Euler's Constant γ=0.577... Its Mathematics and History
– an extensive and long-term research project by Stefan Krämer –

Euler's constant is defined by

It is the third important mathematical constant after π and e.

In 2007 – the Leonhard Euler Tercentenary – it would be a good occasion to remember the discovery of this constant by Euler in 1734. The project began in 1993 with the discovery of an unknown algorithm of Brandes from 1824 (to compute γ without using Bernoulli numbers), using the Universitätsbibliothek Leipzig and the Deutsche Nationalbibliothek in Leipzig. From 1995 we mainly used the Niedersächsische Staats- und Universitäsbibliothek Göttingen (which is nearly complete in mathematics and history of mathematics). After a short time it became clear that many unkown identities are hidden in the old literature. It is often pointed out that the supposed irrationality of γ is not yet proved. In fact this could continue to be a deep question for the next 100 years (Hilbert called it inaccessible), but there are a lot of unsolved problems related to Euler's constant and an extensive monograph about γ is missing.

Principal aims of the project

The current German version has over 300 A4-pages and 1250 items of bibliography.
Up until now there have been only two monographs about Euler's constant:

The thesis of Anastassow is not at the level of his time (from mathematical and historical viewpoints). Some important relations are missing and it is far from an extensive study.
Havil's book has a completely different viewpoint from our project. His book is based on secondary literature and is not original research. Unfortunately, too, it contains many mathematical and historical errors. It is sad to see that the errors in the original have not been corrected in the German translation.

If you feel the project is interesting you can write to:

Dipl.Math. Stefan Krämer
Mathematisches Institut
Bunsenstr. 3-5
D-37073 Göttingen

On the Internet there are some pages about Euler's constant. Notable are:

Web pages about Leonhard Euler:
German keywords: Eulersche Konstante, Mascheroni
last modification: 19.02.2007
Stefan Krämer
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