Related papers: Our Mathematical Universe?
This book is a philosopher's introduction to the idea that our universe is just one of many universes. I present and assess three versions of the idea: one version from philosophy, and two from physics. In short, they are: all the logically…
This is a personal and historical essay based on the Shaw Prize Lecture given in Hong Kong in September 2017 in association with the 2017 Shaw Prize in Astronomy.
In 2011, I published a popular-level book, The Fallacy of Fine-Tuning: Why the Universe is Not Designed for Us. It investigated a common claim found in contemporary religious literature that the parameters of physics and cosmology are so…
This contribution covers the topics presented by the authors at the {\it ``Fundamental Problems of Turbulence, 50 Years after the Marseille Conference 1961"} meeting that took place in Marseille in 2011. It focuses on some of the…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
Multi-connected Universe models with space idenfication scales smaller than the size of the observable universe produce topological images in the catalogs of cosmic sources. In this review, we present the recent developments for the search…
Strong dynamics constitutes one of the pillars of the standard model of particle interactions, and it accounts for the bulk of the visible matter in the universe. It is therefore a well posed question to ask if the rest of the universe can…
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
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…
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…
The report is devoted to the current state of the MathPartner computer algebra web project. We discuss the main directions of development of the project and give several examples of using it to solve selected problems.
The fine-tuning of the universe for intelligent life has received a great deal of attention in recent years, both in the philosophical and scientific literature. The claim is that in the space of possible physical laws, parameters and…
The purpose of this work is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. This paper concentrates on general…
This is a critical review of the book 'A New Kind of Science' by Stephen Wolfram. We do not attempt a chapter-by-chapter evaluation, but instead focus on two areas: computational complexity and fundamental physics. In complexity, we address…
The distinction between sciences is becoming increasingly more artificial -- an approach from one area can be easily applied to the other. More exciting research nowadays is happening perhaps at the interfaces of disciplines like Physics,…
One of the most stimulating recent ideas in particle physics involves a possibility that our universe has additional compactified spatial dimensions, perhaps as large as 1 mm. In this review, we discuss the results of recent experimental…
There has been a recent media blitz on a cohort of mathematicians valiantly working to fix America's democratic system by combatting gerrymandering with geometry. While statistics commonly features in the courtroom (forensics, DNA analysis,…
Some aspects of Computer Algebra (notably Computation Group Theory and Computational Number Theory) have some good databases of examples, typically of the form "all the X up to size n". But most of the others, especially on the polynomial…
An information service for mathematical software is presented. Publications and software are two closely connected facets of mathematical knowledge. This relation can be used to identify mathematical software and find relevant information…
The metaverse was first introduced in 1992. Many people saw Metaverse as a new word but the concept of Metaverse is not a new term. However, Zuckerberg's press release drew all the attention to the Metaverse. This study presents a…