**Thue** studied Diophantine equations, showing that, for example, $y^3-2x^2=1$ cannot be satisfied by infinitely many pairs of integers.

- Axel was brought up in Tönsberg, a town on the Oslofjord, and attended middle school there.
- When Thue discovered that it was a mathematics book rather than the physics book he had expected, nevertheless he read it.
- In fact, the book documents the influence on modern geometry of Jean-Victor Poncelet, and Thue became fascinated by the mathematics it described.
- When Thue became a pupil at the school in 1880, Elling Holst was his mathematics teacher.
- It is clear that Holst meant the same to Thue.
- Thue has shown in a series of original investigations that he has many of the qualifications needed to become an outstanding mathematician.
- After the award of the scholarship, Thue went to Leipzig in 1891 to study under Lie.
- his works do not reveal Lie's influence, probably because of Thue's inability to follow anyone else's line of thought.
- This tells us that Thue was seriously ill while in Leipzig and it must have meant that he did not profit as much as he might have done.
- Again we have a nice description of Thue's opinion of Berlin and the mathematicians who lectured there in a letter he wrote to Holst in June 1891.
- Back in Olso, Thue held a scholarship in mathematics from 1891 to 1894.
- Lucie had been born on 4 August 1873 and was ten years younger than Thue.
- After his scholarship ended, Thue was appointed to Trondheim Technical College where he worked from 1894 until 1903.
- Although this was an excellent college, considered the best in the country to train engineers, Thue was not happy there.
- However, the period from 1906 to 1916 was when Thue did his best work, although it was not accomplished in easy circumstances.
- Let us now look at some of Thue's mathematical contributions.
- Another famous contribution made by Thue was his four papers Über unendliche Zeichenreihen Ⓣ(On infinite rows of characters) (1906), Die Lösung eines Spezialfalles eines generellen logischen Problems Ⓣ(The solution of a special case of a general logical problem) (1910), Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen Ⓣ(On the mutual position of equal parts of certain character strings) (1912) and Probleme über Veränderungen von Zeichenreihen nach gegebenen Regeln Ⓣ(Issues concerning changes in character strings by given rules) (1914).
- These papers were not seen as important when Thue wrote them but subsequent developments have shown him to be well ahead of his time in considering difficult problems that have since attracted a great deal of interest.
- Many of his results were rediscovered by mathematicians who were unaware of Thue's contributions.
- In particular, Thue systems, semi-Thue systems and his work on the combinatorics of words are well-known.
- Thue's 1910 paper deals with transformations between trees, and is thus a more direct predecessor of his 1914 paper.
- Thue's 1914 paper ...
- is mainly famous for proving an early example of an undecidable problem, cited prominently by Emil Post in 'Recursive unsolvability of a problem of Thue' (1947).
- If this work seems a little strange for a professor of applied mathematics then some quotes from Thue will clarify where he stood on the issue of applications.
- One characteristic of Thue's work should be mentioned.
- Thue was honoured by being elected to the Norwegian Academy of Science and Letters in 1894 and to the Royal Norwegian Society of Sciences in Trondheim 1895.

Born 19 February 1863, Tönsberg, Norway. Died 7 March 1922, Oslo, Norway.

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Origin Norway

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive