Johann Carl Friedrich Gauss or Gauß (listen (help·info); Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. Sometimes known as "the prince of mathematicians" and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians.
Gauss was a child prodigy, of whom there are many anecdotes pertaining to his astounding precocity while a mere toddler, and made his first ground-breaking mathematical discoveries while still a teenager. He completed Disquisitiones Arithmeticae, his magnum opus, at the age of 21 (1798), though it would not be published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.

Early years
In his 1799 dissertation, A New Proof That Every Rational Integer Function of One Variable Can Be Resolved into Real Factors of the First or Second Degree, Gauss gave a proof of the fundamental theorem of algebra. This important theorem states that every polynomial over the complex numbers must have at least one root. Other mathematicians had tried to prove this before him, e.g. Jean le Rond d'Alembert. Gauss's dissertation contained a critique of d'Alembert's proof, but his own attempt would not be accepted owing to implicit use of the Jordan curve theorem. Gauss over his lifetime produced three more proofs, probably due in part to this rejection of his dissertation; his last proof in 1849 is generally considered rigorous by today's standard. His attempts clarified the concept of complex numbers considerably along the way.
Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae, which contained a clean presentation of modular arithmetic and the first proof of the law of quadratic reciprocity. In that same year, Italian astronomer Giuseppe Piazzi discovered the dwarf planet Ceres, but could only watch it for a few days. Gauss predicted correctly the position at which it could be found again, and it was rediscovered by Franz Xaver von Zach on December 31, 1801 in Gotha, and one day later by Heinrich Olbers in Bremen. Zach noted that "without the intelligent work and calculations of Doctor Gauss we might not have found Ceres again." Though Gauss had up to this point been supported by the stipend from the Duke, he doubted the security of this arrangement, and also did not believe pure mathematics to be important enough to deserve support. Thus he sought a position in astronomy, and in 1807 was appointed Professor of Astronomy and Director of the astronomical observatory in Göttingen, a post he held for the remainder of his life.
The discovery of Ceres by Piazzi on January 1, 1801 led Gauss to his work on a theory of the motion of planetoids disturbed by large planets, eventually published in 1809 under the name Theoria motus corporum coelestium in sectionibus conicis solem ambientum (theory of motion of the celestial bodies moving in conic sections around the sun). Piazzi had only been able to track Ceres for a couple of months, following it for three degrees across the night sky. Then it disappeared temporarily behind the glare of the Sun. Several months later, when Ceres should have reappeared, Piazzi could not locate it: the mathematical tools of the time were not able to extrapolate a position from such a scant amount of data—three degrees represent less than 1% of the total orbit.
Gauss, who was 23 at the time, heard about the problem and tackled it. After three months of intense work, he predicted a position for Ceres in December 1801—- just about a year after its first sighting—and this turned out to be accurate within a half-degree. In the process, he so streamlined the cumbersome mathematics of 18th century orbital prediction that his work—- published a few years later as Theory of Celestial Movement—- remains a cornerstone of astronomical computation.
The survey of Hanover later led to the development of the Gaussian distribution, also known as the normal distribution, for describing measurement errors. Moreover, it fuelled Gauss's interest in differential geometry, a field of mathematics dealing with curves and surfaces. In this field, he came up in 1828 with an important theorem, the theorema egregium (remarkable theorem in Latin) establishing an important property of the notion of curvature. Informally, the theorem says that the curvature of a surface can be determined entirely by measuring angles and distances on the surface; that is, curvature does not depend on how the surface might be embedded in (3-dimensional) space.

Middle years
In 1831 Gauss developed a fruitful collaboration with the physics professor Wilhelm Weber; it led to new knowledge in the field of magnetism (including finding a representation for the unit of magnetism in terms of mass, length and time) and the discovery of Kirchhoff's circuit laws in electricity. Gauss and Weber constructed the first electromagnetic telegraph in 1833, which connected the observatory with the institute for physics in Göttingen. Gauss ordered a magnetic observatory to be built in the garden of the observatory and with Weber founded the magnetischer Verein ("magnetic club"), which supported measurements of earth's magnetic field in many regions of the world. He developed a method of measuring the horizontal intensity of the magnetic field which has been in use well into the second half of the 20th century and worked out the mathematical theory for separating the inner (core and crust) and outer (magnetospheric) sources of Earth's magnetic field.
Gauss died in Göttingen, Hanover (now part of Lower Saxony, Germany) in 1855 and is interred in the cemetery Albanifriedhof there. Two individuals gave eulogies at his funeral, Gauss's son-in-law Heinrich Ewald and Wolfgang Sartorius von Waltershausen, who was Gauss's close friend and biographer. His brain was preserved and was studied by Rudolf Wagner who found its weight to be 1,492 grams and the cerebral area equal to 219,588 square centimeters. Highly developed convolutions were also found, which in the early 20th century was suggested as the explanation of his genius.

Family
Gauss was an ardent perfectionist and a hard worker. According to Isaac Asimov, Gauss was once interrupted in the middle of a problem and told that his wife was dying. He is purported to have said, "Tell her to wait a moment 'til I'm through." He supported monarchy and opposed Napoleon, whom he saw as an outgrowth of revolution.

Commemorations

List of topics named after Carl Friedrich Gauss