Conformal invariance is a property in physics and mathematics where certain equations or systems remain unchanged under conformal transformations. These transformations preserve angles but not necessarily distances, allowing for a flexible way to analyze shapes and structures. This concept is particularly important in fields like theoretical physics and complex analysis. In statistical mechanics and quantum field theory, conformal invariance helps simplify complex problems by revealing underlying symmetries. For example, in string theory, it plays a crucial role in understanding how strings behave in different dimensions, leading to insights about the fundamental nature of space and time.