All the way with Gauss-Bonnet and the sociology of Mathematics

My reasons for writing this story were stimulated by the discussion in The American Mathematical Monthly between Peter Hilton and Jean Pederson on the one hand and Branko Grunbaum and G. C. Shephard on the other hand [HP] [GS]. The discussion as well as my story involves the Euler-Poincare Number, alias the Euler Characteristic. The discussion centers on whether the Euler-Poincare Number should be discussed in a historical way without mentioning the vast and dramatic generalization and depth of understanding that this most interesting invariant has acquired in this century. My story spans the history of mathematics. It concerns the, perhaps, most widely known non-obvious theorem of mathematics and it contains the same stunning generalization that characterizes the recent history of the Euler-Poincare number. In fact it concerns one of the most important and earliest of the applications of the Euler-Poincare number. It shows the reticence of mid century topologists to explain their work to the wider mathematical public. It shows the fickleness of mathematical fame, and it shows the unreasonable power of unreasonable points of view, and it shows how easy it is for mathematicians to miss and forget beautiful and important theorems. This is a history of the Gauss-Bonnet theorem as I see it. I am not a mathematical historian. I am quoting only secondary sources or first hand papers which I quickly scanned and I did not conduct any thorough interviews. Nontheless, I am writing this history because I have contributed the last sentence to it (for the moment).