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 ${\displaystyle p}$ 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]

See also

• Four-vertex theorem