Related papers: Our Mathematical Universe?
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…
The main goal of the project Math-Net.Ru is to collect scientific publications in Russian and Soviet mathematics journals since their foundation to today and the authors of these publications into a single database and to provide access to…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
The intriguing suggestion of Tegmark (1996) that the universe--contrary to all our experiences and expectations--contains only a small amount of information due to an extremely high degree of internal symmetry is critically examined. It is…
I will propose the notion that the universe is digital, not as a claim about what the universe is made of but rather about the way it unfolds. Central to the argument will be the concepts of symmetry breaking and algorithmic probability,…
Mathematical and astronomical achievements of the Islamic World during its golden era are briefly exposed. Thie article is based on the invited talk delivered remotely at the ICRANet-Isfahan Astronomical meeting, November 2-5, 2021, which,…
Our laws of nature and our cosmos appear to be delicately fine-tuned for life to emerge, in a way that seems hard to attribute to chance. In view of this, some have taken the opportunity to revive the scholastic Argument from Design,…
Toposes can be pictured as mathematical universes. Besides the standard topos, in which most of mathematics unfolds, there is a colorful host of alternate toposes in which mathematics plays out slightly differently. For instance, there are…
If there is a "platonic world" M of mathematical facts, what does M contain precisely? I observe that if M is too large, it is uninteresting, because the value is in the selection, not in the totality; if it is smaller and interesting, it…
We show how our Universe can emerge from a symmetry breaking of a multicomponent $W_3$ algebra, where the components in addition form a Jordan algebra. We discuss how symmetry breaking related to the Jordan algebras $H_3(C)$ and $H_3(O)$…
An introductory guide to mathematical cosmology is given focusing on the issue of the genericity of various important results which have been obtained during the last thirty or so years. Some of the unsolved problems along with certain new…
This paper provides some reflections on the field of mathematical software on the occasion of John Rice's 65th birthday. I describe some of the common themes of research in this field and recall some significant events in its evolution.…
In recent years, the intersection of algebra, geometry, and combinatorics with particle physics and cosmology has led to significant advances. Central to this progress is the twofold formulation of the study of particle interactions and…
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…
The Planetary project develops a general framework - the Planetary system - for social semantic portals that support users in interacting with STEM (Science/Technology/Engineering/Mathematics) documents. Developed from an initial attempt to…
The idea of a World digital mathematics library (DML) has been around since the turn of the 21th century. We feel that it is time to make it a reality, starting in a modest way from successful bricks that have already been built, but with…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
This is a Snowmass whitepaper on physical mathematics. It briefly summarizes and highlights some of the key questions drawn from a much more extensive essay, by the same authors, entitled, "A Panorama Of Physical Mathematics 2021."
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…