Discrete Mathematics is a subject that has gained prominence in recent times. Unlike regular Maths, where we deal with real numbers that vary continuously, Discrete Mathematics deals with logic that ...

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 ...

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 ...

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 ...

On a recent train trip from Lyon to Paris, Vladimir Voevodsky sat next to Steve Awodey and tried to convince him to change the way he does mathematics. Voevodsky, 48, is a permanent faculty member at ...

The theory of sets provides a foundation for all of mathematics. We shall discuss, informally, axioms for sets and develop the theory of infinite ordinal and cardinal numbers and their 'arithmetic'.

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 ...

In a breakthrough that disproves decades of conventional wisdom, two mathematicians have shown that two different variants of infinity are actually the same size. The advance touches on one of the ...