Kurt Heegner (; 16 December 1893 – 2 February 1965) was a German private scholar from Berlin, who specialized in
radio
Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmit ...
engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
and
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
. He is famous for his
mathematical
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
discoveries 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 (1777â ...
and, in particular, the
Stark–Heegner theorem
In number theory, the Baker–Heegner–Stark theorem states precisely which quadratic imaginary number fields admit unique factorisation in their ring of integers. It solves a special case of Gauss's class number problem of determining the number ...
.
Life and career
Heegner was born and died in Berlin. In 1952, he published the
Stark–Heegner theorem
In number theory, the Baker–Heegner–Stark theorem states precisely which quadratic imaginary number fields admit unique factorisation in their ring of integers. It solves a special case of Gauss's class number problem of determining the number ...
which he claimed was the solution to a classic
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 (1777â ...
problem proposed by the great mathematician
Gauss
Johann Carl Friedrich Gauss (; german: GauĂź ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
, the
class number 1 problem
In mathematics, the Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each ''n'' ≥ 1 a complete list of imaginary quadratic fields \mathbb(\sqrt) (for negative integers ''d'') having ...
. Heegner's work was not accepted for years, mainly due to his quoting of a portion of
Heinrich Martin Weber
Heinrich Martin Weber (5 March 1842, Heidelberg, Germany – 17 May 1913, StraĂźburg, Alsace-Lorraine, German Empire, now Strasbourg, France) was a German mathematician. Weber's main work was in algebra, number theory, and analysis. He is ...
's work that was known to be incorrect (though he never used this result in the proof).
Heegner's proof was accepted as essentially correct after a 1967 announcement by
Bryan Birch
Bryan John Birch FRS (born 25 September 1931) is a British mathematician. His name has been given to the Birch and Swinnerton-Dyer conjecture.
Biography
Bryan John Birch was born in Burton-on-Trent, the son of Arthur Jack and Mary Edith Birch. ...
, and definitively resolved by a paper by
Harold Stark
Harold Mead Stark (born August 6, 1939 in Los Angeles, California)
is an American mathematician, specializing in number theory. He is best known for his solution of the Gauss class number 1 problem, in effect correcting and completing the earli ...
that had been 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 used a textbook by Weber that contained some results with incomplete proofs.
The book ''The Legacy of Leonhard Euler: A Tricentennial Tribute'' by Lokenath Debnath claims on page 64, that Heegner was a "retired Swiss mathematician", but he appears to have been neither Swiss nor retired at the time of his 1952 paper.
The Legacy of Leonhard Euler: A Tricentennial Tribute
/ref>
See also
*List of amateur mathematicians
This is a list of amateur mathematicians—people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics.
*Ahmes (scribe)
*Ashutosh Muk ...
*Stark–Heegner theorem
In number theory, the Baker–Heegner–Stark theorem states precisely which quadratic imaginary number fields admit unique factorisation in their ring of integers. It solves a special case of Gauss's class number problem of determining the number ...
*Heegner number In number theory, a Heegner number (as termed by Conway and Guy) is a square-free positive integer ''d'' such that the imaginary quadratic field \Q\left sqrt\right/math> has class number 1. Equivalently, its ring of integers has unique factoriza ...
*Heegner point In mathematics, a Heegner point is a point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane. They were defined by Bryan Birch and named after Kurt Heegner, who used similar ideas to prove Gauss's conject ...
*Heegner's lemma
In mathematics, Heegner's lemma is a lemma used by Kurt Heegner
Kurt Heegner (; 16 December 1893 – 2 February 1965) was a German private scholar from Berlin, who specialized in
radio engineering and mathematics. He is famous for his mathematic ...
Literature
*
*
References
External links
Heegner's entry in "Foundation for German communication and related technologies"
{{DEFAULTSORT:Heegner, Kurt
1893 births
1965 deaths
20th-century German mathematicians