Algebraic structures, encompassing groups, rings, fields and modules, have long formed the backbone of modern mathematics. Category theory, with its focus on objects and morphisms, provides a unifying ...

On a crisp fall New England day during my junior year of college, I was walking past a subway entrance when a math problem caught my eye. A man was standing near a few brainteasers he had scribbled on ...

The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is ...

The human ecosystem is made of open and closed systems. While the earth is a closed system for matter but an open system for energy, the human body is considered an open system. There is a growing ...

Emily Riehl thinks hard about objects that don't exist in the material world yet mysteriously seem to underlie many things that do. These objects have no concrete existence of their own, but they do ...

Baez called for the development of new mathematics — he called it “green” math — to better capture the workings of Earth’s biosphere and climate. For his part, he sought to apply category theory, a ...

Homotopy theory is a cornerstone of modern algebraic topology, concerned with the study of spaces up to continuous deformations. This approach characterises topological spaces by their intrinsic ...

Excerpted with permission from Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, by Max Tegmark. Available from Random House/Knopf. Copyright ...