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Timothy Gowers presents his lecture of the year in the series les courTs du Collège de France

Combinatorics is a field that tends to focus more on problem solving than on theory development. Nevertheless, the solutions to problems that are most celebrated are often those that introduce a new tool or technique that can be applied in many other situations. This lecture focuses on six such tools. Each of them can be used to solve problems that would otherwise be very difficult to solve.