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When he was six years old, Roger Penrose discovered a sundial in a clearing near his house. Through that machine made of light, shadow, and time, Roger glimpsed a “world behind the world” of transcendently beautiful geometry. It spurred him on a journey to become one of the world’s most influential mathematicians, philosophers, and physicists. Penrose would prove the limitations of general relativity, set a new agenda for theoretical physics, and astound colleagues and admirers with the elegance and beauty of his discoveries.

A vital book for leaders and decision makers, The Evolution of Cooperation reveals how cooperative principles help us think better about everything from military strategy, to political elections, to family dynamics.

Many of the artists that we encounter are completely unaware of the mathematics that bubble beneath their craft, while some consciously use it for inspiration. Our instincts might tell us that these two subjects are incompatible forces with nothing in common – mathematics being the realm of precise logic and art being the realm of emotion and aesthetics – but what if we’re wrong? Blueprints asks us to consider that mathematics and art may not be polar opposites after all.

An award-winning mathematician shows how we prove what’s true, and what to do when we can’t.