Thue

Axel Thue

Born: 19 Feb 1863 in Tönsberg, Norway
Died: 7 March 1922 in Oslo, Norway

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Thue studied under Lie. In 1909 he produced an important paper on algebraic numbers showing that, for example, y^3 - 2x^2 = 1 cannot be satisfied by infinitely many pairs of integers. His work was extended by Siegel in 1920 and again by Roth in 1958.

Landau, in 1922, described Thue's work as

the most important discovery in elementary number theory that I know .
Thue's Theorem states that:-
If f(x,y) is a homogeneous polynomial with integer coefficients, irreducible in the rationals and of degree > 2 and c is a non-zero integer then f(x,y) = c has only a finite number of integer solutions .
References:
  1. Dictionary of Scientific Biography
  2. V Bjerknes, Axel Thue, Norsk matematisk tidsskrift 4 (1922), 33-46.
  3. A Thue, Selected mathematical papers of Axel Thue, Introduction by Carl Ludwig Siegel (Oslo, 1977). 
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