How do we fairly divide resources among individuals or groups with different preferences? This talk explores the rich mathematical landscape of fair division, drawing on decades of interdisciplinary research across mathematics, computer science, and economics. We'll examine fundamental fairness concepts, see how these principles apply to real-world challenges, and discuss algorithmic approaches that provide these fairness guarantees. Along the way, we'll highlight major open questions and explore applications from assigning courses to students and resolving inheritance disputes to allocating tasks efficiently. No background is needed just curiosity about how fairness can be achieved when dividing the indivisible!