Proof that Pi is Irrational

This is the mathematical result, and its proof, showing that pi cannot be written as a ratio of two integers. Johann Heinrich Lambert gave the first proof of this fact in the 1760s. In the nineteenth century Charles Hermite found a proof requiring nothing beyond basic calculus, and this proof was later simplified further by Mary Cartwright, Ivan Niven, and the collective mathematician known as Nicolas Bourbaki, with most of these arguments proceeding by contradiction. In 1882 Ferdinand von Lindemann went further and proved that pi is not merely irrational but transcendental, meaning it is not the root of any polynomial with rational coefficients.