Karl Friedrich Gauss

Karl Friedrich Gauss (1777-1855), the son of a bricklayer, was a child prodigy. He demonstrated his potential at the age of 10, when he quickly solved a problem assigned by a teacher to keep the class busy. The teacher asked the students to find the sum of the first 100 integers. This brilliance attracted the sponsorhip of patrons, including Duke Ferdinand of Brunswick, who made it possible for Gauss to attend Caroline College and the University of Göttingen. While a student, he invented the method of least squares, which is used to estimate the most likely value of a variable from experimental results. In 1796 Gauss made a fundamental discovery in geometry, advancing a subject that had not advanced since ancient times. He showed that a 17-sided regular polygon could be drawn using just a ruler and compass.

In 1799 Gauss presented the first rigorous proof of the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n roots (counting multiplicities). Gauss achived world-wide fame when he successfully calculated the orbit of the first asteroid discovered, Ceres, using scanty data.

Gauss was called the Prince of Mathematics by his contemporary matematicians. Although Gauss is noted for his many discoveries in geometry, algebra, analysis, and physics (Gauss' Law), he had a special interest in number theory, which can be seen from his statement "Mathematics is the queen of the sciences, and the theory of numbers is the queen of mathematics." Gauss laid the foundations for modern number theory with the publication of his book Disquisitiones Arithmeticae in 1801.

Sources: MacTutor History of Mathematics Archive (http://www-groups.dcs.st-andrews.ac.uk/~history/), Encyclopedia Britannica, Discrete Math and Its Applications

Oh, but there's so much more! Gauss devised Gauss' Theorem in vector calculus, which says the integral of a vector field over a volume is equal to the integral of the outward flowing normal component of the vector field over the surface area enclosing the volume, it's application to electrostatics, Gauss' Law, which says the electric field normal to the surfaces of an enclosed area is equal to the total charge in that area, the Gaussian Distribution, which is the 'natural' and easiest to work with probability distribution, and Gauss' Formula, which gives a quick formula for summing all of the integers in a given interval.

Regarding the latter, by far the most mundane of these discoveries, there is an interesting story. When Gauss was a small boy his mathematics teacher decided to punish him and his rowdy classmates by making them add all the numbers from 1 to 100. A minute later the young Gauss said 'finished!' The teacher was stunned. While all the other students were busy with long columns of addition, Gauss had given the problem some thought and come up with his formula. He was obviously gifted.

1777-1855
A German mathematician, astronomer and physicist, Gauss studied at the Collegium Carolinum at Brunswick and later the University of Gottingen, paid for by the Duke of Brunswick, who had noted his mathematical precocity. Gauss is widely regarded as one of the greatest mathematicians of all time, having made contributions to the fields of number theory, statistics, geometry, differential equations, the hypergeometric function and the curvature of surfaces. He created four new proofs of the fundamental theorem of algebra, one of prime number theory at a young age, and six of quadratic reciprocity.

Gauss spent most of his life the director of the Gottingen Observatory, where he studied celestial mechanics and introduced a new mathematical theory of optics and lenses, as well as discovering the theory of elleptic functions. He also extensively studied the Earth's magnetism and developed the magnetometer along with Wilhelm Weber, as well as publishing a new law of electric field strength, Gauss's Law.