Impacts of Johann Carl Friedrich Gauss as a Mathematician - Term Paper Example

In his lifetime, Gauss had hardly made a contribution to the field of mathematics. It is said that the German mathematician was aloof to the pubic world of the mathematicians notable in his days. Gauss only communicated to a few of his trusted friends who were also strongly inclined to mathematics. Besides Bolyai, Schumacher was one of Gauss’s trusted correspondence in which the latter confided to the former about his spending a “considerable time on geometry” (Tent, 2006, p. 214). On the other hand, upon the death of the gifted mathematician -- and the subsequent discovery of his mathematical notes and ideas -- the world of mathematics had never been the same.

Particularly his contribution to the shaping of the so-called non-Euclidean geometry, Gauss had made an impact to the sphere of geometry. His schoolmate Bolyai had asked him, for several times, pertaining to his view to Euclid’s fifth postulate -- also known as the parallel postulate. But Gauss did not disclose his discovery concerning the existence of the non-Euclidean geometry for the reason that he did not want to “rock the boat” (Tent, 2006, p. 215). True, Gauss’s non-Euclidean geometry -- first he called it as anti-Euclidean -- had caused a stir in the area of mathematics marked in the late 18th century.

Non-Euclidean geometry is basically defined as an area in geometry in which Euclid’s first four postulates are held but the fifth postulate has a quite different and distinct version in contrast to what is stated in the Elements (Weisstein, 2011). Among various versions of non-Euclidean geometry, the so-called hyperbolic geometry is where Gauss belongs to. In one of their conversations, Gauss revealed to Schumacher about his anti-Euclidean geometry: “I realized that there also had to be triangles whose three angles add up to more or less than 1800 in the non-Euclidean world.

I had it all mapped out” (Tent, 2006, 214, my italics). Here, Gauss categorized the fundamental elements of his newly found mathematics. That is to say, Gauss’s non-Euclidean geometry is a departure from two-dimensional geometry characterized in Euclidean mathematics. Gauss’s hyperbolic geometry, in fact, works greatly in three-dimensional geometry or space. Thence, the impact of Gauss’s mathematical discovery, if not innovation, was quite evident especially within the field of mathematics.

For one, Gauss had opened up a new world or knowledge about the wider space or scope of mathematics, particularly geometry. That is, man does not live in a narrow two-dimensional space. Based from this paradigm (i.e., hyperbolic geometry), one can explore the multifarious possibilities laid open by non-Euclidean geometry. Perhaps the greatest impact of Gauss’s hyperbolic mathematics is found in the sphere of astronomy. In 1801, for instance, Gauss’s mathematics had greatly facilitated the discovery of a dwarf planet named Ceres (Tyson, 2004).

Evidently, this is the triumph of mathematics. Utilizing the non-Euclidean geometry, it became possible for man to calculate the universe even without the use of advanced technology such as the telescope. Using Gauss’s hyperbolic geometry, man is able to see the cosmos beyond the Euclidean geometry can offer. Space, after all, is three-dimensional -- be it space in/on earth or in the universe. Generally, non-Euclidean geo