Romantic numbers are a type of real number that are irrational and transcendental. They are named after the German mathematician Karl Friedrich Gauss, who first studied them in the early 19th century. Romantic numbers have an infinite number of decimal places and cannot be expressed as a fraction or a ratio of TWO integers. They are also known as transcendental numbers, and they are important in mathematics because they can be used to solve certain equations that cannot be solved using rational numbers.