Transcendental numbers are a special type of real or complex number that cannot be the root of any non-zero polynomial equation with rational coefficients. This means they cannot be expressed as solutions to algebraic equations, making them more complex than algebraic numbers, which can be. Famous examples of transcendental numbers include π and e, both of which play significant roles in mathematics. The discovery of transcendental numbers was a significant advancement in number theory. The first number proven to be transcendental was e, shown by Charles Hermite in 1873. Later, Ferdinand von Lindemann proved that π is also transcendental in 1882, establishing that certain important constants are not algebraic.