most recent 30 from http://mathoverflow.net 2013-05-20T03:04:49Z http://mathoverflow.net/feeds/user/30978 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/119015/what-precisely-does-kleins-erlangen-program-state/120094#120094 Catherine Goldstein 2013-01-28T09:49:07Z 2013-01-28T09:49:07Z

<p>For the historical part of the question, what about reading the (professional) historians of mathematics, for instance, as a point of departure : Jeremy Gray, Felix Klein's Erlangen programme, in <em>Landmark Writings in Western Mathematics</em>, ed. I. Grattan-Guinness, Elsevier, p. 544-552, 2005, which explains the circumstances of the paper and its main contents, and gives a bibliography.<br> Indeed, the programme was not a series of conjectures ! It states a view of geometry in which a geometry was associated to a group of transformations (not uniquely, of course), and (a part often forgotten) this also should provide explicit invariants. It was important because 1) geometry was still currently understood as "geometry" and not "geometries" at the time, 2) it allows to classify them and show the analogies/identity between different geometries (some quite bizarre to-day). As said by others above, from our point of view, a lot was not included, of course, for instance, Riemannian geometry was explicitely out of it (it was of the achievements of the Elie Cartan generation, and specially Elie Cartan himself, to integrate Riemann to this picture). The influence of the programme has been also studied extensively. Best, C. Goldstein</p>