Higher dimensional spheres, or hyperspheres, are counter-intuitive and almost impossible to visualize. Mathematician Kelsey Houston-Edwards explains higher dimensional spheres and how recent ...

We are said that the real world in which humans live is present in three dimensions or four dimensions. "Three-dimensional" is a relatively easy-to-understand concept for people who live while ...

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American Earlier this year, Maryna Viazovska showed ...

Mathematicians, freed in their imaginations from physical constraints, can conjure up descriptions of objects in many more dimensions than that. Points in a plane can be described with pairs of ...

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In a pair of papers posted online this month, a Ukrainian mathematician has solved two high-dimensional versions of the centuries-old “sphere packing” problem. In dimensions eight and 24 (the latter ...

Michael Freedman’s momentous 1981 proof of the four-dimensional Poincaré conjecture was on the verge of being lost. The editors of a new book are trying to save it. One of the most important pieces of ...