Hermite-Jacobi Problem

"In 1848, Hermite asked Jacobi for methods of expressing a real number as a sequence of integers such that the algebraic properties of the real number are reflected in the periodicity of its sequence. In other words, Hermite wanted a generalization to cubic and higher degree algebraic numbers of the fact that the decimal expansion of a real number is periodic if and only if the real is rational and, more importantly, of the fact that the continued fraction expansion of a real number is periodic if and only if the real is a quadratic irrational. Such attempts are called multidimensional continued fractions."

This quote is from:

Assaf et al.

This problem is still with us.