Tell me and I forget. Ask me and I discover.
The greatest and most important impact of the Global Math Circle is on the individual mind: discovering that you can engage with the beautiful structures that underlie our universe and our thought without having to go through rote memorization, repetitive problem sets or competitive tests. Getting the chance, from the earliest acquaintance and the youngest age, to pursue mathematics the same way mathematicians do: as a joyous, boundless quest.
Extend this individual impact over the total number of students and you find it increasing, not in multiples, but by powers: experiencing learning in its purest form, a collegial grappling with real, rewarding problems. Developing confidence in oneself and admiration for others. Gaining the ability to think creatively and critically. Realizing that there’s a point to learning. Achieving freedom of mind… for mathematics, fundamentally, is freedom.
And because the Math Circle technique requires no expensive facilities or tools, but is passed on naturally from one enthusiastic mind to another, it can soon have a measurable impact, even in large societies facing complex challenges. In Brazil, for instance, Bob and Ellen Kaplan began in 2013 by training 108 teachers employed by O Círculo da Mathemàtica do Brasil and funded by the Instituto TIM (backed by TIM, the telecommunications company). Those class leaders then taught others, including more than 4,500 schoolteachers in the public school system. By 2017, more than 3,000 Math Circles had reached more than 25,000 children – each of whom got the opportunity to experience that precious liberation of the individual mind.
One of the deepest human desires is to engage with the world: confidently, productively, creatively, collegially. Our ideal life is one long discovery, not of received platitudes and opinions, but of truths: new forms and arguments that, once understood, are indisputably so – 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 confidence in themselves 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.