Related papers: Response to comments on ``Theoretical mathematics'…
Physics issues at the upcoming and planned colliders are discussed. We critically review the the different arguments that suggest that New Physics is bound to materialise at the TeV scale and why we should keep an open minded approach. The…
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
The relationship that is widely presumed to hold between physical theories and their successors, in which the successors in some sense explain the success of the theories they replace, is known commonly as 'reduction.' I argue that one…
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
Our notions of what is physically 'real' have long been based on the idea that the real is what is immediately apprehended, that is the local or observable, the physically tangible, though there has always been an alternative philosophical…
What is a physical theory? Although this intriguing question has been addressed from many different perspectives, some physicists and philosophers of physics have implicitly or explicitly embraced a philosophically-neutral definition of a…
We discuss in this work the contradictory position in modern Physics between the existence of a microphysical quantum Reality and macrophysical classical one. After discussing some basic concepts in Philosophy, we revisit the situation of…
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
The paper contains critical comments to the paper mentioned in the title from the mathematical point of view
In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…
We discuss the nature of reality in the ontological context of Penrose's math-matter-mind triangle. The triangle suggests the circularity of the widespread view that math arises from the mind, the mind arises out of matter, and that matter…
This article is a response to the recent Worrying Trends in Econophysics critique written by four respected theoretical economists. Two of the four have written books and papers that provide very useful critical analyses of the shortcomings…
Quantum mechanics has enjoyed a multitude of successes since its formulation in the early twentieth century. At the same time, it has generated puzzles that persist to this day. These puzzles have inspired a large literature in physics and…
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…
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 introduces into the whole section on Social Sciences, edited by A. Nowak for this Encyclopedia, concentrating on the applications of mathematics and physics. Here under "mathematics" we include also all computer simulations if…
After the rejection of their comment [arXiv:cond-mat/0609399v1] to our Phys. Rev. Lett. {\bf 97}, 100601 (2006), the Authors informed us that an extended version of their comment is going to be published in a different journal under the…
A general information-theoretic framework for deriving physical laws is presented and a principle of informational physics is enunciated within its context. Existing approaches intended to derive physical laws from information-theoretic…
We search for a possible mathematical formulation of some of the key ideas of the relational interpretation of quantum mechanics and study their consequences. We also briefly overview some proposals of relational quantum mechanics for an…
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…