Stability of Vortex Heptagon

The configuration of n line vortices spaced regularly around the circumference of a circle is stable for n <= 7, and unstable for n > 7. The theorem was first proved by J. J. Thomson (1883) in connection with Lord Kelvin's vortex theory of atoms. However, for the case of n >= 7, his proof is wrong, and was corrected by T. H. Havelock almost 50 years later. The stability for n=7 still remained unknown until L. G. Kurakin & V. I. Yudovich successfully tackled the problem in 2002. The magical number 7 appears in an innocent inequality to ensure the eigenvalues of the linearized system are imaginary.

Proof:
J. J. Thomson, 1883 (erroneous)
T. H. Havelock, 1931 (without n=7)
L. G. Kurakin & V. I. Yudovich, 2002 (n=7)

Experiments:
A. M. Mayer, 1878 (floating magnets)
E. Yarmchuk, M. Gordon & R. Packard, 1979 (superfluid helium)
D. Durkin & J. Fajans, 2000 (Malmberg-Penning trap)