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 ...

Category theory, K theory and homological algebra are interrelated branches of mathematics that comprise a powerful conceptual framework for studying structures and their interconnections. Category ...

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 ...

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 ...

Hidden Fibonacci numbers, a new shape and the search for a grand unified theory of mathematics are among our choices for most ...

Math as both profession and course of study can be a hard sell, something even Don Draper might have trouble pitching. The field unites numbers, theories, and ideas that, yes, can be physically ...

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

Every pure mathematician has experienced that awkward moment when asked, “So what’s your research good for?” There are standard responses: a proud “Nothing!”; an explanation that mathematical research ...