Carl Friedrich Gauss
<person> 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
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.
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