Alexandrov Par Excellence

This is a short tribute to Alexandr Alexandrov (1912--1999).Comment: Corrected typo

Convexity and Cone-Vexing

The idea of convexity feeds generation, separation, calculus, and approximation. Generation appears as duality; separation, as optimality; calculus, as representation; and approximation, as stability. This is an overview of the origin, evolution, and trends of convexity. Study of convexity in the Sobolev Institute was initiated by Leonid Kantorovich (1912--1986) and Alexandr Alexandrov (1912--1999). This talk is a part of their memory.Comment: 11 page

Excursus into the History of Calculus

This is a brief overview of some turning points in the history of infinitesimals

The Tragedy of Mathematics in Russia

This is a brief overview of the role of mathematicians in the so-called "Luzin Case" as well as some analysis of the mathematical and humanitarian roots of the affair.Comment: An enlarged and revised version citing new sources with typos correcte

Apology of Euclid

This is a short apology of the style of the Elements by Euclid and Bourbaki

Alexandrov's Approach to the Minkowski Problem

This article is dedicated to the centenary of the birth of Aleksandr D. Alexandrov (1912-1999). His functional-analytical approach to the solving of the Minkowski problem is examined and applied to the extremal problems of isoperimetric type with conflicting goals

Traits

Reminiscences about Alexandr Danilovich Alexandrov (1912--1999

What Is Boolean Valued Analysis?

This is a brief overview of the basic techniques of Boolean valued analysis.Comment: 25 pages with a few improvement

Nonstandard Models and Optimization

This is an overview of a few possibilities that are open by model theory in applied mathematics. Most attention is paid to the present state and frontiers of the Cauchy method of majorants, approximation of operator equations with finite-dimensional analogs, and the Lagrange multiplier principle in multiobjective decision making.Comment: An extended version of a talk prepared for the International Conference "Methods of Logic in Mathematics V," June 1--6, 2008, St. Petersbur

Pareto Optimality and Isoperimetry

Under study is the new class of geometrical extremal problems in which it is required to achieve the best result in the presence of conflicting goals; e.g., given the surface area of a convex body $\mathfrak x$, we try to maximize the volume of $\mathfrak x$ and minimize the width of $\mathfrak x$ simultaneously. These problems are addressed along the lines of multiple criteria decision making