Short answers, pulled from the story.
Carl Friedrich Gauss was a German mathematician, astronomer, geodesist, and physicist, born on the 30th of April 1777 and died on the 23rd of February 1855. He contributed to number theory, algebra, analysis, geometry, statistics, and probability, and more than 100 mathematical and scientific concepts are named after him.
At nineteen, Gauss proved that a regular heptadecagon, a seventeen-sided polygon, could be constructed with a compass and straightedge. It was the first progress in regular polygon construction in over 2000 years and led him to choose mathematics over philology.
Gauss predicted where the lost object Ceres would reappear after Giuseppe Piazzi discovered it on the 1st of January 1801 and lost it behind the Sun's glare. His prediction proved accurate within half a degree when Franz Xaver von Zach and Heinrich Olbers found it near the predicted position in December 1801.
The Theorema Egregium, or remarkable theorem, holds that the curvature of a surface can be determined by measuring angles and distances on the surface alone, regardless of how it sits in space. Gauss published it in 1828, and one consequence is that a sphere cannot be flattened to a plane without distortion.
Gauss published only work he considered complete and above criticism, following his personal seal's motto Pauca sed Matura, meaning "Few, but Ripe." This perfectionism delayed many discoveries, including his work on non-Euclidean geometry, which appeared only with the publication of his Nachlass in 1900.
Gauss provided the first absolute measurement of Earth's magnetic field in 1832 and built a magnetometer about ten times more precise than earlier instruments. With Wilhelm Weber he built the first electromechanical telegraph in 1833 and used spherical harmonic analysis to show that most of Earth's magnetic field comes from internal sources.