Gauss — Prince of Mathematicians
The mathematician who set the standard for rigor and depth
15.1 The Child Prodigy
Carl Friedrich Gauss (1777–1855) showed extraordinary talent from childhood. At 19, he proved that the regular 17-gon could be constructed with compass and straightedge — the first new constructible polygon since antiquity.
15.2 Disquisitiones Arithmeticae
Gauss's Disquisitiones Arithmeticae (1801), written at age 21, systematized number theory, introduced modular arithmetic, proved the law of quadratic reciprocity, and established the theory of quadratic forms. His motto was “Pauca sed matura” (Few but ripe).
15.3 Across Mathematics
Gauss contributed to number theory, algebra, differential geometry (Theorema Egregium), statistics (normal distribution, least squares), and astronomy (predicting the orbit of Ceres). He also privately developed non-Euclidean geometry but never published it.