The paper [Tarski: Les fondements de la géométrie des corps, Annales de la Société Polonaise de Mathématiques, pp. 29-34, 1929] is in many ways remarkable. We address three historico-philosophical ...

THIS book is a sequel to “Euclid Revised” by the same author. It consists of one hundred pages, divided into three chapters and an appendix. The first chapter is devoted to the discussion of planes ...

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In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space. When you gaze out ...

Physicists recently mapped the hidden shape that underlies the quantum behaviors of a crystal, using a new method that’s expected to become ubiquitous. Famously, at the quantum scale, particles can be ...