Editing Carl Friedrich Gauss (section)

===Potential theory===
Since Isaac Newton had shown theoretically that the Earth and rotating stars assume non-spherical shapes, the problem of attraction of ellipsoids gained importance in mathematical astronomy. In his first publication on potential theory, the "Theoria attractionis..." (1813), Gauss provided a [[closed-form expression]] to the gravitational attraction of a homogeneous [[triaxial ellipsoid]] at every point in space.{{sfn|Geppert|1933|p=32}} In contrast to previous research of [[Colin Maclaurin|Maclaurin]], Laplace and Lagrange, Gauss's new solution treated the attraction more directly in the form of an elliptic integral. In the process, he also proved and applied some special cases of the so-called [[divergence theorem|Gauss's theorem]] in [[vector analysis]].{{sfn|Geppert|1933|pp=32&ndash;40}}

In the ''General theorems concerning the attractive and repulsive forces acting in reciprocal proportions of quadratic distances'' (1840) Gauss gave a basic theory of [[Magnetic vector potential|magnetic potential]], based on Lagrange, Laplace, and Poisson;{{sfn|Klein|1979|pp=21–23}} it seems rather unlikely that he knew the previous works of [[George Green (mathematician)|George Green]] on this subject.{{sfn|Schaefer|1929|p=6}} However, Gauss could never give any reasons for magnetism, nor a theory of magnetism similar to Newton's work on gravitation, that enabled scientists to predict geomagnetic effects in the future.<ref name="Rupke" />