Related papers: Truth as value and duty: lessons of mathematics
Reflections on the Concept of Data and its Implications for Science and Society
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
Decisions about how the population of the United States should be divided into legislative districts have powerful and not fully understood effects on the outcomes of elections. The problem of understanding what we might mean by "fair…
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.
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
Quantum computing is a new form of computing that is based on the principles of quantum mechanics. It has the potential to revolutionize many fields, including the humanities and social sciences. The idea behind quantum humanities is to…
This is a very basic introduction to some notions related to logic and complexity.
The mathematical universe discussed here gives models of possible structures our physical universe can have.
In this note I describe reliability standards for writing and reviewing mathematical papers; these standards are (in my opinion) vital for the progress of mathematics. I give examples of applying the described or other reliability…
In which a review of the concept of countability is done in mathematics, subjecting review some of the theorems so far accepted, showing their inconsistency and also taking concrete elements on the countability of all the powers of the set…
This article is a collection of letters solicited by the editors of the Bulletin in response to a previous article by Jaffe and Quinn [math.HO/9307227]. The authors discuss the role of rigor in mathematics and the relation between…
Research in information systems includes a wide range of approaches which make a contribution in terms of knowledge, understanding, or practical developments. The measure of any research is, ultimately, its validity: are its finding true,…
Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…
The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an…
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving…
In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the…
It brings into attention briefly the genuine significance of uncertainty relations and of their extrapolations for which conventional(usual) doctrine promotes unjustified ideas.
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…
Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification: that…
This paper is concerned with a dialogue between Rabindranath Tagore and Albert Einstein, where Tagore argued that our knowledge is essentially human, while Einstein maintained that some kinds of knowledge are more objective. Arguments by…