In 1611 German mathematician Johannes Kepler made a conjecture about the densest way to stack oranges or other spheres with a minimum of space between them. It seemed nothing could beat the standard ...

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 ...

The telescope conjecture gave mathematicians a handle on ways to map one sphere to another. Now that it has been disproved, the universe of shapes has exploded. In early June, buzz built as ...

For most of us, or perhaps all of us, it's impossible to imagine a world consisting of more than three spatial dimensions. Are we correct when we intuit that such a world couldn't exist? Or is it that ...