Related papers: The Call of Mathematics
Statistics is one of the most valuable of disciplines. Science is based on proof and it alone produces results, other approaches are not, and do not. Statistics is the only acceptable language of proof in science. Yet statistics is…
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce…
The mathematical universe discussed here gives models of possible structures our physical universe can have.
This essay inquires how mathematical beings could be inserted into the architecture of modes of existence proposed by Bruno Latour in the framework of his pluralist and renewed ontology of the modern world. After a description of the…
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…
A brief historical introduction for the enigmatic number Zero is given. The discussions are for popular consumption.
This is a philosophy-intense physics article, or, if you wish, a physics-intense philosophy article. Also, being a mathematician, I tend to view the physics, in particular the essence of quantum physics, in emphasizing the mathematical…
We consider the paradoxical concept of free will from the perspective of Theoretical Computer Science (TCS), a branch of mathematics concerned with understanding the underlying principles of computation and complexity, including the…
Before Alan Turing made his crucial contributions to the theory of computation, he studied the question of whether quantum mechanics could throw light on the nature of free will. This article investigates the roles of quantum mechanics and…
The concept of number and its generalization has played a central role in the development of mathematics over many centuries and many civilizations. Noteworthy milestones in this long and arduous process were the developments of the real…
This article has his origin in some lectures given at the University of Bologna, inside an interdisciplinary program of mathematics, history of science, physics and philosophy. Since they are at the junction of these fields, movement and…
This text (in Spanish) hopes to offer the reader a starting point to deliver good talks on mathematical topics.
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
Engineering needs mathematics, but the converse is also increasingly evident. Indeed, mathematics is still recovering from the drawbacks of several "reforms". Encouraging is the revived interest in proofs indicated by various recent…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
In science and beyond, numbers are omnipresent when it comes to justifying different kinds of judgments. Which scientific author, hiring committee-member, or advisory board panelist has not been confronted with page-long "publication…
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…
This essay traces the history of three interconnected strands. Firstly, changes in the concept of number, secondly, the study of the qualities of number, which evolved into number theory, and thirdly, the nature of mathematics itself, from…
In the last decade, major efforts have been made to promote inquiry-based mathematics learning at the tertiary level. The Inquiry-Based Mathematics Education (IBME) movement has gained strong momentum among some mathematicians, attracting…
The classical platonist / formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: \emph{Is new mathematics discovered or invented? Using examples from my own mathematical work during the…