This book is about mathematics in the management of innovation, showing how recent advances in mathematics help us grasp and support innovation as a social activity of thinking and imagining together. It will make the reader rethink both innovation and mathematics by having them interplay in practical organizational settings. Told as fiction to make its argument more accessible, the book is nonetheless grounded in theoretical reflections and recent mathematical advances. In recounting the adventures of a committed and enthusiastic inventor-designer hampered by the increasing industrial bureaucratization of his world, it accounts for the fate of many innovation processes in large companies and administrations. Successful innovation hinges on having everyone involved in the process share a space of conceptual exploration. This philosophical aspect of the innovation process is about collective imagination, a notion that customary styles of thought have great difficulty dealing with. This is where mathematics, of a new kind, might prove to be a new platform for better management of innovation.