Carl Friedrich Gauss

Johann Carl Friedrich Gauss was a German mathematician, astronomer, geodesist, and physicist whose work touched many areas of science and mathematics, including number theory, algebra, analysis, geometry, statistics, and probability. He served as director of the Göttingen Observatory and as a professor of astronomy from 1807 until his death in 1855.

Recognized as a child prodigy, Gauss proved several mathematical theorems while still a student at the University of Göttingen. Working independently, he produced the major works Disquisitiones Arithmeticae and Theoria motus corporum coelestium. He gave the second and third complete proofs of the fundamental theorem of algebra and introduced the triple bar symbol (≡) for congruence. In number theory, his contributions included the composition law, the law of quadratic reciprocity, and a proof of the triangular case of the Fermat polygonal number theorem.

He also worked on binary and ternary quadratic forms and hypergeometric series. At age 19, he proved the construction of the heptadecagon, the first advance in regular polygon construction in over two thousand years. He introduced the concept of Gaussian curvature and proved its key properties, notably in his Theorema Egregium. He was the first to prove Gauss's inequality and helped develop the arithmetic–geometric mean.

He introduced the normal, or Gaussian, distribution in probability. More than one hundred mathematical and scientific concepts bear his name.

Gauss helped identify the dwarf planet Ceres. His study of planetoid motion disturbed by large planets led to the Gaussian gravitational constant and the method of least squares, which he discovered before Adrien-Marie Legendre published it. He also introduced the recursive least squares algorithm. From 1820 to 1844, he led the geodetic survey of the Kingdom of Hanover and an arc measurement project.

A founder of geophysics, he formulated fundamental principles of magnetism and made the first absolute measurement of Earth's magnetic field in 1832. He later used spherical harmonic analysis, one of his inventions, to show that most of the Earth's magnetic field originates internally. He was the first to discover and name non-Euclidean geometry. He also developed a fast Fourier transform about 160 years before John Tukey and James Cooley.

His practical work led to the invention of the heliotrope in 1821, a magnetometer in 1833, and, with Wilhelm Eduard Weber, the first electromagnetic telegraph in 1833.

Gauss received the Lalande Prize in 1809 for his work on planetary theory and orbit determination, and the Copley Medal in 1838 for his mathematical research in magnetism. He was known for not publishing incomplete work, which delayed the spread of many of his discoveries; several works were edited posthumously. He believed the act of learning, not possessing knowledge, brought the greatest enjoyment. Though not a committed or enthusiastic teacher, preferring his own research, his students included Richard Dedekind and Bernhard Riemann, who became influential mathematicians. He married twice and had six children, several of whom later emigrated to the United States.

Gauss was born on 30 April 1777 in Brunswick, in the Duchy of Brunswick-Wolfenbüttel (now Lower Saxony, Germany), into a family of relatively low social status. His father, Gebhard Dietrich Gauss, worked as a butcher, bricklayer, gardener, and treasurer of a death-benefit fund. Gauss described his father as honorable and respected but rough and dominating at home. His father was experienced in writing and calculating, while his mother, Dorothea, was nearly illiterate. Gauss had one older half-brother from his father's first marriage.

When 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 from 1792 to 1795, where Eberhard August Wilhelm von Zimmermann was one of his teachers. The Duke then funded his studies in mathematics, sciences, and classical languages at the University of Göttingen until 1798. His mathematics professor was Abraham Gotthelf Kästner, whom Gauss called "the leading mathematician among poets, and the leading poet among mathematicians" for his epigrams.

Astronomy was taught by Karl Felix Seyffer, with whom Gauss corresponded after graduation; Gauss and Olbers mocked Seyffer in their letters. He thought highly of his physics teacher Georg Christoph Lichtenberg and of Christian Gottlob Heyne, whose classics lectures he enjoyed. Fellow students included Johann Friedrich Benzenberg, Farkas Bolyai, and Heinrich Wilhelm Brandes. Gauss was likely a self-taught mathematician, independently rediscovering several theorems.

In 1796, he solved a geometric problem that had occupied mathematicians since ancient Greece, determining which regular polygons can be constructed with compass and straightedge. This discovery led him to choose mathematics over philology as a career.