Jacobi_bound_problem
The Jacobi bound problem concerns the veracity of Jacobi's inequality which is an inequality on the absolute dimension of a differential algebraic variety in terms of its defining equations. This is one of Kolchin's Problems.
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The inequality is the differential algebraic analog of Bezout's theorem in affine space. Although first formulated by Jacobi, In 1936 Joseph Ritt recognized the problem as non-rigorous in that Jacobi didn't even have a rigorous notion of absolute dimension (Jacobi and Ritt used the term "order" - which Ritt first gave a rigorous definition for using the notion of transcendence degree). Intuitively, the absolute dimension is the number of constants of integration required to specify a solution of a system of ordinary differential equations. A mathematical proof of the inequality has been open since 1936.