相关论文: Truth as value and duty: lessons of mathematics

The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…

This article of mathematical education reflects author's experience with job applications and teaching methods and procedures to employ in the American Higher Education. It is organized as a standard questionnaire.

The fundamental role of mathematics as an inspiration for artists, but also as a tool for art creation, is presented in this paper following different art fields, like architecture, sculpture, painting, photography, literature and poetry,…

We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…

I give a short introduction to data ethics. I begin with some background information and societal context for data ethics. I then discuss data ethics in mathematical-science education and indicate some available course material. I briefly…

The role of mathematics in physical sciences is discussed, particularly how higher mathematics found applications in empirical problems. Several examples are given to illustrate this role.

This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…

In a first article (referred here as B-O), we studied the first part of the so-called 'mathematical part' of Plato's Theaetetus, i.e. Theodorus' lesson. In the present one, we consider the sequel and the end of the passage (147d7-148b2), as…

Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…

Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…

In mathematics information is a number that measures uncertainty (entropy) based on a probabilistic distribution, often of an obscure origin. In real life language information is a datum, a statement, more precisely, a formula. But such a…

The paper discusses relationships between aesthetics theory and mathematical models of mind. Mathematical theory describes abilities for concepts, emotions, instincts, imagination, adaptation, learning, cognition, language, approximate…

This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions.…

This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…

We discuss how the concept of equality is used by mathematicians (including Grothendieck), and what effect this has when trying to formalise mathematics. We challenge various reasonable-sounding slogans about equality.

Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…

The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.

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…

The main subjects of this text are: (1) Generalization of concepts and operations, like distance and size, to situations where they are not definable in the usual way. (2) A pragmatic theory of handling contradictions using reliability of…

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…