Heinrich Eduard Heine

---

Born: 16 March 1821 in Berlin, Germany
Died: 21 Oct 1881 in Halle, Germany

 

Eduard Heine is important for his contributions to analysis. He went to lectures by Gauss and was taught by Dirichlet. Heine worked on Legendre polynomials, Lamé functions and Bessel functions. He is best remembered for the Heine-Borel theorem:-

a subset of the reals is compact if and only if it is closed and bounded.

Heine also formulated the concept of uniform continuity.

The paper [2] analyses letters written by Heine and found in 1988 in the Institut Henri Poincaré. The second part of this paper covers the history of the Heine-Borel theorem and is summarised in the following review:-

The last half of the paper is devoted to a more systematic account of the gradual discovery and formulation of the so-called Heine-Borel theorem. It begins with the implicit use of the theorem in various proofs of the theorem stating that a continuous function on a closed, bounded interval is uniformly continuous. The first proof of this theorem was given by Dirichlet in his lectures of 1862 (published 1904) before Heine proved it in 1872. Dugac shows that Dirichlet used the idea of a covering and a finite subcovering more explicitly than Heine. This idea was also used by Weierstrass and Pincherle. Borel formulated his theorem for countable coverings in 1895 and Schönflies and Lebesgue generalized it to any type of covering in 1900 and 1898 (published 1904), respectively. Dugac shows that the story is in fact much more complicated and includes names such as Cousin, Thomae, Young, Vieillefond, Lindelöf. The priority questions are nicely illustrated with quotes from the correspondence between Lebesgue and Borel and other letters.