相关论文: The Role of Symmetry in Mathematics

We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…

Symmetry is a fundamental concept in modern physics and other related sciences. Being such a powerful tool, almost all physical theories can be derived from symmetry, and the effectiveness of such an approach is astonishing. Since many…

In contemporary theoretical physics, the powerful notion of symmetry stands for a web of intricate meanings among which I identify four clusters associated with the notion of transformation, comprehension, invariance and projection. While…

Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…

Spacetime and internal symmetries can be used to severely restrict the form of the equations for the fundamental laws of physics. The success of this approach in the context of general relativity and particle physics motivates the…

A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…

This is the introductive paper to the volume "Symmetries in Physics: Philosophical Reflections", Cambridge University Press, 2003. We begin with a brief description of the historical roots and emergence of the concept of symmetry that is at…

Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has…

"Symmetry" was one of the most important methodological themes in 20th-century physics and is probably going to play no lesser role in physics of the 21st century. As used today, there are a variety of interpretations of this term, which…

We investigate the concept of symmetry and its role in problem solving. This paper first defines precisely the elements that constitute a "problem" and its "solution," and gives several examples to illustrate these definitions. Given…

The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…

Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…

The role of mathematics in physical sciences is discussed, particularly how higher mathematics found applications in empirical problems. Several examples are given to illustrate this role.

Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…

It is hard to overstate the importance that the concept of symmetry has had in every field of physics, a fact alluded to by the Nobel Prize winner P.W. Anderson, who once wrote that physics is the study of symmetry. Whereas the idea of…

The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…

Symmetry, a central concept in understanding the laws of nature, has been used for centuries in physics, mathematics, and chemistry, to help make mathematical models tractable. Yet, despite its power, symmetry has not been used extensively…

The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…

Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…

A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…