Gauss's range of accomplishments is so remarkable that legends, often unverified, have grown around his youth and work. The story of how he was able to find the sum of all the integers from 1 to 100 is often told. Although he published very few works in his lifetime, he is credited with making a conjecture regarding the distribution of prime numbers, among the integers, elaborating the complete classification of polygons that can be constructed using a straightedge and compass, proving the fundamental theorem of algebra, introducing modular arithmetic, describing non-Euclidean geometries and various other accomplishments in mathematics, astronomy and physics.