Kurt Heegner (German: [ˈheːɡnɐ]; 16 December 1893 – 2 February 1965) was a German private scholar from Berlin, who specialized in radio engineering and mathematics. He is now famous for his mathematical discoveries in number theory.
Heegner was born and died in Berlin. In 1952, he published what he claimed was the solution of a classic problem proposed by the great mathematician Gauss, the class number 1 problem, a significant and long standing problem in number theory. Heegner's work was not accepted for years, due mainly to quoting a portion of Weber's work that was known to be incorrect (though he never used this result in the proof), and the rather mystical and unorthodox style of the paper (calling Pythagorean triangles as Harpedonapten triangles for instance).
Heegner's proof was finally accepted as essentially correct after a 1967 announcement by Bryan Birch, and definitively resolved by a paper of Harold Stark which was delayed in publication until 1969 (Stark had independently arrived at a similar proof, but disagrees with the common notion that his proof is "more or less the same" as Heegner's). Stark attributed Heegner's mistakes to the fact he was using a textbook by Weber which contained some results with incomplete proofs.
The recent book The Legacy of Leonhard Euler: A Tricentennial Tribute (by Lokenath Debnath) on page 64 claims that Heegner was a "retired Swiss mathematician", but he appears to be neither Swiss nor retired at the time of his 1952 paper.
- Heegner, Kurt (1952), "Diophantische Analysis und Modulfunktionen", Mathematische Zeitschrift, 56: 227–253, MR 0053135, doi:10.1007/BF01174749
- Stark, H.M. (1969). "On the gap in the theorem of Heegner", Journal of Number Theory, 1: 16–27.