IntroductionPublishing more than 150 works, Carl Friedrich Gauss, born in Brunswick, Germany (1777), is notably a world-renowned mathematician. He contributed to some of the most influential and fundamental mathematical theories and concepts, including geometry, probability theory, number theory, function theory, planetary astronomy, and, most importantly, the theorem of algebra. Born into an underprivileged family, Gauss was fortunate that his mother and uncle recognized his genius abilities in mathematics and thus provided him with an education to develop his gift. Gauss attended college, devoting his life to mathematics, discovering and exhuming major mathematical concepts along the way, which he preserved in private journals until they were perfected enough to be published. Gauss is considered, alongside Isaac Newton and Archimedes, one of the three greatest mathematicians of all time. Mathematical Concepts Fundamental Theory of Algebra Gauss contributed significantly to the fundamental theory of algebra in more ways than one. After completing his university studies (1792), he discovered that a ruler and a compass alone could construct a regular polygon with 17 sides. This was a substantial discovery because it opened the door to further insights from Galois theory, through not only results but also evidence found in the analysis of factoring polynomial equations. This foundation of knowledge that he created led him to be the first mathematician to give a rigorous proof of the theorem. This theorem was first stated by d'Alembert (1764), but was fully proven by Gauss at the age of 21, leading to his doctoral dissertation (1797), which provided further proof of the theorem fundamentals of algebra. The three proofs can be located in the middle of a paper. The proofs present in today's society would not be possible without Gauss's efforts on number theory.• In addition to providing attributes such as the Fundamental Theorem from algebra to mathematics Gauss also contributed the principle development of energy conservation, discovered Ceres, an asteroid orbiting the sun and introduced the method of least squares, which is a method used in all sciences to minimize the impact of measurement errors. . Without these contributions, mathematicians and scientists would not have the knowledge and equipment to continue to advance these questions.• On a fundamental note, Gauss's theorems and theories enabled a smoother transaction in life everyday, whether known to individuals or not, his work has left an everlasting imprint on the development of mathematics in areas such as technology and practical problem solving.