In this paper I attempt to show that mathematical economics is unreasonably ineffective. Unreasonable, because the mathematical assumptions are economically unwarranted; ineffective because the mathematical formalizations imply non-constructive and uncomputable structures. A reasonable and effective mathematization of economics entails Diophantine formalisms. These come with natural undecidabil...

The Hahn–Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using non-constructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn–Banach theorems in mathematical economics and a...

Discrete convex analysis, which is a unified framework of discrete optimization, is being recognized as a basic tool for mathematical economics. This paper surveys the recent progress in applications of discrete convex analysis to mathematical economics.

This paper is modeled as a hypothetical first lecture in a graduate Microeconomics or Mathematical Economics Course. We start with a detailed scrutiny of the notion of a utility function to motivate and describe the common patterns across Mathematical concepts and results that are used by economists. In the process we arrive at a classification of mathematical terms which is used to state mathe...

This chapter presents an original continuous time methodology and mathematical models applied for analyzing the effectiveness of technical and economic aspects of the operation of heat and electricity sources.

This chapter presents an original continuous time methodology and mathematical models applied for analyzing the effectiveness of technical and economic aspects of the operation of heat and electricity sources.