Carl Friedrich Gauss was born in Brunswick, Germany on April 30th, 1777. His parents were illiterate and quite poor, but he altered this unsuccessful pattern in his family history by evolving into a child prodigy, he was also known as an indefinite genius. Gauss was attracted to the fields of Mathematics and Physics in his early childhood and began changing human history from his teens onward. Carl Friedrich Gauss changed mathematics as we know it, he was an influential figure that not only solved problems, but proved theories no one else could threw his magnum opus (masterpiece), Disquisitiones Arithmeticae.
The famous textbook Disquisitiones Arithmeticae published in 1798 was exceptionally advanced for its time. Carl pieced together as well as transformed the works of Fermat, Euler, Lagrange, & Legendre into a powerful book concerning algebraic concepts, such as: Imaginary Quadratic Number Fields with Even and Odd Discriminants, L-functions, Complex Multiplication, but over all it consolidates the Number Theory as a discipline. This exemplary resource set the precedent for modern mathematics in that Gauss used logical proof to prove and support his theories. Carl most definitely sent a wave through the scientific community, influencing many others like Sophie Germain and Ferdinand Minding.
Also, Carl discovered the heptadecagon, which is a 17 sided polygon. He found it was a constructible polygon as well, meaning it can be constructed with only a compass and straight edge. He proved this figures existence in two ways. The first way being: the constructibility is equivalent to the trigonometric functions of the common angle in terms of arithmetic operations and square root extractions. The second being: this figure can form if the odd prime factors of n are distinct Fermat primes, which are of the form ￼. This discovery represented the first progression concerning regular polygons in over 2000 years.
Modular arithmetic is a...