Does every compactum with no converging sequences contain a copy of $\beta \mathbb{N}$? -- is, of course, Efimov's problem. Failing to answer Efimov's problem we consider compactum with no converging sequences. Every infinite compactum with weight less than the splitting number, $\mathfrak s$, will contain a converging sequence. What is the minimum weight of a compactum with no converging sequences? Might it be the cardinal $\mathfrak{s}(\mathbb{R})$ -- the splitting number of the reals? Is it at least the bounding number $\mathfrak{b}$? What are the positions of these new cardinals with respect to the known cardinal invariants?