Lindemann’s Conjecture

Lindemann’s Conjecture, now a proven theorem, states that for any non-zero algebraic number (a root of a polynomial with rational coefficients), its exponential is transcendental—meaning it cannot satisfy any algebraic equation with rational coefficients. Essentially, this implies that numbers like e (the base of natural logarithms) and π (pi) are transcendental, confirming that certain constants involved in mathematics are fundamentally non-algebraic. This result has profound implications in number theory, especially in understanding the nature of transcendental numbers and proving the irrationality or transcendence of particular mathematical constants.