Related papers: Physics in Riemann's mathematical papers
Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is…
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the…
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for…
The authors discuss various objections and rejoinders in the collected responses [math.HO/9404229,math.HO/9404236] to their original article on the relationship between mathematics and theoretical physics [math.HO/9307227].
For more than half a century, dualities have been at the heart of modern physics. From quantum mechanics to statistical mechanics, condensed matter physics, quantum field theory and quantum gravity, dualities have proven useful in solving…
A generalisation of Riemannian geometry is considered, based exclusively on the minimal assumptions that the line element $ds$ is a regular function of position and direction and that the distance of every point from itself is equal to…
Motivated by a paper of Zirnbauer, we develop a theory of Riemannian supermanifolds up to a definition of Riemannian symmetric superspaces. Various fundamental concepts needed for the study of these spaces both from the Riemannian and the…
In the first part we present the number theoretical properties of the Riemann zeta function and formulate the Riemann Hypothesis. In the second part we review some physical problems related to this hypothesis: the links with Random Matrix…
Many physicists, following Einstein, believe that the ultimate aim of theoretical physics is to find a unified theory of all interactions which would not depend on any free dimensionless constant, i.e., a dimensionless constant that is only…
Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated…
Both metamathematics and physics are posited to emerge from samplings by observers of the unique ruliad structure that corresponds to the entangled limit of all possible computations. The possibility of higher-level mathematics accessible…
I argue for a full mathematisation of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: "physics from no physics". Although this may seem an oxymoron, it is the royal road to keep…
This article explores the overall geometric manner in which human beings make sense of the world around them by means of their physical theories; in particular, in what are nowadays called pregeometric pictures of Nature. In these, the…
In this paper, we argue that there are foundational dilemmas in theoretical physics related to the concept of reality and the nature of mathematics in physics. Physical theory is treated as a conceptual organism which develops under the…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
I discuss Ren{\'e} Thom's approach to philosophy based on his mathematical background. At the same time, I will highlight his connection with Aristotle, his criticism of the modern view of science as a predictive process, his ideas on…
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
I provide a critical commentary regarding the attitude of the logician and the philosopher towards the physicist and physics. The commentary is intended to showcase how a general change in attitude towards making scientific inquiries can be…
Contrary to claims about the irrelevance of philosophy for science, I argue that philosophy has had, and still has, far more influence on physics than is commonly assumed. I maintain that the current anti-philosophical ideology has had…
The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…