Related papers: On mathematics and knowledge
Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these questions.
Existing physical theories do not predict every feature of our experience but only certain regularities of that experience. That difference between what could be observed and what can be predicted is one kind of limit on scientific…
This is a short overview of the influence of mathematicians and their ideas on the creative contribution of Mikhailo Lomonosov on the occasion of the tercentenary of his birth.
This chapter presents a brief review of complexity research in mathematics education. We argue how research on complexity, as it pertains to mathematics education, can be viewed as an epistemological discourse, an historical discourse, a…
Physics is so successful today in understanding the nature of matter. What can it say about mind ? Is it possible to have a unified theory of matter and mind within the framework of modern science ? Is Consciousness an accident or is it a…
A century ago physicists and mathematicians worked in tandem and established quantum mechanism. Indeed, algebras, partial differential equations, group theory, and functional analysis underpin the foundation of quantum mechanism. Currently,…
This article is a short review on the concept of information. We show the strong relation between Information Theory and Physics, and the differences between classical and quantum information, with emphasis in their manipulation through…
Pure type systems arise as a generalisation of simply typed lambda calculus. The contemporary development of mathematics has renewed the interest in type theories, as they are not just the object of mere historical research, but have an…
This article focuses on evolvement of the history of mathematics as a science and development of its methodology from the 4th century B.C. to the age of Enlightenment.
This is the first expression of my thoughts and my experiments with Nature about the mathematical description of the Universe. The theories about our surrounding Nature became popular from our ancient civilizations and may be from the…
The study of opinions, their formation and change, is one of the defining topics addressed by social psychology, but in recent years other disciplines, as computer science and complexity, have addressed this challenge. Despite the…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
The recognition of the agency of the knower has enormously enriched our understanding of knowledge production. There is a growing realization that what we know about how we know affects our interpretation of reality. This realization…
This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about 'information compression via the matching and unification of patterns' (ICMUP). ICMUP is itself a novel approach to…
We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community.…
William Oliver Martin published "The Order and Integration of Knowledge" in 1957 to address the problem of the nature and the order of various kinds of knowledge; in particular, the theoretical problem of how one kind of knowledge is…
Optimization has been becoming a central of studies in mathematic and has many areas with different applications. However, many themes of optimization came from different area have not ties closing to origin concepts. This paper is to…
Theory of Probability is distinguished by several high-level philosophical attitudes, some stressed by Jeffreys, some implicit. By reviewing these we may recognize the importance in this work in the historical development of statistics.…
This is the introduction I wrote for the multi-authored book "From Riemann to differential geometry and relativity", edited by L. Ji, A. Papadopoulos and S. Yamada (Berlin, Springer verlag, 2017). The book consists of twenty chapters,…
Knowledge representation is a popular research field in IT. As mathematical knowledge is most formalized, its representation is important and interesting. Mathematical knowledge consists of various mathematical theories. In this paper we…