Related papers: Our Mathematical Universe?
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…
In this essay, I attempt to provide supporting evidence as well as some balance for the thesis on `Transforming socio-economics with a new epistemology' presented by Hollingworth and Mueller (2008). First, I review a personal highlight of…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
Starting from Greg Moore's description about Physical Mathematics, a framework is proposed in order to understand it, based on Gilles Ch\^atelet's philosophy. It will be argued that Ch\^atelet's ideas of inverting, splitting, augmenting and…
This is neither an elementary introduction to singularity theory nor a specialized treatise containing many new theorems. The purpose of this little book is to invite the reader on a mathematical promenade. We pay a visit to Hipparchus,…
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
In a forthcoming book, professional computer scientist and physicist Paul Budnik presents an exposition of classical mathematical theory as the backdrop to an elegant thesis: we can interpret any model of a formal system of Peano Arithmetic…
What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and…
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.
This report is the first of two publications of a joint Working Group of the International Mathematical Union (IMU) and the International Council of Industrial and Applied Mathematics (ICIAM). In it, we shall analyze the current state of…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or…
A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…
An introduction to the physics and mathematics of the expanding universe, using no more than high-school level / undergraduate mathematics. Covered are the basics of scale factor expansion, the dynamics of the expanding universe, various…
Aversion to mathematics is a recognised and widespread problem. Following a review of the literature on this subject, this paper presents an education program which has been developed to test the hypothesis that transferring attention from…
The author recalls general tendencies of the "mathematization" of the sciences and derives challenges and tentative obstructions for a successful merger of mathematics and physics on fancied steps towards "Quantum Gravity". This is an…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…
The purpose of this paper is to elucidate, by means of concepts and theorems drawn from mathematical logic, the conditions under which the existence of a multiverse is a logical necessity in mathematical physics, and the implications of…
The literature on ethics and sustainability in mathematics and its education is increasingly complex and fragmented, potentially leading to communication breakdowns between different scholarly traditions. To address this, the paper…