Birthday of Joseph Liouville (1809)

Joseph Liouville was the first to prove the existence of transcendental numbers — numbers that are not roots of any polynomial with integer coefficients. In 1844, he constructed an explicit example: 0.1100010000000000000000010000… where 1s appear only at positions 1!, 2!, 3!, 4!, … This number, now called Liouville's constant, cannot be algebraic. It was only later that Hermite (1873) proved e is transcendental and Lindemann (1882) proved π is — resolving the 2,000-year-old question of squaring the circle.