~History of Carl F. Gauss~ Carl Friedrich Gauss(1777-1855) was born on April 30, 1777, in Brunswick, Germany. Gauss is considered to be one of the last mathematicians to know everything in his subject. Gauss's genius was revealed at a very early age. He was able to do long calculations in his head. He rediscovered the law of quadratic reciprocity, related the arithmetic-geometric mean to infinite series expansion, and conjectured the prime number theorem. Before the age of twenty, he showed that a regular polygon of seventeen sides was constructible with ruler and compass - an unsolved problem since Greek times. At the age of twenty, he published the first proof of the fundamental theorem of algebra. He completed his Ph.D. at the University of Helmstedt, under the supervision of Pfaff, when he was twenty-two. In 1801, Gauss published his monumental book on number theory, Disquisitiones Arithmeticae. In his Disquisitiones, Gauss summarized previous work in a systematic way and solved some of the most difficult outstanding questions. He introduced the notion of congruence of integers modulo an integer and extensively studied Z    and obtained many of its important properties. He is credited for coining the term complex number and the notation i for (-1). He showed that Z[i] is a unique factorization domain. In his honor, Z[i] is called the ring of Gaussian integers. Disquisitiones laid the foundations of algebraic number theory. Leopold Kronecker said, "It is really astonishing to think a single man of such young years was able to bring to light such a wealth of results, and above all, to present such a profound and well-organized treatment of an entirely new discipline." Besides being a mathematician he was also a physicist and an astronomer. In January 1801, a new planet was briefly observed, which the astronomers were unable to locate later. Gauss calculated the position of the planet by using a more accurate orbit theory than the usual circular approximation. Gauss used a theory based on the ellipse. At the end of the year the planet was discovered at the precise location he predicted. The methods he developed are still in use. They include the theory of least squares.