1. Gauss elimination method: Gauss invented an algorithm for solving linear equations, namely Gauss elimination method. This method is widely used in numerical calculation and is still widely used today.
2. Least square method: Gauss proposed the least square method, which is the best method to fit the data. The least square method has important applications in statistics, physics and engineering.
3. Gaussian distribution: Gaussian put forward the famous Gaussian distribution (normal distribution), which is a probability distribution that describes continuous random variables. Gaussian distribution is widely used in many fields, such as probability theory, statistics, physics and so on.
4. Complex number theory: Gauss has made an important contribution to the study of complex numbers. He proved that the addition and multiplication of complex numbers satisfy the laws of exchange, association and distribution, thus laying the foundation of complex number theory.
5. Gauss integration: Gauss proposed a new integration method, namely Gauss integration. This method has high efficiency in solving complex integral problems and has an important influence on the development of integral.
6. Gaussian function: Gaussian proposed a special function, namely Gaussian function. This function is widely used in probability theory, statistics, physics and other fields.
7. Magnetic research: Gauss has also made important achievements in magnetic research. He discovered the law of magnetic flux, which laid the foundation for the development of electromagnetism.
In a word, Gauss's mathematical achievements are rich and varied, which have had a far-reaching impact on later generations. Many of his theories and methods are still widely used and become an important part of modern mathematics.