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
on an ellipsoid other than umbilical points has exactly four cusps.
[1] Numerical experiments had indicated the statement is true[2] before it was proven rigorously in 2004 by Itoh and Kiyohara.
[3] It has since been extended to a wider class of surfaces beyond the ellipsoid.
[4] This differential geometry-related article is a stub.