Carl Friedrich Gauss

Lore & Background

Gauss was born on 30 April 1777 in Brunswick, in the Duchy of Brunswick-Wolfenbüttel (now in the German state of Lower Saxony). His family was of relatively low social status. His father Gebhard Dietrich Gauss (1744–1808) worked variously as a butcher, bricklayer, gardener, and treasurer of a death-benefit fund. Gauss characterized his father as honourable and respected, but rough and dominating at home. He was experienced in writing and calculating, whereas his second wife Dorothea, Carl Friedrich's mother, was nearly illiterate. He had one elder brother from his father's first marriage. Gauss was a child prodigy in mathematics. When the elementary teachers noticed his intellectual abilities, they brought him to the attention of the Duke of Brunswick who sent him to the local Collegium Carolinum, which he attended from 1792 to 1795 with Eberhard August Wilhelm von Zimmermann as one of his teachers. Thereafter the Duke granted him the resources for studies of mathematics, sciences, and classical languages at the University of Göttingen until 1798. His professor in mathematics was Abraham Gotthelf Kästner, whom Gauss called 'the leading mathematician among poets, and the leading poet among mathematicians' because of his epigrams. Astronomy was taught by Karl Felix Seyffer, with whom Gauss stayed in correspondence after graduation; Olbers and Gauss mocked him in their correspondence. On the other hand, he thought highly of Georg Christoph Lichtenberg, his teacher of physics, and of Christian Gottlob Heyne, whose lectures in classics Gauss attended with pleasure. Fellow students of this time were Johann Friedrich Benzenberg, Farkas Bolyai, and Heinrich Wilhelm Brandes. He was likely a self-taught student in mathematics since he independently rediscovered several theorems. He solved a geometrical problem that had occupied mathematicians since the Ancient Greeks when he determined in 1796 which regular polygons can be constructed by compass and straightedge. This discovery ultimately led Gauss to choose mathematics instead of philology as a career. Gauss's mathematical diary, a collection of short remarks about his results from the years 1796 until 1814, shows that many ideas for his mathematical magnum opus Disquisitiones Arithmeticae (1801) date from this time. An apocryphal story recounts that as an elementary student, Gauss and his class were tasked by their

Reader's Guide

From an early age, Gauss was known as a child prodigy in mathematics. While studying at the University of Göttingen, he propounded several mathematical theorems. As an independent scholar, he wrote the masterpieces Disquisitiones Arithmeticae and Theoria motus corporum coelestium. Gauss produced the second and third complete proofs of the fundamental theorem of algebra. He also introduced the triple bar symbol (≡) for congruence. In number theory, he made numerous contributions, such as the composition law, the law of quadratic reciprocity, and proved the triangular case of the Fermat polygonal number theorem. He also contributed to the theory of binary and ternary quadratic forms, and the theory of hypergeometric series. When Gauss was only 19 years old, he proved the construction of the heptadecagon, the first progress in regular polygon construction in over 2000 years. He also introduced the concept of Gaussian curvature and proved its key properties, especially with his Theorema Egregium. Gauss was the first to prove Gauss's inequality. Further, he was instrumental in the development of the arithmetic–geometric mean. He introduced the normal or Gaussian distribution in probability. Due to Gauss's extensive and fundamental contributions to science and mathematics, more than 100 mathematical and scientific concepts are named after him. Gauss was instrumental in the identification of Ceres as a dwarf planet. His work on the motion of planetoids disturbed by large planets led to the introduction of the Gaussian gravitational constant and the method of least squares, which he had discovered before Adrien-Marie Legendre published it. Gauss also introduced the algorithm known as recursive least squares. Gauss led the geodetic survey of the Kingdom of Hanover together with an arc measurement project from 1820 to 1844; Gauss was one of the founders of geophysics and formulated the fundamental principles of magnetism. He provided the first absolute measurement of Earth's magnetic field in 1832, later applying one of his inventions, that of spherical harmonic analysis, to show that most of Earth's magnetic field was internal. He was the first to discover and study non-Euclidean geometry, which he also named. Gauss was the first to develop a fast Fourier transform, doing so some 160 years before John Tukey and James Cooley. His practical work led to the invention of

Did You Know?

• Gauss was a child prodigy who, at age 19, proved the construction of the heptadecagon, the first progress in regular polygon construction in over 2000 years.
• He introduced the triple bar symbol (≡) for congruence in number theory.
• Gauss was the first to discover and study non-Euclidean geometry, which he also named.
• He developed a fast Fourier transform some 160 years before John Tukey and James Cooley.
• Gauss invented the heliotrope in 1821 and, with Wilhelm Eduard Weber, the first electromagnetic telegraph in 1833.

Notable Quotes (Wikiquote)

"Johann Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a German mathematician, astronomer and physicist." — Carl Friedrich Gauss "But in our opinion truths of this kind should be drawn from notions rather than from notations." — Carl Friedrich Gauss "Less depends upon the choice of words than upon this, that their introduction shall be justified by pregnant theorems." — Carl Friedrich Gauss "Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density." — Carl Friedrich Gauss