Inevitable randomness in discrete mathematics [Book Review]

Abstract

Complex systems arise naturally throughout mathematics, computer science, economics and the physical sciences. However, when faced with such intricate systems, we are often powerless to understand their behaviour. Without simplifying assumptions, such as that of the rational agent in economics, the size of the space of possibilities and its apparent lack of order can become overwhelming. In this book, József Beck explores this issue, suggesting that discrete systems which are not simple should always behave in a random-like fashion, even when different parts of the system do not behave independently. The central focus of the book is, to use the author's own term, the following 'vague' metaconjecture.

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