In differential geometry, the last geometric statement of Jacobi is a conjecture named after Carl Gustav Jacob Jacobi, which states:
<blockquote> Every caustic from any point on an ellipsoid other than umbilical points has exactly four cusps. </blockquote>
Numerical experiments had indicated the statement is true before it was proven rigorously in 2004 by Itoh and Kiyohara. It has since been extended to a wider class of surfaces beyond the ellipsoid.