Worlds within Worlds

Like 'Fermat's Last Theorem', Jim Holt reveals the hidden history and personalities behind one of the most dangerous ideas in mathematics -- the infinitesimal. For most people the idea of the infinite conjures up images of inconceivable vastness, worlds without end. But there is another kind of infinite, one that is equally marvellous and, for all its seeming humility, far more important to the course of civilization -- that is the infinitely small -- the infinitesimal. The idea of the infintely small has been one of the most powerful tools in the history of science. Invented by the Greeks to 'save the reality' of the world, it was quickly attacked by Zeno and banned from natural philosophy by Aristotle and Euclid. Regarded as fundamentally destabilising by governments and radical thinkers such as Hume and Marx, the infinitesimal has continued a shadowy existence in the thoughts of mystics and theologians, until it was rehabilitated in the 1960s by the brilliant Abraham Robinson. 'Worlds within Worlds' is a corruscating study in the history of mathematics and a brilliant biography of an idea.