Три синтетических сюжета из анализа и геометрии

This is a short overview of the synthetical problems of analysis and geometry which are connected with multiple objective problems of convex geometry, the theory of linear inequalities, and Boolean valued analysis. Some attention is paid to the related historical-philosophical aspects of the problems that were inspired by A. D. Alexandrov, L. V. Kantorovich, and S. L. Sobolev.