## 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 17^{th} century, geometrical bodies were material objects, complex tapestries of interwoven lines, points, surfaces.