Gauss's contributions to number theory, algebra, astronomy, and geometry

Carl Friedrich Gauss

This is a template and guideline. Please do not use as a final turn-in paper.

Biography

Gauss, a German mathematician and scientist, was born in 1777. His contributions range over many fields including: geophysics, electrostatics, optics, astronomy, statistics, theory of numbers, differential geometry and more. His nickname was "Prince of Mathematicians" due to his outstanding impact on so many fields of math and science, and he is noted as one of the most influential mathematicians in history. At the age of 21, he wrote Disquisitiones Arithmeticae, a work that became fundamental in making the theory of numbers a discipline. It is still used today. While still in college, at the age of 19, he rediscovered a number of quite significant mathematical theorems, and invented modular arithmetic. In 1801, astronomers had discovered a small planet, Ceres, but lost it in the heavens. Using mathematics, Gauss correctly predicted where it could be relocated, and it was rediscovered. It began his path towards becoming Director of the astronomical observatory in Gottingen, a position he held and cherished the rest of his life (O'Connor & Robertson, 1996, para. 7). He invented the heliotrope, and discovered the potential of non-Euclidean geometry, which eventually led to the research that allowed Einstein to create his theory of general relativity. In 1831, he worked with physics professor Wilhelm Weber to study magnetism and constructed the first electromagnetic telegraph (Bell, 1986, p. 255). Gauss also developed a method of delineating the intensity of the earth's magnetic field. Gauss died in 1855

Algebra and Analysis

Up to Gauss's time, no one had been able to prove that every algebraic equation has at least one root. Gauss offered three proofs. And he modified the definition of a prime number.

Astronomical Calculations

We discussed briefly his assistance to astronomers in relocating Ceres. His success in this effort spurred him to develop the mathematical methods he used further. In 1809 his Theoria motus corporum coelestium used the method of least squares to determine the orbits of celestial bodies from observational data. In arguing his method, Gauss invented the Gaussian law of error, or, as we know it today, the normal distribution.

Non-Euclidean Geometry

Mathematicians, for centuries, had been attempting to prove Euclid's postulate concerning parallels (the sum of the angles of a triangle is two right angles). Gauss proved that a geometry could be developed without the parallel postulate, i.e. non-Euclidean geometry. And in his study of differential geometry developed the idea that the geometry of a curved surface could be considered as two-dimensional non-Euclidean geometry (Encyclopedia of World Biography, 2005, para. 13)

The pure greatness of Gauss is that his contributions are as influential today as they were in his time.