turning mathematical structure into something imaginative and playful.

Throughout Day One, the MIπ mission gives the mathematics a strong sense of momentum. Students are not just moving from topic to topic – they are gathering ideas, tools, and clues that will matter later.

10.00 – 12.30 Doughnuts, Double Agents and Impossible Maps

On Day Two, the story continues. Students return to MIπ not as new recruits, but as agents with a mission. They travel to Topolograd, where the mathematics becomes even more imaginative. The day begins with strategy and decision-making, using games and quick-fire challenges to explore risk, judgement, and the strange fact that the smartest choice is not always the most obvious one.

The main mathematical focus of the morning is topology – a topic that feels almost magical when students first meet it. This is the mathematics of shape, space, and connection. Students encounter puzzles that seem impossible on an ordinary flat surface, then discover that everything changes if you think about space differently. A doughnut, a coffee mug, and a network puzzle suddenly become part of the same conversation. It is a brilliant topic for this age group because it feels visual, weird, and genuinely new.

The morning also introduces a famous decision problem about how to choose well when you do not get a second chance. Again, the appeal is not just that the problem has a clever answer, but that it shows students mathematics being used to think about uncertainty, timing, and judgement.

12.30 – 1.30 Lunch

1.30 – 3.30 Trust, Ciphers and the Final Challenge

The afternoon begins with the prisoner’s dilemma, a classic problem in game theory. Here the mathematics becomes social: students explore trust, cooperation, bluffing, and strategy, and begin to see how mathematical ideas can help explain behaviour as well as numbers and shapes. This part of the course is lively and interactive, and it often leads to exactly the kind of conversation bright students enjoy – not just “what is the answer?” but “why do people behave like this?”

The course then moves into cryptography, where mathematics becomes the art of secret messages. Students explore codes, ciphers, and code-breaking, and see how patterns in language can help reveal hidden meaning. This is the kind of mathematics that feels immediately exciting – secret writing, hidden structures, clever decoding – but it also opens onto deeper mathematical ideas about pattern, frequency, and logical deduction.

Finally, the two days come together in a larger mission-based finale. By this stage, students have built up a whole collection of mathematical tools through the MIπ story, and the final challenge asks them to use those ideas together. This gives the course a strong ending: not just a final puzzle, but the sense that all the different topics have been leading somewhere.

This outline provides a detailed view of the themes, ideas, and activities explored during the online Young Mathematicians Summer School. The programme is designed to introduce students to a wide range of mathematical thinking – from codebreaking, number systems, and logical puzzles to probability, topology, and collaborative problem-solving – in a way that is challenging, accessible, and enjoyable.

You can also return to the main Young Mathematicians course page for full details about the course and how to apply.