What were the contributions of Carl Friedrich Gauss to mathematics?

Carl Friedrich Gauss, often referred to as the "Prince of Mathematicians," made numerous significant contributions to the field of mathematics that have had a lasting impact. Some of his most notable contributions include:

Number Theory:

Gauss made important contributions to number theory with his work on prime numbers. He formulated the prime number theorem, which gives a rough estimate of the distribution of prime numbers.

Statistics:

One of Gauss's most well-known contributions to statistics is the Gaussian distribution, also known as the normal distribution. This distribution is widely used in various fields to model random variables.

Differential Geometry:

Gauss made significant contributions to differential geometry, including the development of Gauss's Law, which relates the curvature of a surface to the geometry of the surface itself.

In addition to these areas, Gauss also made contributions to complex numbers, differential equations, geodesy, astronomy, and theoretical physics. His work has had a profound impact on many branches of mathematics and science, earning him a lasting legacy as one of the greatest mathematicians of all time.