Mathematical  Culture and Thought

Mathematical Culture and Thought

Physical ‎A‎rguments ‎vs.‎ Mathematical Proofs

Document Type : Survey

Authors
1 Faculty of Statistics, Mathematics, and Computer, Allameh Tabataba’i University, Iran
2 Department of Mechanical ‎Engineering‎‎, ‎University of Zanjan‎, ‎Iran
Abstract
In this article, intuitive proofs of some well-known mathematical theorems are reviewed using basic principles of physics. In this article, proof is introduced as a part of any mathematical curriculum, with a potential contribution to the classroom and to the promotion of mathematical understanding. It is emphasized that observation and measurement should not be abandoned in the name of providing mathematical proof. In addition, the possible role of the laws of physics (which are traditionally an important source of some mathematical problems) in mathematical proof and how this role can be played in the classroom is explained. This article attempts to make proof in the classroom meaningful with the help of empirical (physical) arguments and to strengthen the role of applications in teaching mathematics. To achieve these goals, for example, numerous examples, including the two-dimensional and three-dimensional Seva theorem, the Fermat point theorem, and the two-dimensional and three-dimensional Pythagorean theorem, are presented and proven by presenting mathematical arguments. Finally, as a more advanced topic of the application of physical arguments in mathematics, the condition of consistency and singularity of the solution of singular integral equations of the Cauchy type is mentioned.
Keywords
Subjects

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  • Receive Date 13 April 2025
  • Revise Date 26 August 2025
  • Accept Date 26 August 2025
  • Publish Date 22 May 2026