The linear programming problem: find a strongly-polynomial time algorithm which for given matrix A  Rmn and b  Rm decides whether there exists x  Rn with Ax  b.I know that Steve Smale's lists some of the unsolved problems in mathematics. But such a linear programming problem is it until now not-solvable ?
Does linear programming admit a strongly polynomial-time algorithm?
algorithms;polynomial time;linear programming
This problem is still open. See for example Wikipedia, which while not a dependable source in general, will probably be updated if a strongly polynomial time algorithm is ever found.