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We present MathChem, an open-source and cross-platform Python package, aimed at supporting research in mathematical chemistry. MathChem enables researchers to load batches of molecules or molecular graphs, calculate topological indices, perform statistical analyses and visualize the results. As a Python package, MathChem is easily integrable with Sage and other Python libraries such as NumPy and SciPy, which offer numerous further possibilities for analysis of calculated data. We present an example of such use by determining networks of correlations between various topological indices, which lead to an unexpected conjecture on relation between the graph energy and the atom-bond-connectivity index.