The Tammes problem for N=14
  The Tammes problem is to find the arrangement of N points on a unit sphere which maximizes the minimum distance between any two points. This problem is presently solved for several values of N, namely for N=3,4,6,12 by L. Fejes Toth (1943); for N=5,7,8,9 by Schutte and van der Waerden (1951); for N=10,11 by Danzer (1963) and for N=24 by Robinson (1961). Recently, we solved the Tammes problem for N=13. The optimal configuration of 14 points was conjectured more than 60 years ago. In the paper, we give a solution of this long-standing open problem in geometry. Our computer-assisted proof relies on an enumeration of the irreducible contact graphs. 
Oleg R. Musin and Alexey S. Tarasov
math.MG math.CO