How Hard is too Hard? An Introduction to Complexity

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Some mathematical problems can easily be solved on a computer, whilst some are probably impossible. Complexity theory is how we analyse difficulty, and one of the most famous open problems in mathematics is the question of whether P = NP: if the answer to a problem is easy to check, is the problem actually easy to solve? This lecture introduces the work of Alan Turing and other pioneers in the subject, before bringing us up-to-date with some recent progress.