## Carl Friedrich Gauss

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A German mathematician (1777 - 1855), one of all time greatest. Gauss discovered the method of least squares and Gaussian elimination.

Gauss was something of a child prodigy; the most commonly told story relates that when he was 10 his teacher, wanting a rest, told his class to add up all the numbers from 1 to 100. Gauss did it in seconds, having noticed that 1+...+100 = 100+...+1 = (101+...+101)/2. He did important work in almost every area of mathematics. Such eclecticism is probably impossible today, since further progress in most areas of mathematics requires much hard background study. Some idea of the range of his work can be obtained by noting the many mathematical terms with "Gauss" in their names. E.g. Gaussian elimination (linear algebra); Gaussian primes (number theory); Gaussian distribution (statistics); Gauss [unit] (electromagnetism); Gaussian curvature (differential geometry); Gaussian quadrature (numerical analysis); Gauss-Bonnet formula (differential geometry); Gauss's identity (hypergeometric functions); Gauss sums (number theory). His favourite area of mathematics was number theory. He conjectured the Prime Number Theorem, pioneered the theory of quadratic forms, proved the quadratic reciprocity theorem, and much more. He was "the first mathematician to use complex numbers in a really confident and scientific way" (Hardy & Wright, chapter 12). He nearly went into architecture rather than mathematics; what decided him on mathematics was his proof, at age 18, of the startling theorem that a regular N-sided polygon can be constructed with ruler and compasses if and only if N is a power of 2 times a product of distinct Fermat primes.Last updated: 1995-04-10

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Caribou CodeWorks ♦ **Carl Friedrich Gauss** ♦ Carnegie Mellon University

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