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Johann Carl Friedrich Gauss (IPA /'ga?s/, Audio&_160;(help·info), German Gauß, Latin Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. Sometimes known as the princeps mathematicorum[1] (Latin, usually translated as "the Prince of Mathematicians", although Latin princeps also can simply mean "the foremost") and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians.[2] Gauss was a child prodigy. There are many anecdotes pertaining to his precocity while a toddler, and he made his first ground-breaking mathematical discoveries while still a teenager. He completed Disquisitiones Arithmeticae, his magnum opus, in 1798 at the age of 21, though it would not be published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day. Gauss was born in Braunschweig, in the Electorate of Brunswick-Lüneburg, now part of Lower Saxony, Germany, as the only son of poor working-class parents.[3] There are several stories of his early genius, all of them open to doubt; according to one, his gifts became very apparent at the age of three when he corrected, in his head, an error his father had made on paper while calculating finances. Another famous story, and one that has evolved in the telling, has it that in primary school his teacher, J.G. Büttner, tried to occupy pupils by making them add a list of integers. The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher and his assistant Martin Bartels. Gauss's presumed method, which supposes the list of numbers was from 1 to 100, was to realise that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050 (see arithmetic series and summation).[4] However whilst the method works, the incident itself is probably apocryphal; some, such as Joseph Rotman in his book A first course in Abstract Algebra, question whether it ever happened.
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