Probability theory has long provided a rigorous framework for quantifying uncertainty, yet its extension to infinite sets introduces profound conceptual challenges and opportunities. Contemporary ...

One question has preoccupied humankind for thousands of years: Do infinities exist? More than 2,300 years ago Aristotle distinguished between two types of infinity: potential and actual. The former ...

Most patterns eventually repeat themselves. But in the 1970s, mathematician Roger Penrose discovered a set of shapes that could cover an infinite plane without ever repeating. Known as Penrose tilings ...