Theodor Schönemann, also written Schoenemann (4 April 181216 January 1868), was a German mathematician who obtained several important results in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

concerning the theory of

congruences In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done wit ...

, which can be found in several publications in

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'' (in English: ''Journal for Pure and Applied Mathematics''). History The journal was founded by Augus ...

, volumes 17 to 40. Notably he obtained

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 univariate polynomial has a simple root modulo a prime number , then this root can be ''lifted'' to a ...

before Hensel,

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 Suppose that ''p'' and ''q'' are rational primes congruent to 1 mod 4 such t ...

before Scholz, and formulated

Eisenstein's criterion In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers – that is, for it to not be factorizable into the product of non-constant polynomials wit ...

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

modulo In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is t ...

both a

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

and an

irreducible polynomial In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility depends on the nature of the coefficients that are accepted ...

(remaining irreducible modulo that prime number), what can nowadays be recognized as

finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...

s (more general than those of prime order).David A. Cox, "Why Eisenstein proved the Eisenstein criterion and why Schönemann discovered it first",

American Mathematical Monthly ''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an e ...

118 Vol 1, January 2011, pp. 3–31. See p. 10. He was educated in

Königsberg Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was named ...

and Berlin, where among his teachers were

Jakob Steiner Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry. Life Steiner was born in the village of Utzenstorf, Canton of Bern. At 18, he became a pupil of Heinrich Pestalozzi and afterwards st ...

and

Carl Gustav Jacob Jacobi Carl Gustav Jacob Jacobi (; ; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants, and number theory. His name is occasiona ...

. He obtained his doctorate in 1842, after which he became Gymnasialoberlehrer (professor at a gymnasium) in

Brandenburg an der Havel Brandenburg an der Havel () is a town in Brandenburg, Germany, which served as the capital of the Margraviate of Brandenburg until it was replaced by Berlin in 1417. With a population of 72,040 (as of 2020), it is located on the banks of the H ...

. Apart from the mentioned mathematical papers, he also published, mainly after 1850, in mechanics and physical technique.

Works

* ''Ueber die Bewegung veränderlicher ebener Figuren, welche während der Bewegung sich ähnlich bleiben in ihrer Ebene''. 186
digital

References

Biography
(in German) * H. L. Dorwart
Irreducibility of polynomials
American Mathematical Monthly 42 Vol 6 (1935), 369–381, . Reference to Schoenemann on page 370. 1812 births 1868 deaths People from Drezdenko People from the Province of Brandenburg 19th-century German mathematicians Number theorists {{Germany-mathematician-stub