Gauss is a giant among mathematical giants. As a young man he gave a rule-and-compass construction of the 17-gon. He made fundamental contributions to number theory, for which he invented the theory of congruences, a basic tool to this day. His theorems on line and surface integrals lie at the heart of modern physics and are essential for understanding electromagnetism. Gauss was one of the discoverers of non-Euclidean geometry. He conducted experiments to determine whether space was flat, negatively curved, or positively curved by accurately surveying a large triangle with vertices at three mountain tops, then seeing whether the sum of the interior angles is equal to zero, less than zero, or greater than zero. He found space to be flat, within the limits of experimental error. Gauss developed many computational tools and applied them to computing the orbits of planets and moons.

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