Mathematical theories of citation

Structures in Mathematical Theories

Axiomatizing Mathematical Theories: Multiplication

Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some mathematical structures are now classical theorems in Logic, Algebra and Geometry. In this paper we will study the axiomatizability of the theories of multiplication i...

Mathematical Representations of Development Theories

In this paper we explore the consequences of particular stage linkage structures for the evolution of a population. We first argue the importance of constructing "dynamic" models of developmental theories and show through a series of examples the implications of various stage connections for population movements. In discussing dynamic models, one thrust of our comments is to identify the sorts ...

Managing Automatically Formed Mathematical Theories

The HR system forms scientific theories, and has found particularly successful application in domains of pure mathematics. Starting with only the axioms of an algebraic system, HR can generate dozens of example algebras, hundreds of concepts and thousands of conjectures, many of which have first order proofs. Given the overwhelming amount of knowledge produced, we have provided HR with sophisti...

Examples of admissible simplification of mathematical theories

cation of mathematical models, questionnaire " Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding , and you wouldnt do it without some strong urge. " [D. Ruelle]. We shall give some examples from our experience, when we were able to simplify some serious mathematical models to make them under...