Number theory is a branch of mathematics, which mainly studies the properties of integers and their relationship with other mathematical concepts. Although number theory may not seem to be directly related to our daily life, in fact, it has important applications in many fields.

1. Cryptography: Number theory is widely used in cryptography. For example, RSA, a public key encryption algorithm, is based on the difficulty of large number decomposition. In addition, elliptic curve cryptography (ECC) is also based on number theory.

2. Computer science: In computer science, number theory is used to solve some complex problems, such as prime number test and factor decomposition. These problems have applications in computer security, data compression and cryptography.

3. Physics: In quantum mechanics, the representation and operation of quantum states involve complex numbers, and complex number theory is an important branch of number theory. Therefore, number theory has important applications in quantum mechanics.

4. Economics: In economics, number theory is used to study market equilibrium, auction theory and other issues. For example, the concept of Nash equilibrium is based on number theory.

5. Biology: In biology, number theory is used to study the dynamic behavior of biological populations, such as predator-prey model and epidemic model.

6. Social science: In social science, number theory is used to study the structure of social networks, group behavior and other issues.

Generally speaking, the application of number theory is very extensive. It not only plays an important role in mathematics itself, but also is widely used in other scientific fields.