When mathematician Georg Cantor first glimpsed the true nature of infinity, it changed mathematics forever. He demonstrated that infinity isn’t just endless—it exists in different sizes, each opening ...

For centuries, the concept of infinity has captivated mathematicians and philosophers alike, stretching far beyond the simple idea of endless counting. Recent groundbreaking discoveries, however, have ...

A starry firmament, or sand cascading through one’s open fingers, or weeds springing up time after time: the first conception of infinity, of the uncountable and the unending, is not recorded, but it ...

Receive emails about upcoming NOVA programs and related content, as well as featured reporting about current events through a science lens. Reviel Netz: Something which is equal to some of its parts.

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 ...

IF YOU were forced to learn long division at school, you might have had cause to curse whoever invented arithmetic. A wearisome whirl of divisors and dividends, of bringing the next digit down and ...

Bounded lattices (that is lattices that are both lower bounded and upper bounded) form a large class of lattices that include all distributive lattices, many nondistributive finite lattices such as ...

NOVA: How do mathematicians define infinity? Netz: Something which is equal to some of its parts. That's really the technical definition. NOVA: Is there a difference between the mathematical concept ...