The mathematician and scientist Carl Friedrich Gauss (1777-1855) was born in Braunschweig, Germany and his work has had a significant influence on modern mathematics. This influence stretches across a variety of fields in both mathematics and science, including algebra, analysis, astronomy, geometry, number theory, and statistics, amongst others. He was a child prodigy, and the body of influential work that he built up during his distinguished career earned him the nickname the Prince of Mathematicians and he was considered to be the best mathematician since antiquity.
He helped to establish number theory as a well-founded mathematical field. The field of number theory (also known as higher arithmetic) deals with the integers and their properties and relations and their algebraic and analytic extensions. He did this with the publication of his major work, entitled Disquisitiones arithmeticae, in 1801, whilst still only 21 years old. More remarkably, he had come up with his astonishing advances whilst still a teenager. He provided an excellent treatment of modular arithmetic and he also became the first to prove the law of quadratic reciprocity.
In algebra he proved the fundamental theorem of algebra using his own developments in complex number theory from his doctoral thesis, entitled A New Proof of the Theorem that Every Integral Rational Algebraic Function of One Variable Can Be Resolved into Real Factors of the First or Second Degree. This was one up on a number of established mathematicians of the age, who themselves had produced wrong proofs.
Gauss also contributed to the mathematics behind the physics of electricity, gravity, and magnetism. In astronomy he made advances in orbital theory that allowed to predict the position of the newly discovered dwarf planet Ceres.
His name has appeared in a variety of modern disciplines. The Gauss is a unit of magnetic field, for example. Degaussing means to demagnetise an object. Then there's the Gauss map, the Gauss error function, the Gauss hypergeomtric theorem, Gauss's constant in number theory, the Gauss Lemma for polynomials, another Gauss Lemma for number theory, and so on.
There is even a prize named after him the Carl Friedrich Gauss Prize for mathematics. Another commemoration is the naming of a crater on the moon after him. But there are also numerous buildings and departments at universities named after him as well. But the bottom line is that with all of the advances that he made Gauss undoubtedly was one of the major players in laying the foundations for the modern world that we know today including all of our high technology.