相关论文: The roots of mathematical thought
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…
"Is math useful?" might sound as a trick question. And it is. Of course math is useful, we live in a data-filled world and every aspect of life is totally entwined with math applications, both trivial and subtle applications, of both basic…
We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…
Mathematicians occasionally discover interesting truths even when they are playing with mathematical ideas with no thoughts about possible consequences of their actions. This paper describes two specific instances of this phenomenon. The…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
A few remarks on how mathematics quests for freedom.
The purpose of this manuscript is to gather together a large amount of source material pertaining to women in mathematics, from studies of girls in elementary school through data on females winning prizes for mathematical research. Along…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
This is a tract on the art and practice of mathematical writing. Not only does the book cover basic principles of grammar, syntax, and usage, but it takes into account developments of the last twenty years that have been inspired by the…
People sometimes change their opinions when they discuss things with other people. Researchers can use mathematics to study opinion changes in simplifications of real-life situations. These simplified settings, which are examples of…
Perhaps one of the most intriguing questions in philosophy concerns the true nature of external reality. In this paper, we discuss some of the theories that have been put forth regarding the nature of reality and of our perceived universe.…
Modern mathematics is known for its rigorous proofs and tight analysis. Math is the paradigm of objectivity for most. We identify the source of that objectivity as our knowledge of the physical world given through our senses. We show in…
The aim of this paper is to study the historical evolution of mathematical thinking and its spatial spreading. To do so, we have collected and integrated data from different online academic datasets. In its final stage, the database…
This paper presents mathematics as a general science of computation in a way different from the tradition. It is based on the radical philosophical standpoint according to which the content, meaning and justification of experience lies in…
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
Remarks on mathematical proof and the practice of mathematics.
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…
A significant amount of research has considered mathematical proofs, the students who learn them, and the instructors that teach them, from a variety of perspectives. This paper considers this topic from four main perspectives: students'…