%0 Journal Article %T On Some Unsolved Problems of Mathematica %A E. Vorozhtsov %J Engineering, Technology & Applied Science Research %D 2012 %I %X In this paper, some unsolved problems of the Mathematica software package are documented. At first, it is shown, using a number of examples, that the processing (simplification) of rational-fractional expressions involving powers in the general form, has been implemented in Maple more carefully than in Mathematica. Then, an error in Mathematica is demonstrated, leading to incorrect results at a change of a function¡¯s body. For each example of symbolic or symbolic-numeric computations, alternate routes for solving the emerged problem are proposed (where possible). An added problem, related to Mathematica¡¯s computing speed is documented, employing examples related to two-dimensional gas dynamics problems. It is shown that Mathematica computes rather slowly (about one thousand times slower) compared to a Fortran code. %K Mathematica %K analytic %K numerical %K computations %K simplification %K expressions %K Fortran %U http://www.etasr.com/index.php/ETASR/article/view/205/131