Baker's theorem

Baker's theorem is a mathematical result that helps us understand how closely certain types of numbers—called algebraic numbers—can be approximated by rational numbers (fractions). Specifically, it establishes limits on how accurate these approximations can be, ensuring that algebraic numbers cannot be too closely approximated by fractions with very small denominators. This theorem is important in number theory because it provides bounds on how well algebraic numbers can be approximated, which has implications for the study of transcendental numbers and the nature of irrationality.