The Collected Works of Bernhard Riemann

Bernhard Riemann fascinates people. Despite having died young, he made a huge impact in many areas of mathematics, making him a central figure in nineteenth century mathematics. His actual published work is often quite difficult to understand, but his ideas have lasted. So it is perfectly reasonable for Dover to reprint his Collected Works: there is still much to learn from them.

The Dover edition is a photographic reprint of the 1892 edition of the Gesammelte Mathematische Werke, edited by Richard Dedekind and Heinrich Weber, bound together with the volume of supplementary material edited by Max Noether and Wilhelm Wirtinger and published in 1902. Each part has separate page numbering: 558 pages for the main volume, 116 pages in the supplement. Everything is, of course, in German.

A new critical edition of Riemann’s papers is currently in preparation, but it is unclear when that will appear. Until then, this is the edition of choice for those who can read German. Luckily, almost everything here (specifically, everything from the 1892 edition except for a paper on the mechanism of the ear and some philosophical fragments, but not any of the supplementary material) has been translated in the Collected Papers published by Kendrick Press, so those who cannot read German (or can do so only with difficulty) will want to have both or to get that volume instead.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College and editor of MAA Reviews.