Carl Friedrich Gauss and his mathematical contributions

Carl Friedrich Gauss

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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

Main Contribution

It being impossible to present one main contribution as Gauss's foremost effort, we can separate four areas of contribution/focus for Gauss: (Encyclopedia of World Biography, 2005)

In his Disquisitiones arithmeticae he addressed the area of quadratic residues and his own discovery of the law of quadratic reciprocity, which he had discovered in his late teens. He made three main contributions to the theory of numbers: congruence theory, studies on the separation of the circle into equal parts, and theory of quadratic forms.

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.