Mathematics must be creative, else it ain't mathematics - 0 views
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There are no topics in mathematics; only artificial barriers that we have erected to help organise the curriculum. At school, we study topics in discrete chunks and come to understand them as separate islands of knowledge. Yet the most powerful and interesting mathematics arises when we cut through these barriers.
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Knowledge has its place; you cannot connect or create what you don’t know. Tokio Myers is a trained pianist; his thousands of hours of deliberate practice are the foundation of his creativity. But he is more than a pianist (he’s a BGT winner!), and that is because he dared to defy the the conventional norms of music. Wiles is similarly the world class mathematician that he is because his field of vision is not restricted to any one topic.
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The tyranny of school maths lies in the false promise that stuffing oneself with facts and procedures prepares you for creativity. The act of creativity is deferred to an unspecified time — presumably it is for older, more knowledgeable people.
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Young age is no barrier — my most impressive students are also the shortest; it only takes a well-crafted maths problem to unleash their innate creativity.
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There are obvious benefits to going deep in a particular area and I always offer a gracious nod to the fluency and fundamentals of mathematics. But mathematics at its most fundamental is an integrated body of ideas, replete in patterns. The patterns and connections are what makes it mathematics. Let that be your next headline.