Amir Alexander: On the Materiality of Mathematics 1

Geometrical figures are like pieces of cloth. The Italian mathematician Bonaventura Cavalieri (1598-1647) thought so, and invited others to think in this way: “plane figures should be conceived by us as pieces of cloth are made up of parallel threads” he wrote in his Geometria Indivisibilibus of 1635. “And solids are like books, which are composed of parallel pages.”

Cavalieri’s view counted for much, because he was widely credited as a founder of infinitesimal mathematics, which led ultimately to the Calculus. His teacher Galileo believed that infinitesimals were like threads, which woven together make up a rope, and their English contemporary Thomas Harriot (1560-1621) argued that the mathematical continuum is made up of points in the same way that a physical body is composed of atoms. In the 17th century, geometrical bodies were material objects, complex tapestries of interwoven lines, points, surfaces.


Math Rutgers

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Bonaventura Cavalieri I

Bonaventura Cavalieri II

Bonaventura Cavalieri III

Bonaventura Cavalieri IV

Bonaventura Cavalieri V

Bonaventura Cavalieri VI

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