Related papers: A Primer of Mathematical Writing, Second Edition
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
This is a case study of teaching 3D design and 3D printing in a project-based computing course for undergraduate math majors. This article discusses content organization, implementation, project grading, and includes a personal reflection.…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
Recent developments show that AI can prove research-level theorems in mathematics, both formally and informally. This essay urges mathematicians to stay up-to-date with the technology, to consider the ways it will disrupt mathematical…
The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are…
This paper provides some reflections on the field of mathematical software on the occasion of John Rice's 65th birthday. I describe some of the common themes of research in this field and recall some significant events in its evolution.…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
This is a discussion of some themes in Max Tegmark's recent book, Our Mathematical Universe. It was written as a review for Plus Magazine, the online magazine of the UK's national mathematics education and outreach project, the Mathematics…
This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. This is camera-ready copy prepared for publication as a book, but at the last minute I decided to publish it…
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 problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
We give an overview of our philosophy of pictures in mathematics. We emphasize a bi-directional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different…
This introduction to arithmetic coding is divided in two parts. The first explains how and why arithmetic coding works. We start presenting it in very general terms, so that its simplicity is not lost under layers of implementation details.…
This essay examines how automation has reconfigured mathematical proof and labor, and what might happen in the future. It discusses practical standards of proof, distinguishes between prominent forms of automation in research, provides…
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,…
This work presents the current collection of mathematical models related to neural networks and proposes a new family of such with extended structure and dynamics in order to attain a selection of cognitive capabilities. It starts by…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
Scientific literature has itself been the subject of much scientific study, for a variety of reasons: understanding how results are communicated, how ideas spread, and assessing the influence of areas or individuals. However, most prior…
Given the present state of work in natural language processing, this address argues first, that advance in both science and applications requires a revival of concern about what language is about, broadly speaking the world; and second,…
This project investigated new approaches and technologies to enhance the accessibility of mathematical content and its semantic information for a broad range of information retrieval applications. To achieve this goal, the project addressed…