Joseph Liouville

Joseph Liouville was a French mathematician born in 1809, known for his significant contributions to number theory and mathematical analysis. He is famous for Liouville's theorem, which states that every smooth function can be approximated by rational functions to any degree of accuracy. Additionally, he introduced the concept of "Liouville numbers," which are numbers that cannot be the roots of any polynomial equation with rational coefficients, highlighting a distinction between algebraic and transcendental numbers. His work laid important groundwork in fields such as algebraic number theory and transcendental number theory.