German mathematician who is sometimes called the "prince of mathematics." He was a prodigious child, at the age of three informing his father of an arithmetical error in a complicated payroll calculation and stating the correct answer. In school, when his teacher gave the problem of summing the integers from 1 to 100 to his students to keep them busy, Gauss immediately wrote down the correct answer 5050 on his slate. At age 19, Gauss demonstrated a method for constructing a heptadecagon using only a straightedge and compass which had eluded the Greeks. (The explicit construction of the heptadecagon was accomplished around 1800 by Erchinger.) Gauss also showed that only regular polygons of a certain number of sides could be in that manner (a heptagon, for example, could not be constructed).

Gauss proved the fundamental theorem of algebra, which states that every polynomial has a root of the form a+bi. In fact, he gave four different proofs, the first of which appeared in his dissertation. In 1801, he proved the fundamental theorem of arithmetic, which states that every natural number can be represented as the product of primes in only one way.

At age 24, Gauss published one of the most brilliant achievements in mathematics, Disquisitiones Arithmeticae (1801). In it, Gauss systematized the study of number theory (properties of the integers). Gauss proved that every number is the sum of at most three triangular numbers and developed the algebra of congruences.

[Source: http://scienceworld.wolfram.com/biography/Gauss.html]