The story of how Gauss as a schoolboy discovered the formula for summing an arithmetic series -- to the astonishment or consternation of his teacher -- is a bit of mathematical lore that has been told many times. I have been collecting versions of the story, and I now have about 75 examples. Few of these publications give any explicit acknowledgement of sources, but all of the versions seem to derive either directly or indirectly from the memoir published in 1856 by Wolfgang Sartorius von Waltershausen (_Gauss zum Gedächtnis_; translated by Helen Worthington Gauss as _Carl Friedrich Gauss: A Memorial_). Not that all the tellings follow Sartorius exactly -- on the contrary, there are many variations, some of them highly creative -- but nothing I've seen so far points to the existence of another primary source, independent of Sartorius.
This is a little surprising. Sartorius himself introduces his account of Gauss's schoolroom triumph with the words: "Here occurred an incident which [Gauss] often related in old age with amusement and relish." Thus one might think that other colleagues and acquaintances of the mathematician would have made note of the incident, or perhaps preserved letters from Gauss that mention it.
Does anyone know of another early version of this story, one that might be traced back to Gauss via some route other than Sartorius?
many thanks, and best regards to all
Brian Hayes Senior Writer American Scientist email@example.com