Carl Friedrich Gauss, one of the most important and prolific mathematicians of all times, was born in Braunschweig, Germany on April 30, 1777. Gauss was recognized as a prodigy in elementary school, in part because of his now famous closed solution to the problem of summing the first \(n\) integers: \[1 + 2 + \cdots + n = \frac{n (n + 1)}{2}\] obtained by noting that twice the sum could be represented as \(n\) pairs of numbers, each summing to \(n + 1\). Gauss attended Göttingen University from 1795 to 1798, where he made fundamental discoveries on the construction of regular \(n\)-gons by compass and straight edge. He received the doctoral degree from the University of Helmstedt, writing his dissertation on what is now known as the fundamental theorem of algebra (every polynomial equation has a complex solution). This result, along with many in number theory were published in his book Disquisitiones Arithmeticae (Inquiries into Arithmetic) in 1801, one of the most important and famous mathematical books ever written. In 1807, Gauss was appointed professor of mathematics and director of the observatory at Göttingen, positions that he held for the rest of his life.
The breadth of Gauss' contributions in mathematics is extraordinary. These include fundamental results in number theory, differential equations, infinite series, conic sections, numerical integration, the hypergeometric functions, differential geometry, non-Euclidean geometry, linear algebra, and potential theory. The mathematical discoveries were often made in order to solve problems in physics, where the list of subjects strongly influenced by Gauss is equally impressive: astronomy, electricity, magnetism, optics, and geodesy.
In probability and statistics, Gauss is famous for his development of the method of least squares and the discovery of the normal distribution, now also known as the Gaussian distribution in his honor.
Gauss was elected a Fellow of the Royal Society in 1804, and received the society's Copley Medal in 1838. A crater on the moon is named after Gauss. Gauss died on February 23, 1855 in Hanover, Germany.