The original version of this story appeared in Quanta Magazine. Mathematics started with numbers—clear, concrete, intuitive. Over the last two centuries, however, it has become a far more abstract ...

Heine Borel and the Finite Subcovers, a band composed of Notre Dame honors math graduates, now has their work out on vinyl.

This study extends algebraic perspectives to non-topological closure spaces by introducing Hopf structures. We define closure Hopf spaces and groups, investigate their properties, and explore homotopy ...