Axel Thue | |
---|---|

Axel Thue (1863-1922) | |

Born | |

Died | 7 March 1922 59) | (aged

Nationality | Norwegian |

Alma mater | University of Kristiania |

Known for | Thue's theorem, Thue systems |

Scientific career | |

Fields | Mathematician |

Institutions | University of Kristiania Trondheim Technical College |

Thesis | (1889) |

Doctoral advisor | Elling Holst |

Doctoral students | Thoralf Skolem |

**Axel Thue** (Norwegian: [tʉː] ; 19 February 1863 – 7 March 1922), was a Norwegian mathematician, known for his original work in diophantine approximation and combinatorics.

Thue published his first important paper in 1909.^{ [1] }

He stated in 1914 the so-called word problem for semigroups or Thue problem, closely related to the halting problem.^{ [2] }

His only known PhD student was Thoralf Skolem.

The esoteric programming language Thue is named after him.

- Thue, A. (1909), "Über Annäherungswerte algebraischer Zahlen",
*Journal für die reine und angewandte Mathematik*,**135**: 284–305, doi:10.1515/crll.1909.135.284, ISSN 0075-4102 - Thue, A. (1977) [1912], "Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen",
*Selected Math. Papers of Axel Thue, Universiteitsforlaget*: 67

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In number theory, the study of **Diophantine approximation** deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria.

**Ferdinand Georg Frobenius** was a German mathematician, best known for his contributions to the theory of elliptic functions, differential equations, number theory, and to group theory. He is known for the famous determinantal identities, known as Frobenius–Stickelberger formulae, governing elliptic functions, and for developing the theory of biquadratic forms. He was also the first to introduce the notion of rational approximations of functions, and gave the first full proof for the Cayley–Hamilton theorem. He also lent his name to certain differential-geometric objects in modern mathematical physics, known as Frobenius manifolds.

**Thoralf Albert Skolem** was a Norwegian mathematician who worked in mathematical logic and set theory.

In mathematics, the **Thue–Morse sequence**, or **Prouhet–Thue–Morse sequence**, is the binary sequence obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far. The first few steps of this procedure yield the strings 0 then 01, 0110, 01101001, 0110100110010110, and so on, which are prefixes of the Thue–Morse sequence. The full sequence begins:

**Max Wilhelm Dehn** was a German mathematician most famous for his work in geometry, topology and geometric group theory. Born to a Jewish family in Germany, Dehn's early life and career took place in Germany. However, he was forced to retire in 1935 and eventually fled Germany in 1939 and emigrated to the United States.

In mathematics, **Roth's theorem** is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative type, stating that a given algebraic number may not have too many rational number approximations, that are 'very good'. Over half a century, the meaning of *very good* here was refined by a number of mathematicians, starting with Joseph Liouville in 1844 and continuing with work of Axel Thue (1909), Carl Ludwig Siegel (1921), Freeman Dyson (1947), and Klaus Roth (1955).

**Thue's theorem** may refer to the following mathematical theorems named after Axel Thue:

In mathematics, a **Thue equation** is a Diophantine equation of the form

**Transcendental number theory** is a branch of number theory that investigates transcendental numbers, in both qualitative and quantitative ways.

**Lennart Axel Edvard Carleson** is a Swedish mathematician, known as a leader in the field of harmonic analysis. One of his most noted accomplishments is his proof of Lusin's conjecture.

In theoretical computer science and mathematical logic a **string rewriting system** (**SRS**), historically called a **semi-Thue system**, is a rewriting system over strings from a alphabet. Given a binary relation between fixed strings over the alphabet, called **rewrite rules**, denoted by , an SRS extends the rewriting relation to all strings in which the left- and right-hand side of the rules appear as substrings, that is , where , , , and are strings.

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In mathematics, **Siegel's theorem on integral points** states that for a smooth algebraic curve *C* of genus *g* defined over a number field *K*, presented in affine space in a given coordinate system, there are only finitely many points on *C* with coordinates in the ring of integers *O* of *K*, provided *g* > 0.

**Gustav Herglotz** was a German Bohemian physicist. He is best known for his works on the theory of relativity and seismology.

In transcendental number theory and Diophantine approximation, **Siegel's lemma** refers to bounds on the solutions of linear equations obtained by the construction of auxiliary functions. The existence of these polynomials was proven by Axel Thue; Thue's proof used Dirichlet's box principle. Carl Ludwig Siegel published his lemma in 1929. It is a pure existence theorem for a system of linear equations.

In geometry, **circle packing** is the study of the arrangement of circles on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap. The associated packing density, *η*, of an arrangement is the proportion of the surface covered by the circles. Generalisations can be made to higher dimensions – this is called sphere packing, which usually deals only with identical spheres.

In number theory, **Fermat's Last Theorem** states that no three positive integers *a*, *b*, and *c* satisfy the equation *a*^{n} + *b*^{n} = *c*^{n} for any integer value of *n* greater than 2. The cases *n* = 1 and *n* = 2 have been known since antiquity to have an infinite number of solutions.

**Combinatorics on words** is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages. The subject looks at letters or symbols, and the sequences they form. **Combinatorics on words** affects various areas of mathematical study, including algebra and computer science. There have been a wide range of contributions to the field. Some of the first work was on square-free words by Axel Thue in the early 1900s. He and colleagues observed patterns within words and tried to explain them. As time went on, combinatorics on words became useful in the study of algorithms and coding. It led to developments in abstract algebra and answering open questions.

**Eduard Wirsing** is a German mathematician, specializing in number theory.

- ↑ O'Connor, John J.; Robertson, Edmund F., "Axel Thue",
*MacTutor History of Mathematics archive*, University of St Andrews . - ↑ Ronald V. Book and Friedrich Otto,
*String-rewriting Systems*, Springer, 1993, ISBN 0-387-97965-4, p. 36.

- Axel Thue at the Mathematics Genealogy Project
- Axel Thue private archive exists at NTNU University Library Dorabiblioteket

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