Related papers: Mathemagical 2014 - An Indian Perspective
Music, enchanting and poetic, permeates every corner of human civilization. Although music is not unfamiliar to people, our understanding of its essence remains limited, and there is still no universally accepted scientific description.…
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…
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…
Datacentric enthusiasm is growing strong across a variety of domains. Whilst data science asks unquestionably exciting scientific questions, we argue that its contributions should not be extrapolated from the scientific context in which…
Music has been called the temporal art par excellence. Yet, as this paper explains, it is also the atemporal art par excellence. The contradiction is, however, only apparent, and a result of viewing music from two possible perspectives.…
Astronomy and related fields are at the forefront of science and technology; answering fundamental questions and driving innovation. Although blue-skies research like astronomy rarely contributes directly with tangible outcomes on a short…
This paper proposes a new definition of science based on the distinction between the activity of scientists and the product of that activity: the former is denoted (lower-case) science and the latter (upper-case) Science. These definitions…
"Is math useful?" might sound as a trick question. And it is. Of course math is useful, we live in a data-filled world and every aspect of life is totally entwined with math applications, both trivial and subtle applications, of both basic…
At the intersection of what I call uncomputable art and computational epistemology, a form of experimental philosophy, we find an exciting and promising area of science related to causation with an alternative, possibly best possible,…
There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…
Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as…
Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie…
Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry, and partly from…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
In recent paper "Quantifying Inequities and Documenting Elitism in PhD-granting Mathematical Sciences Departments in the United States" (arXiv:2308.13750) by a group of accomplished and/or aspiring mathematicians, the authors use data to…
What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly…
In this paper, we study aggregation rules with nontrivial symmetric classes of invariant sets (restricted domains), assuming that they, unlike others, have a logical nature. In the simplest case, we provide a complete classification of such…
The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…
We usually construct mathematical objects that are accessible, on which we can put our hands, but a huge part of the mathematical existing is actually wild. Here we explore part of the wild world: its inhabitants are knots that are…
We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a…