Gauss (Schweikart and Taurinus) and Gauss’s Differential Geometry

Abstract

In the 1820s the hitherto unthinkable was gradually thought. Friedrich Karl Schweikart, a law professor, wrote to Carl Friedrich Gauss with some further consequences of Saccheri’s and Lambert’s ideas, which Gauss accepted and improved. Schweikart’s nephew, Franz Adolf Taurinus, however, used a lengthy inverstigation as the basis for a fallacious refutation of the new geometry, and Gauss refused to be associated with his work. As for what Gauss knew, the question is complicated: he accepted the possibility of a new geometry but never gave a connected account of it, even when, as briefly discussed here, he had discovered the intrinsic nature of the curvature of a surface.