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Problem solving 101

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From the outside looking in, maths problem solving can seem like a kind of magic. Here is a typical image: a lone genius, peering at a vexing problem, rubs their chin, paces up and down; then a bolt of inspiration hits and the solution falls neatly into place.

And while it’s true that inspiration can strike the lucky few, for the rest of us this is no more than an illusion (and often a carefully cultivated illusion at that). In reality, problem solving is usually much more prosaic, nothing more than a careful application of well-known, and often quite elementary, techniques.

So what are these elementary techniques? In this article, I’ll look at some of the simplest and easiest to understand. Happily, they are also some of the most powerful and widely applicable. These techniques will be explained by way of example problems; I strongly encourage you to attempt the problems yourself before reading the solutions. Continue reading

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Review of Birth of a Theorem

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Cédric Villani’s Birth of a Theorem tells the story of a mathematical theorem, from its initial conception as a vague, throwaway observation, to its development and formal statement, right through to its proof and eventual publication, a journey lasting several years. The theorem in question is the important result of Villani and his former PhD student Clément Mouhot on the phenomena of ‘Landau damping’, a result that ultimately won Villani the 2010 Fields Medal and widespread acclaim.
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