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Carl Friedrich Gauss was born on April 30, 1777 in Braunschweig, in the duchy of Braunschweig-Wolfenbüttel, now part of Lower Saxony, Germany, as the son of poor working-class parents.[4] Indeed, his mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension, which itself occurs 40 days after Easter. Gauss would later solve this puzzle for his birthdate in the context of finding the date of Easter, deriving methods to compute the date in both past and future years.[5] He was christened and confirmed in a church near the school he attended as a child.[6]

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 DisquisitionesArithmeticae, his magnum opus, in 1798 at the age of 21, though it was not published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.

Gauss's intellectual abilities attracted the attention of the Duke of Braunschweig,[2] who sent him to the Collegium Carolinum (now TechnischeUniversitätBraunschweig), which he attended from 1792 to 1795, and to the University of Göttinge0n from 1795 to 1798. While in university, Gauss independently rediscovered several important theorems;[citation needed] his breakthrough occurred in 1796 when he was able to show that any regular polygon with a number of sides which is a Fermat prime (and, consequently, those polygons with any number of sides which is the product of distinct Fermat primes and a power of 2) can be constructed by compass and straightedge. This was a major discovery in an important field of mathematics; construction problems had occupied mathematicians since the days of the Ancient Greeks, and the discovery ultimately led Gauss to choose mathematics instead of philology as a career. Gauss was so pleased by this result that he requested that a regular heptadecagon be inscribed on his tombstone. The stonemason declined, stating that the difficult construction would essentially look like a circle.[7]

The year 1796 was most productive for both Gauss and number theory. He discovered a construction of the heptadecagon on March 30.[8] He invented modular arithmetic, greatly simplifying manipulations in number theory.[citation needed] He became the first to prove the quadratic reciprocity law on 8 April. This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic. The prime number theorem, conjectured on 31 May, gives a good understanding of how the prime numbers are distributed among the integers. Gauss also discovered that every positive integer is representable as a sum of at most three triangular numbers on 10 July and then jotted down in his diary the famous words, "Heureka! num = Δ + Δ + Δ." On October 1 he published a result on the number of solutions of polynomials with coefficients in finite fields, which ultimately led to the Weil conjectures 150 years later