Theodor Schönemann, also written Schoenemann, (4 April 1812 16 January 1868) was a German

Germans

The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 who obtained several important results in number theory

Number theory

Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

 concerning the theory of congruences

Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus....

, which can be found in several publications in Crelle's journal

Crelle's Journal

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik .- History :...

, volumes 17 to 40. Notably he obtained Hensel's lemma

Hensel's lemma

In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a polynomial equation has a simple root modulo a prime number , then this root corresponds to a unique root of the same equation modulo any higher power...

 before Hensel

Kurt Hensel

Kurt Wilhelm Sebastian Hensel was a German mathematician born in Königsberg, Prussia.He was the son of the landowner and entrepreneur Sebastian Hensel, brother of the philosopher Paul Hensel, grandson of the composer Fanny Mendelssohn and the painter Wilhelm Hensel, and a descendant of the...

, Scholz's reciprocity law

Scholz's reciprocity law

In mathematics, Scholz's reciprocity law is a reciprocity law for quadratic residue symbols of real quadratic number fields discovered by and rediscovered by .-Statement:...

 before Scholz, and formulated Eisenstein's criterion

Eisenstein's criterion

In mathematics, Eisenstein's criterion gives an easily checked sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers...

 before Eisenstein. He also studied, under the form of integer polynomials modulo

Ideal (ring theory)

In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. The ideal concept allows the generalization in an appropriate way of some important properties of integers like "even number" or "multiple of 3"....

 both a prime number

Prime number

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

 and an irreducible polynomial

Irreducible polynomial

In mathematics, the adjective irreducible means that an object cannot be expressed as the product of two or more non-trivial factors in a given set. See also factorization....

 (remaining irreduicble modulo that prime number), what can nowadays be recognized as finite field

Finite field

In abstract algebra, a finite field or Galois field is a field that contains a finite number of elements. Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, and coding theory...

s (more general than those of prime order).

He was educated in Königsberg

Königsberg

Königsberg was the capital of East Prussia from the Late Middle Ages until 1945 as well as the northernmost and easternmost German city with 286,666 inhabitants . Due to the multicultural society in and around the city, there are several local names for it...

 and Berlin, where among his teachers were Jakob Steiner

Jakob Steiner

Jakob Steiner was a Swiss mathematician who worked primarily in geometry.-Personal and professional life:...

 and Carl Gustav Jacob Jacobi. He obtained his doctorate in 1842, after which he became Gymnasialoberlehrer (professor at a gymnasium) in Brandenburg an der Havel. Apart from the mentioned mathematical papers, he also published, mainly after 1850, in mechanics and physical technique.