A mathematical singularity refers to a point at which a mathematical object is not well-defined or behaves unpredictably. This often occurs in functions where certain inputs lead to infinite outputs or undefined values, such as division by zero. Singularities can be found in various areas of mathematics, including calculus and complex analysis. In the context of physics, singularities are significant in theories like general relativity, where they describe points in space-time, such as the center of a black hole, where gravitational forces become infinitely strong. Understanding singularities helps mathematicians and scientists explore the limits of mathematical models and physical theories.