The study of transcendental numbers has made an important contribution to the development of mathematics. First of all, the existence of transcendental numbers challenges mathematicians to know and understand real numbers and algebraic equations. /kloc-in the 9th century, mathematicians found that some numbers could not be obtained by finite addition, subtraction, multiplication, division and square root operations, and these numbers were transcendental numbers. This discovery broke the mathematician's illusion of perfect harmony of real numbers and promoted the deepening of mathematical research.

Secondly, the study of transcendental numbers promotes the development of algebraic theory. For example, in order to solve the problem of whether algebraic equations have solutions, mathematicians introduced the concept of transcendental numbers and developed a series of methods and theories to study transcendental numbers, such as Galois theory and eisenstein discriminant. These theories and methods not only solve some specific mathematical problems, but also provide new ideas and tools for the development of algebraic theory.

Thirdly, the study of transcendental numbers also promotes the development of number theory. For example, the proof of Fermat's last theorem depends on the nature of transcendental numbers. In addition, the study of transcendental numbers also involves many other mathematical fields, such as complex analysis, geometry, probability theory and so on.

Finally, the study of transcendental numbers has also had an impact on other scientific fields. For example, in physics, some theories of quantum mechanics need to use transcendental numbers; In computer science, some algorithms of cryptography also need to use transcendental numbers.

Generally speaking, the study of transcendental numbers has a far-reaching impact on the development of mathematics, which not only promotes the development of mathematical theory, but also provides important tools and methods for research in other scientific fields.