Does linear programming admit a strongly polynomial-time algorithm?

The linear programming problem: find a strongly-polynomial time algorithm which for given matrix A ∈ Rm×n 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 ?

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.

StackExchange Computer Science Q#66796, answer score: 12