Three synthetical plots of analysis and geometry

摘要

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