1798
In 1798 Gauss left Göttingen without his wanted diploma, but that didn't matter too greatly, for by this time Gauss had already completed one of the most important discoveries of his career; the construction of a regular 17-gon by using simply a compass and ruler. This was one huge leap in the field of geometry because many different (and famous) mathematicians has doubted such a construction. It was even considered the biggest leap since the time of Greek mathematicians such as Euclid, Pythagoras and Archimedes. This discovery also earned a spot, actually a chapter, in Gauss's famous book Disquisitiones Arithmeticae which was later published in 1801.
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