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World events in 2017 have revealed the fundamental features of social systems and their trajectories. Is the world becoming a better place in terms of wellbeing, wealth, health, peace and the environment? The structure of power is changing, with the prominent roles played by Trump, Putin and Xi, and, while the West is growing and still dominant, the relative growth in the East is greater. Other cultural formations, such as languages, religions and political cultures, have also risen and fallen. How have different social groups related to one another, and how have social divisions manifested themselves in the different systems of society? An analysis of the surprising election in the UK here leads to a gravitational model of party trajectories in political space, while the fascinating 358-year trajectory of mathematical knowledge relating to Fermat’s Last Theorem and modularity is also presented. As such, this is a book about peace and conflict, politics, international relations, social science and quantitative methods.