Approximation of real numbers by algebraic numbers and estimates for the Hausdorff dimension

The problem of approximating real numbers by algebraic numbers of a given degree and height is a natural development of the classical Dirichlet's theorem from the mid-19th century, which described approximation of real numbers by rational fractions. Approximation by algebraic numbers was first studied in 1961 by a German mathematician E. Wirsing.
This article describes contributions of Belarusian mathematicians V. Sprindzuk, V. Bernik, K. Tishchenko, V. Beresnevich, D. Koleda, A. Gusakova, and D. Bodyagin to the research related to Wirsing's conjecture, as well as studies of the distribution of algebraic numbers, their discriminants and resultants. In addition, a conjecture of V. Beresnevich, V. Bernik and F. Goetze has been proved.