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At the age of seven Carl Friedrich Gauss started elementary school and his potential was noticed almost immediately His teacher Bttner and his assistant Martin Bartels were amazed when Gauss summed the integers from 1 to 100 instantly by spotting that the sum was 50 pairs of numbers each pair summing to 101 In 1788 Gauss began his education at the Gymnasium with the help of Bttner and Bartels where he learnt High German and Latin After receiving a stipend from the Duke of Brunswick- Wolfenbttel Gauss entered Brunswick Collegium Carolinum in 1792 At the academy Gauss independently discovered Bodes law the binomial theorem and the arithmetic- geometric mean as well as the law of quadratic reciprocity and the prime number theorem In 1795 Gauss left Brunswick to study at Gttingen University Gausss teacher there was Kaestner whom Gauss often ridiculed His only known friend amongst the students was Farkas Bolyai They met in 1799 and corresponded with each other for many years Gauss left Gttingen in 1798 without a diploma but by this time he had made one of his most important discoveries - the construction of a regular 17-gon by ruler and compasses This was the most major advance in this field since the time of Greek mathematics and was published as Section VII of Gausss famous work Disquisitiones Arithmeticae Gauss returned to Brunswick where he received a degree in 1799 After the Duke of Brunswick had agreed to continue Gausss stipend he requested that Gauss submit a doctoral dissertation to the University of Helmstedt He already knew Pfaff who was chosen to be his advisor Gausss dissertation was a discussion of the fundamental theorem of algebra With his stipend to support him Gauss did not need to find a job so devoted himself to research He published the book Disquisitiones Arithmeticae in the summer of 1801 There were seven sections all but the last section referred to
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