Johann Carl Friedrich Gauss (1777-1855), a legendary German mathematician, astronomer, and physicist, is considered to be among the leading mathematicians of all time. At age 19, Gauss demonstrated a method for constructing a heptadecagon using only a straightedge and compass, a process that had eluded the Greeks. Gauss proved the fundamental theorem of algebra, which states that every polynomial has a root of the form a+bi. 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 Disquisitiones Arithmeticae (1801), considered to be one of most important mathematical treatises of all time. Gauss also developed the method of least squares fitting, 10 years before Adrien-Marie Legendre, but did not publish his findings. His breadth of knowledge was expansive, from the theory of numbers, to algebra, analysis, geometry, probability, and the theory of errors. He applied these and other insights to an equally impressive range of empirical and theoretical research in observational astronomy, celestial mechanics, surveying, geodesy, capillarity, geomagnetism, electromagnetism, mechanism optics, and actuarial science.
Fundamental theorem of algebra (University of St. Andrews, Scotland, School of Mathematics and Statistics)
Gauss - Biography (University of St. Andrews, Scotland, School of Mathematics and Statistics)