Related papers: Intuitionism: an inspiration?
An important step in learning to use math in science is learning to see physics equations as not just calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and…
This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.
Course material for mathematical methods of theoretical physics intended for an undergraduate audience.
We discuss several aspects of infinity in the history of mathematics.
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
This is a very basic introduction to some notions related to logic and complexity.
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
This soliloquy outlines some naive philosophical arguments underlying the thesis that mathematics ought to be viewed simply as a universal set of languages, some of precise expression, and some of effective communication.
The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
As one type of incidence theory, the geometry of pentagram map seems quite classical at first. However, this is an excellent example of such a classical idea developed into a marvellous insight by some modern approach. We introduce an…
This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the…
This text serves as an introduction to $\mathbb{F}_1$-geometry for the general mathematician. We explain the initial motivations for $\mathbb{F}_1$-geometry in detail, provide an overview of the different approaches to $\mathbb{F}_1$ and…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
This is a survey article to be part of the Encyclopedia of Mathematical Physics, to be published by Elsevier in the beginning of 2006.
This paper discusses the mathematical representation of an empirically observed phenomenon, referred to as Incremental Similarity. We discuss this feature from the viewpoint of stochastic processes and present a variety of non-trivial…
This paper has been withdrawn by the author. In this article I review W\"ust's recent handbook on mathematical physics from a philosophical standpoint. It emerges a structural approach to mathematics which evidences the utility of logic in…
These lectures are a brief introduction to supersymmetry.
This article is an updated version of an entry of the Encyclopedia of Mathematics Education (2018). In the same time, it is the seed of the HAL collection DAD-MULTILINGUAL, constituted by the translation of this entry in various…
We review the history of the automation of mathematical induction