Nicolas Bourbaki, whose mathematical publications began to appear in the late 1930s, was a direct product of and major force behind an important revolution that took place in the early part of the 20th Century. The area of his work - pure maths - is a seemingly abstract field of human study with no direct connection to the real world, but in reality closely linked to the culture that surrounds it. This is the story of Bourbaki and the world that created him - the story of an elaborate intellectual joke, because this extremely influential mathematician never existed.