The deepest human need is to engage with the world: confidently, productively, creatively, sociably. Our ideal life is one long discovery, not of received opinions, but of truths: new forms and arguments that, once understood, are indisputably true for everyone. That is what mathematics offers: beautiful concepts and powerful tools for making sense of a fascinating, puzzling universe.
This does not sound like the average math lesson, because what most schools teach is not what mathematicians do. Mathematicians don’t repeat the same technique twenty times; they play with problems, they discuss them, they explore side-branches, they make mistakes. The “right answer” – the proof, the demonstration – simply sets a mile-marker between one phase of discovery and the next.
In our Math Circles, young people invent and discover their shared way to the insights that will make them citizens of mathematics. Through collegial exchange of free imagination and logical argument, they gain admiration for each other and self-esteem as the harmonious forms they are studying emerge.
The class leader simply poses an accessible mystery – a deep, resonant problem – and invites conjectures on ways to solve it. Like a sherpa’s, the leader’s role is to assist the expedition, bringing up supplies, shifting the base camp, and giving helpful readings of the landscape… but it is the students who will do all the climbing. As the first mystery resolves, it reveals farther vistas: insight leads to outlook.
We don’t conclude with tests or grades or awards: curiosity is always a finer spur than rivalry. Nor do we diminish the students’ discoveries by reciting the famous names of those who had gone this way before. Mathematics is our universal language — but each of us learns to make our own.
We offer online circles for children of all ages, offering scholarships based solely on financial need.
We train teachers, both from school and university backgrounds, in the art of guiding shared discovery.
We work with communities and countries who see the value of this simple but profound approach to discovering mathematics.
We maintain and constantly refine a resource of accessible mysteries, or fruitful problems – not as lesson plans or texts, but in schematic form, suggesting avenues along which the conversation might develop.