Borel's normality conjecture for algebraic irrational numbers

Let $x$ be a real irrational algebraic number and let $g\geqslant2$ be a positive integer. A real number is normal in base $g$ if it is simply normal in base $g^m$ for every $m\geqslant1$, equivalently, every sequence of $m$ digits occurs with frequency $1/g^m$ in its $g$-ary expansion. Borel's conjecture. The number $x$ is normal in base $g$. Borel's conjecture is a central open problem concerning the digit distribution of algebraic irrational numbers; the source presents it as Borel's 1950 suggestion.