Amir Alexander, Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World (Scientific American/Farrar, Straus and Giroux): The paradoxical idea of infinitesimal quantities preoccupied ancient Greek mathematicians, especially Archimedes, who used the concept to calculate volumes of circles, cylinders, and spheres. But the mathematical mysteries the idea presented were largely ignored until the fifteen-hundreds, when the problem of the infinitesimal became a source of philosophical dispute. In his new book, Alexander, a professor of history at U.C.L.A., explains how the mathematical debate was a battle over differing visions for modern Europe, between those who sought to protect the status quo and those who embraced progress and reform. newyorker.

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