Last geometric statement of Jacobi

In differential geometry and algebraic geometry, the last geometric statement of Jacobi is a conjecture named after Carl Gustav Jacob Jacobi. According to this conjecture, every caustic from any point $p$ on an ellipsoid other than umbilical points has exactly four cusps.

References

Arnold, V. I. (1999), "Topological problems in wave propagation theory and topological economy principle in algebraic geometry", The Arnoldfest (Toronto, ON, 1997), Fields Inst. Commun. 24, Providence, RI: Amer. Math. Soc., pp. 39–54, MR 1733567 . See in particular p. 45.
Sinclair, R. (2003), "On the last geometric statement of Jacobi", Experimental Mathematics 12 (4): 477–485, doi:10.1080/10586458.2003.10504515, MR 2043997 .
Sinclair, Robert; Tanaka, Minoru (2006), "Jacobi's last geometric statement extends to a wider class of Liouville surfaces", Mathematics of Computation 75 (256): 1779–1808, doi:10.1090/S0025-5718-06-01924-7, MR 2240635 .