Normality conjecture for irrational algebraic numbers

Let $\alpha\in\mathbb{R}$ be an irrational algebraic number. A real number is normal if its digit frequencies are uniform in every integer base. Normality conjecture for irrational algebraic numbers. Every irrational algebraic number $\alpha\in\mathbb{R}$ is normal. Despite substantial results on normal numbers and their behavior across bases, normality of irrational algebraic numbers remains open.