The [[Thomson problem]] in mathematics seeks the optimal distribution of equal point charges on the surface of a sphere. Unlike the original Thomson atomic model, the sphere in this purely mathematical model does not have a charge, and this causes all the point charges to move to the surface of the sphere by their mutual repulsion. There is still no general solution to Thomson's original problem of how electrons arrange themselves within the positivea sphere of his atomicpositive modelcharge.<ref>{{Cite journal |last1=Levin |first1=Y. |last2=Arenzon |first2=J. J. |year=2003 |title=Why charges go to the Surface: A generalized Thomson Problem |journal=Europhys. Lett. |volume=63 |issue=3 |pages=415–418 |arxiv=cond-mat/0302524 |bibcode=2003EL.....63..415L |doi=10.1209/epl/i2003-00546-1 |s2cid=250764497}}</ref><ref>{{Cite journal |last=Roth |first=J. |date=2007-10-24 |title=Description of a highly symmetric polytope observed in Thomson's problem of charges on a hypersphere |url=https://link.aps.org/doi/10.1103/PhysRevE.76.047702 |journal=Physical Review E |language=en |volume=76 |issue=4 |pages=047702 |bibcode=2007PhRvE..76d7702R |doi=10.1103/PhysRevE.76.047702 |issn=1539-3755 |pmid=17995142 |quote=Although Thomson's model has been outdated for a long time by quantum mechanics, his problem of placing charges on a sphere is still noteworthy.}}</ref>
