A transcendental number is a type of real or complex number that is not a root of any non-zero polynomial equation with rational coefficients. This means that transcendental numbers cannot be expressed as solutions to algebraic equations, distinguishing them from algebraic numbers, which can be. Famous examples of transcendental numbers include π (pi) and e (Euler's number). Both of these numbers have important applications in mathematics, particularly in calculus and geometry. The discovery of transcendental numbers was significant in understanding the nature of numbers and their classifications.