Related papers: The Mathematics
We describe and explain the desire, common among mathematicians, both for unity and independence in its major themes. In the dialogue that follows, we express our spontaneous and considered judgment and reservations by contrasting the…
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics…
Cities are systems with a large number of constituents and agents interacting with each other and can be considered as emblematic of complex systems. Modeling these systems is a real challenge and triggered the interest of many disciplines…
Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…
Even if students can make the blend, interpret physics correctly in mathematical symbology and graphs, they still need to be able to apply that knowledge in productive and coherent ways. As instructors, we can show our solutions to complex…
We review the role of mathematics from a historical and a conceptual perspective in the light of modern data science.
In this paper, we introduce a mathematical structure called Euclidean Universe. This structure provides a basic framework for Non-Archimedean Mathematics and in particular for Nonstandard Analysis.
Traditionally, semantics has been seen as a feature of human language. The advent of the information era has led to its widespread redefinition as an information feature. Contrary to this praxis, I define semantics as a special kind of…
Children can take many paths to become scientists. But they undoubtedly include the following steps Play, play and play; Observe; Ask (themselves). In this paper I will talk about some of my experiences teaching girls and boys, teenagers…
In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
Argumentation is the process of constructing arguments about propositions, and the assignment of statements of confidence to those propositions based on the nature and relative strength of their supporting arguments. The process is modelled…
In order to describe natural phenomena, science develops sophisticated models that use mathematical and formal languages which seem, and often are, very far from common experience. When a phenomenon is not accessible to our senses, its…
Some personal thoughts and opinions on what ``good quality mathematics'' is, and whether one should try to define this term rigorously. As a case study, the story of Szemer\'edi's theorem is presented.
Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated…
To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the…
We pursue research leading towards the nature of causality in the universe. We establish the equation of the universe's evolution from the universe-state function and its series expansion, in which causes and effects connect together to…
There are many scientific problems generated by the multiple and conflicting alternative definitions of linguistic recursion and human recursive processing that exist in the literature. The purpose of this article is to make available to…
Theory and empirical science should be in constant dialogue, but often find it hard to understand one another. Here we describe a graduate-level university course we developed to improve matters. The course was designed to help…
This article, dedicated, with admiration to Reuben Hersh, for his forthcoming 90th birthday, argues that mathematics today is not yet a science, but that it is high time that it should become one.