– an extensive and long-term research project by Stefan Krämer –

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**

- finding and collecting all papers related to Euler's constant
- ordering, correlating and generalizing the material
- finding early appearances of formulas, expressions and theorems related to Euler's constant
- correcting mathematical and historical errors in past publications
- describing the history of Euler's constant
- creating a nearly complete
*autoptical*bibliography on Euler's constant (including many items with biographical information of unknown mathematicians) - giving biographical information about related mathematicians

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:

- Theodor Anastassow. Die Mascheroni'sche Konstante: Eine historisch-analytisch zusammenfassende Studie. Phd-thesis, philosophische Fakultät der Universität Bern. Wetzikon: J. Wirz, 1914 (64 pages)
- Julian Havil. Gamma: exploring Euler's constant. Princeton University Press, 2003. Zbl 1023.11001, MR 1968276. (266 pages)
- Julian Havil. Gamma. Eulers Konstante, Primzahlstrände und die Riemannsche Vermutung. Springer, 2007. Transl. from the English by Manfred Stern. (307 pages)

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:

Email: skraemer@math.uni-goettingen.de

or:

Mathematisches Institut

Bunsenstr. 3-5

D-37073 Göttingen

Germany

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

- The Euler Society
- The Euler Commission (The Euler Committee of the Swiss Academy of Sciences, gegründet 1907)
- The Euler Archive
- The Leonhard Euler Tercentenary - Basel 2007
- EULER à Saint Petersbourg

German keywords: Eulersche Konstante, Mascheroni

last modification: 19.02.2007

Stefan Krämer

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