Mathematical logic, set theory, lattices and universal algebra form an interconnected framework that underpins much of modern mathematics. At its heart, mathematical logic provides rigorous formal ...

We recently wrote about how infinitely large sets are not all the same size as each other, but we were a bit vague about what we meant by a set. The people who invented set theory also started out ...

Transfinite set theory encompasses the rigorous study of infinite hierarchies, particularly those structured by ordinals and cardinals. This field has been instrumental in deepening our comprehension ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...

Can mathematics handle things that are essentially the same without being exactly equal? Category theorist Eugenia Cheng and host Steven Strogatz discuss the power and pleasures of abstraction.

Set theory is a mathematical abstract concerned with the grouping of sets of numbers that have commonality. For example, all even numbers make up a set, and all odd numbers comprise a set. All numbers ...

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, ...

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