Last geometric statement of Jacobi

In differential geometry, the last geometric statement of Jacobi is a conjecture named after Carl Gustav Jacob Jacobi, which states: Every caustic from any point p {\displaystyle p} on an ellipsoid other than umbilical points has exactly four cusps. Numerical experiments had indicated the statement is true before it was proven rigorously in 2004 by Itoh and Kiyohara.