Theories of class S[A], a family of N=2 supersymmetric field theories, exhibit a quirky phenomenon: generating series for BPS indices -- "counts" of special states in supersymmetric field theories -- are secretly algebraic functions over the rationals. Beside having deep implications for the geometry of the moduli space of vacua, this "algebraicity" property leads to exponential growth of BPS indices with the charge -- a rather surprising and unexpected result. The most tangible example of where this phenomenon occurs is N=2 pure SU(3) super Yang Mills (a theory of class S[A]).