Bernhard Riemann, Collected Papers

Roger Baker and his co-translators have put us all in their debt. Everyone knows that Bernhard Riemann was one of the most important mathematicians of the 19th century, and that his influence has been considerable. Reading his papers, however, has been an option only for those who could read German. There were exceptions, of course, such as the papers on the zeta function (translated in H. M. Edwards' The Riemann Zeta Function) and on the foundations of geometry (translated in various different sources). But, as far as I know, this is the first translation of the whole (well, almost the whole) set of papers included in Weber's edition of Riemann's Gesammelte Mathematische Werke.

Baker, Orde, and Christenson have translated all the mathematical and physical papers in Weber's volume. Only three items have been omitted: an article on "The Mechanism of the Ear" and two fragments on philosophy. The numbering of the papers in Weber's edition is preserved. Weber's notes have been translated, and also Dedekind's essay on Riemann's life. Finally, notes on each of the papers have been added. These provide brief comments and pointers to the literature (both historical and mathematical).

The book is nicely, if simply, produced. My only wishes would have been a heavier paper stock for the cover and a non-computer modern font (but I know most of my colleagues don't much worry about the latter). The contents are what matters most, and those are very welcome indeed. This is an indispensable book. No library should be without it.

Fernando Gouvêa is the editor of FOCUS, FOCUS Online, and MAA Reviews. He describes himself as a "historian wannabe" and he thinks volumes of collected mathematical works are really cool.