Dehn's solution to Hilbert's 3rd: 1901 or 1902? - MathOverflow

Dehn's solution to Hilbert's 3rd: 1901 or 1902?

2011-08-25T18:06:16Z

This is a simple bibliographic request that I have been unable to pin down. Max Dehn's solution to Hilbert's 3rd problem is:

Max Dehn, "Über den Rauminhalt." Mathematische Annalen 55 (190x), no. 3, pages 465–478.

It is variously cited as either 1901 or 1902 (but always volume 55; Hilbert's own footnote cites volume 55 "soon to appear"). E.g.,

Mathworld cites it as 1902.
The Encyclopedic Dictionary of Mathematics cites it as 1902.
Wikipedia says 1901.
Various papers, e.g., this one, and Tao's book, cite it as 1901.

I have been unsuccessful in finding the definitive year via the web, because of all the conflicting citations. The next step is to retrieve Mathematische Annalen volume 55, but perhaps someone can spare me that trouble...? Thanks!

Answer by Carlo Beenakker for Dehn's solution to Hilbert's 3rd: 1901 or 1902?

2011-08-25T19:09:43Z

the journal has been scanned and can be read here:

http://www.archive.org/details/mathematischean33behngoog

volume 55 has four issues, covering both years 1901 and 1902; that is where the confusion comes from; Dehn's article is from the third issue, published in September 1901.

you can read the table of contents here:

http://www.springerlink.com/content/0025-5831/55/3/

Answer by Andreas Thom for Dehn's solution to Hilbert's 3rd: 1901 or 1902?

2011-08-25T19:12:41Z

Dehn, M.; Ueber den Rauminhalt. (German) Math. Ann. 55 (1901), no. 3, 465–478

according to MathSciNet and Springer confirms this here. But on the scanned original provided by the Göttingen Center for Digitalisation here, the bottom line of the first page shows 1902. However, this refers to all issues of Volume 55. Looking more closely, only issues 1-3 were published in 1901 and issue 4 was published in 1902.

I guess, this means that MathSciNet is correct. However, the confusion is somewhat understandable.

Answer by John Stillwell for Dehn's solution to Hilbert's 3rd: 1901 or 1902?

2011-08-25T22:26:48Z

Another point to consider is whether "Über den Rauminhalt" is in fact Dehn's first solution to Hilbert's 3rd Problem. I believe his first solution was in the paper "Über raumgleiche Polyeder" in the Nachrichten der Königliche Gesellschaft der Wissenschaften zu Göttingen of 1900, pp. 345 -- 354.