Related papers: On mathematics and knowledge
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, not just in traditional areas of artificial…
The comments relate to the often overlooked, if not in fact intentionally disregarded depths of what the so called internal aspects of mathematical knowledge may involve, depths concerning among others issues such as its unreasonable…
In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level…
This is a tract on the art and practice of mathematical writing. Not only does the book cover basic principles of grammar, syntax, and usage, but it takes into account developments of the last twenty years that have been inspired by the…
In this chapter, concepts related to information and computation are reviewed in the context of human computation. A brief introduction to information theory and different types of computation is given. Two examples of human computation…
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.
Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the…
Laymen and sometimes even physicists think of natural sciences, in particular of theoretical and mathematical physics often as subjects, which unfold according to an intrinsic logical pattern, with the limitations being set only by the…
QCD sheds considerable light on several of the most basic features of the natural world including the origin of mass, the feebleness of gravity, the extent to which the properties of matter can be determined conceptually, the possible…
Can mathematics help us find our way through all the wonders and mysteries of the universe? When physicists describe the laws governing the physical world, mathematics is always involved. Is this due to the fact that the universe is, at…
We present a short survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 72 papers and tentative taxonomies of both retrieval problems and recurring techniques.
Network (as a general notion) is not a mathematical object - there is no even any definition. However, there is a lot of good rigorous mathematics for well-defined classes of networks. In sections 1-3 we give a short overview of classes of…
We describe in dialogue form a possible way of discovering and investigating 10-adic numbers starting from the naive question about a `largest natural number'. Among the topics we pursue are possibilities of extensions to transfinite…
``The purpose of life is to obtain knowledge, use it to live with as much satisfaction as possible, and pass it on with improvements and modifications to the next generation.'' This may sound philosophical, and the interpretation of words…
The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even to the way we interpret mathematical…
We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of…
This article analyzes the emerging ethical turn in mathematics education, arguing that it is a nuanced extension of the sociopolitical turn. While sociopolitical studies of mathematics have highlighted systemic issues and group concerns…
The purpose of this paper is to emphasize the role of language in the process of teaching and learning mathematics. We will begin with the definition of mathematics given by Cassiodorus (in its essential features repeated in Kolmogorov's…
This book invites readers to see mathematics not just as formulas and rules, but as the deepest expression of human thought. It begins by exploring the timeless idea of mathematics as a universal language, contrasting its precision with the…
One purpose -- quite a few thinkers would say the main purpose -- of seeking knowledge about the world is to enhance our ability to make good decisions. An item of knowledge that can make no conceivable difference with regard to anything we…